Chapter 10 · Class 10 CBSE
A Circles two-mark solution usually begins with perpendicular radii or equal tangents. Practise selected board and official sample questions below, with one logical step per line and both alternatives of original OR pairs.
Review draft · Final question transcription, marking-scheme page matching and tutor review are pending.
64 question groups · 72 worked answers · 8 OR pairs · 124 board-paper and 8 official-sample appearances
| Situation | Result to use |
|---|---|
| Radius at tangent contact | OT ⟂ PT |
| Tangents from the same external point | PA = PB |
| Tangent length t; centre distance d; radius r | t² = d² − r² |
| Chord tangent to a concentric circle | Half-chord² = outer radius² − inner radius² |
| Two tangents and their contact radii | Angle between tangents + minor central angle = 180° |
| Circumscribed quadrilateral ABCD | AB + CD = BC + AD |
Showing 64 question groups
Q1.Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Let XY and LM touch the circle at the ends A and B of diameter AB.
OA ⟂ XY and OB ⟂ LM, by the tangent–radius theorem.
Thus XY and LM are both perpendicular to the same straight line AB.
Therefore, XY ∥ LM.
Answer: The tangents are parallel.
Appeared in: 2023 · Standard · Main; 2024 · Basic · Main; 2025 · Standard · Main; 2022 · Standard · Term II · Supplementary
Q2.Prove that the tangent drawn at any point of the circle is perpendicular to the radius through the point of contact.
Let XY be tangent at P to a circle with centre O.
Every other point Q on XY lies outside the circle, so OQ > OP.
Thus OP is the shortest distance from O to the line XY.
The shortest distance from a point to a line is the perpendicular distance.
Therefore, OP ⟂ XY.
Answer: The tangent is perpendicular to the radius at contact.
Appeared in: 2025 · Basic · Main
Q3.Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
Let chord AB touch the smaller circle at P and let O be the common centre.
OP ⟂ AB, by the tangent–radius theorem.
The perpendicular from the centre of the larger circle to chord AB bisects it.
Hence AP = PB.
Answer: The chord is bisected at the point of contact.
Appeared in: 2023 · Basic · Main
Q4.If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA.
Let contact points on AB, BC, CD, DE, EF and FA be P, Q, R, S, T and U.
Equal tangents give AP = AU, BP = BQ, CQ = CR, DR = DS, ES = ET and FT = FU.
AB + CD + EF = (AP + PB) + (CR + RD) + (ET + TF).
Substitute the equal tangent lengths: (AU + BQ) + (CQ + DS) + (ES + FU).
Regrouping gives BC + DE + FA.
Answer: AB + CD + EF = BC + DE + FA.
Appeared in: 2024 · Standard · Main; 2023 · Standard · Main
Q5.Prove that the two tangents drawn from an external point to a circle subtend equal angles at the centre.
Let PA and PB be tangents to the circle with centre O. Join OA, OB and OP.
∠OAP = ∠OBP = 90°, OA = OB and OP is common.
Therefore, △OAP ≅ △OBP by RHS congruence.
Hence ∠AOP = ∠POB, by corresponding parts of congruent triangles.
Answer: The two tangent segments subtend equal angles at the centre.
Appeared in: 2025 · Basic · Supplementary
Q6.(a) Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.
Let PA and PB be tangents at A and B to a circle with centre O.
∠OAP = ∠OBP = 90°.
In quadrilateral OAPB, ∠APB + ∠AOB + 90° + 90° = 360°.
Therefore, ∠APB + ∠AOB = 180°.
Answer: The stated angles are supplementary.
OR
(b) Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Let XY and LM touch the circle at the ends A and B of diameter AB.
OA ⟂ XY and OB ⟂ LM, by the tangent–radius theorem.
Thus XY and LM are both perpendicular to the same straight line AB.
Therefore, XY ∥ LM.
Answer: The tangents are parallel.
Appeared in: 2025 · Basic · Main
Q9.(a) Prove that the line segment joining the points of contact of two parallel tangents to a circle passes through its centre.
Let the parallel tangents touch the circle at A and B, and O be the centre.
OA and OB are perpendicular to the respective parallel tangents.
Through O there is only one line perpendicular to either of these parallel lines.
Therefore A, O and B are collinear.
Hence AB passes through O.
Answer: The segment passes through the centre.
OR
(b) Two tangents PQ and PR are drawn from an external point P to a circle with centre O. Prove that QORP is a cyclic quadrilateral.
OQ ⟂ PQ and OR ⟂ PR.
∠PQO = ∠PRO = 90°.
These opposite angles add to 180°.
Therefore, QORP is cyclic.
Answer: QORP is cyclic.
Appeared in: 2024 · Standard · Supplementary
Q42.PX and PY are two tangents drawn from an external point P to a circle with centre O. If ∠XPY = 120°, then prove that PX + PY = PO.
△OXP ≅ △OYP by RHS, so OP bisects ∠XPY.
∠XPO = 60° and ∠OXP = 90°.
cos 60° = PX/PO, so PX = PO/2.
PY = PX = PO/2.
Therefore, PX + PY = PO.
Answer: PX + PY = PO.
Appeared in: 2025 · Standard · Supplementary
Q43.PA and PB are tangents drawn to the circle with centre O as shown in the figure. Prove that ∠APB = 2∠OAB.
OA ⟂ PA and OB ⟂ PB.
Thus ∠APB = 180° − ∠AOB.
OA = OB, so ∠OAB = ∠OBA.
In triangle OAB, 2∠OAB = 180° − ∠AOB.
Therefore, ∠APB = 2∠OAB.
Answer: ∠APB = 2∠OAB.
Appeared in: 2023 · Basic · Main; 2025 · Standard · Supplementary
Q44.In Figure 2, PQ and PR are tangents to the circle centred at O. If ∠OPR = 45°, then prove that ORPQ is a square.
△OQP ≅ △ORP by RHS, so ∠QPO = ∠RPO = 45°.
Thus ∠QPR = 90°.
∠OQP and ∠ORP are tangent–radius angles, so both are 90°.
The fourth angle ∠QOR is also 90°, so ORPQ is a rectangle.
OQ = OR, since they are radii.
A rectangle with equal adjacent sides is a square.
Answer: ORPQ is a square.
Appeared in: 2022 · Standard · Term II · Main
Q45.In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.
OQ ⟂ PQ and OR ⟂ PR.
Thus ∠PQO = ∠PRO = 90°.
These opposite angles add to 180°.
Therefore, PQOR is cyclic.
Answer: PQOR is cyclic.
Appeared in: 2022 · Standard · Term II · Supplementary; 2026 · Standard · Main
Q46.The two touching circles have common tangents AB and CM as shown in the given figure. Show that M is the midpoint of line segment AB.
MA = MC, by equal tangents from M to the first circle.
MB = MC, by equal tangents from M to the second circle.
Therefore, MA = MB.
M lies on AB, so M is its midpoint.
Answer: M is the midpoint of AB.
Appeared in: 2026 · Basic · Second board examination
Q48.In the given figure, PT is a tangent to the circle centered at O. OC is perpendicular to chord AB. Prove that PA · PB = PC² − AC².
OC is perpendicular to chord AB, so AC = BC.
The collinear points give PA = PC − AC and PB = PC + BC.
PA · PB = (PC − AC)(PC + BC).
Substitute BC = AC to obtain (PC − AC)(PC + AC).
Therefore, PA · PB = PC² − AC².
Answer: PA · PB = PC² − AC².
Appeared in: 2023 · Standard · Main
Q49.AB is diameter of a circle and AC is its chord such that ∠BAC = 30°. If the tangent at C intersects AB extended at D, then prove that BC = BD.
Join OC. Since AB is a diameter, ∠ACB = 90°, so ∠ABC = 60°.
OB = OC, hence ∠OCB = ∠OBC = 60°.
OC ⟂ CD, so ∠BCD = 30°.
BA and BD are opposite rays, so ∠CBD = 120°.
Thus ∠BDC = 180° − 120° − 30° = 30°.
Equal angles ∠BCD and ∠BDC give BC = BD.
Answer: BC = BD.
Appeared in: 2026 · Standard · Second board examination
Q50.Prove that if a quadrilateral is circumscribed about a circle, the angles subtended at the centre by any two opposite sides are supplementary.
Let ABCD circumscribe a circle with centre O.
The two right triangles at each vertex, formed by its tangents and radii, are congruent by RHS.
Thus OA, OB, OC and OD bisect the respective vertex angles.
In triangle AOB, ∠AOB = 180° − (∠A + ∠B)/2.
Similarly, ∠COD = 180° − (∠C + ∠D)/2.
Add these and use ∠A + ∠B + ∠C + ∠D = 360° to get ∠AOB + ∠COD = 180°.
Answer: The angles subtended by opposite sides at the centre are supplementary.
Appeared in: 2026 · Standard · Second board examination
Q56.In the given figure, two radii OA and OB of a circle with centre O are perpendicular to each other. If two tangents drawn at points A and B intersect each other at point T, prove that AB = OT and they bisect each other.
OA ⟂ AT and OB ⟂ BT, by the tangent–radius theorem.
Also OA ⟂ OB, so AT ∥ OB and BT ∥ OA.
Therefore, OATB is a parallelogram with a right angle: it is a rectangle.
OA = OB, so OATB is a square.
The diagonals of a square are equal and bisect each other.
Hence AB = OT, and AB and OT bisect each other.
Answer: AB = OT, and they bisect each other.
Appeared in: 2026 · Standard · Second board examination
Q57.In the given figure, AB and CD are tangents to a circle centred at O. Is ∠BAC = ∠DCA? Justify your answer.
Join OA and OC. Since OA = OC, ∠OAC = ∠OCA.
OA ⟂ AB and OC ⟂ CD.
Thus ∠BAC = 90° − ∠OAC and ∠DCA = 90° − ∠OCA.
Subtracting equal angles from 90° gives ∠BAC = ∠DCA.
Answer: Yes, ∠BAC = ∠DCA.
Appeared in: 2026 · Standard · Second board examination; 2024 · Standard · Main
Q7.(a) If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm, then find the length of each tangent.
Let PA and PB be tangents and O the centre.
△OAP ≅ △OBP by RHS, so OP bisects ∠APB.
Thus ∠APO = 30° and ∠OAP = 90°.
tan 30° = OA/PA = 3/PA.
= 3/PA, so PA = 3√3 cm.
PB = PA, since tangents from P are equal.
Answer: Each tangent is 3√3 cm long.
OR
(b) Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Let XY and LM touch the circle at the ends A and B of diameter AB.
OA ⟂ XY and OB ⟂ LM, by the tangent–radius theorem.
Thus XY and LM are both perpendicular to the same straight line AB.
Therefore, XY ∥ LM.
Answer: The tangents are parallel.
Appeared in: 2024 · Standard · Main
Q10.(a) PQ and PR are two tangents, from an external point P to a circle with centre O and radius 8 cm. If OP = 17 cm, then find the length of each tangent.
OQ ⟂ PQ.
PQ² = OP² − OQ² = 17² − 8² = 225.
PQ = 15 cm.
PR = PQ, by equal tangents.
Answer: Each tangent is 15 cm long.
OR
(b) Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
Let chord AB touch the smaller circle at P and let O be the common centre.
OP ⟂ AB, by the tangent–radius theorem.
The perpendicular from the centre of the larger circle to chord AB bisects it.
Hence AP = PB.
Answer: The chord is bisected at the point of contact.
Appeared in: 2022 · Basic · Term II · Supplementary
Q12.From a point P, the length of the tangent to a circle is 24 cm and the distance of P from the centre of the circle is 25 cm. Find the radius of the circle.
Let PT be the tangent and O the centre.
OT ⟂ PT.
OT² = OP² − PT² = 25² − 24² = 49.
OT = 7 cm.
Answer: The radius is 7 cm.
Appeared in: 2023 · Basic · Main
Q13.The length of a tangent drawn to a circle from a point A, at a distance of 10 cm from the centre of the circle, is 6 cm. Find the radius of the circle.
Let AT be the tangent and O the centre.
OT ⟂ AT.
OT² = OA² − AT² = 10² − 6² = 64.
OT = 8 cm.
Answer: The radius is 8 cm.
Appeared in: 2024 · Basic · Main
Q14.A person is standing at P outside a circular ground at a distance of 26 m from the centre of the ground. He found that his distances from the points A and B on the ground are 10 m (PA and PB are tangents to the circle). Find the radius of the circular ground.
Let O be the centre. OA ⟂ PA.
OA² = OP² − PA² = 26² − 10² = 576.
OA = 24 m.
Answer: The radius is 24 m.
Appeared in: 2025 · Standard · Main
Q15.The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
Let AT be the tangent and O the centre.
OT ⟂ AT.
OT² = OA² − AT² = 5² − 4² = 9.
OT = 3 cm.
Answer: The radius is 3 cm.
Appeared in: 2023–24 · Basic · Official sample
Q40.In the given figure, from a point L which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents LM and LN are drawn to the circle. Find the perimeter of quadrilateral LMON.
OM ⟂ LM.
LM² = LO² − OM² = 13² − 5² = 144.
LM = LN = 12 cm and OM = ON = 5 cm.
Perimeter = 12 + 5 + 5 + 12 = 34 cm.
Answer: The perimeter is 34 cm.
Appeared in: 2025 · Basic · Supplementary
Q59.The distance between two tangents parallel to each other of a circle is 13 cm. Find the radius of the circle.
The radii to the two contact points lie on the perpendicular between the parallel tangents.
The distance between the tangents is the diameter.
2r = 13, so r = 6.5 cm.
Answer: The radius is 6.5 cm.
Appeared in: 2022 · Basic · Term II · Main
Q62.In the given figure, PA is a common tangent and QB and PC are the tangents from Q and P to the smaller and larger circle respectively. If QB = 5 cm and PC = 9 cm, then evaluate length of PQ.
For the smaller circle, QA = QB = 5 cm.
For the larger circle, PA = PC = 9 cm.
In the figure, P and Q lie on the same side of A and Q lies between P and A.
PQ = PA − QA = 9 − 5 = 4 cm.
Answer: PQ = 4 cm.
Appeared in: 2026–27 · Basic · Official sample
Q16.Two concentric circles are of radii 4 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Let AB touch the smaller circle at M and O be the common centre.
OM ⟂ AB, so AM = MB.
AM² = OA² − OM² = 4² − 3² = 7.
AB = 2AM = 2√7 cm.
Answer: The chord is 2√7 cm long.
Appeared in: 2022 · Standard · Term II · Main
Q17.Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Let AB touch the smaller circle at M and O be the common centre.
OM ⟂ AB, so AM = MB.
AM² = OA² − OM² = 5² − 4² = 9.
AB = 2AM = 6 cm.
Answer: The chord is 6 cm long.
Appeared in: 2026 · Standard · Main; 2024 · Standard · Supplementary
Q18.Two concentric circles are of radii 10 cm and 6 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Let AB touch the smaller circle at M and O be the common centre.
OM ⟂ AB, so AM = MB.
AM² = OA² − OM² = 10² − 6² = 64.
AB = 2AM = 16 cm.
Answer: The chord is 16 cm long.
Appeared in: 2025 · Basic · Main
Q19.In two concentric circles, a chord of length 48 cm of the larger circle is a tangent to the smaller circle, whose radius is 7 cm. Find the radius of the larger circle.
Let M be the contact point and A an end of the chord.
OM ⟂ chord, so AM = = 24 cm.
OA² = OM² + AM² = 7² + 24² = 625.
OA = 25 cm.
Answer: The larger radius is 25 cm.
Appeared in: 2022 · Standard · Term II · Main
Q20.The length of a chord of a bigger circle concentric with a circle of radius 3 cm is 8 cm. If the chord is tangent to the smaller circle, then find the radius of the bigger circle.
Let M be the contact point and A an end of the chord.
OM ⟂ chord, so AM = = 4 cm.
OA² = OM² + AM² = 3² + 4² = 25.
OA = 5 cm.
Answer: The bigger radius is 5 cm.
Appeared in: 2024 · Basic · Supplementary
Q21.In two concentric circles, a chord of length 8 cm of the larger circle touches the smaller circle. If the radius of the larger circle is 5 cm, then find the radius of the smaller circle.
Let M be the contact point and A an end of the chord.
OM ⟂ chord, so AM = = 4 cm.
OM² = OA² − AM² = 5² − 4² = 9.
OM = 3 cm.
Answer: The smaller radius is 3 cm.
Appeared in: 2024–25 · Basic · Official sample
Q22.In Fig. 1, there are two concentric circles with centre O. If ARC and AQB are tangents to the smaller circle from the point A lying on the larger circle, find the length of AC, if AQ = 5 cm.
AR = AQ = 5 cm, by equal tangents from A.
OR ⟂ AC at R.
The perpendicular from the common centre O bisects chord AC of the larger circle.
AC = 2AR = 10 cm.
Answer: AC = 10 cm.
Appeared in: 2022 · Standard · Term II · Main
Q23.At point A on the diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. Find the length of the chord CD parallel to XY at a distance of 16 cm from A.
Let O be the centre and OM ⟂ CD, meeting CD at M.
AO = 10 cm and AM = 16 cm, so OM = 6 cm.
CM = MD, since the perpendicular from the centre bisects the chord.
CM² = OC² − OM² = 10² − 6² = 64.
CM = 8 cm, so CD = 16 cm.
Answer: CD = 16 cm.
Appeared in: 2025 · Standard · Main
Q24.In the given figure, AB is a chord of length 16 cm of a circle of radius 10 cm. The tangents at A and B meet at P. Find the length of PA.
Let M denote the perpendicular foot labelled Q in the source figure.
Let O be the centre and M the midpoint of AB. Then OM ⟂ AB.
AM = 8 cm and OM = √(10² − 8²) = 6 cm.
The equal-tangent configuration gives P, M and O collinear.
△OMA ∼ △OAP by AA.
AM/PA = OM/OA, so 8/PA = 6/10.
PA = cm.
Answer: PA = cm.
Appeared in: 2024 · Basic · Supplementary
Q63.Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Let AB touch the smaller circle at M and O be the common centre.
OM ⟂ AB, so AM = MB.
AM² = OA² − OM² = 5² − 3² = 16.
AB = 2AM = 8 cm.
Answer: The chord is 8 cm long.
Appeared in: 2026–27 · Basic · Official sample
Q8.(a) The two tangents drawn from an external point P to a circle with centre O are PR and PS. If ∠RPS = 65°, then find the measure of ∠ROS.
OR ⟂ PR and OS ⟂ PS.
In quadrilateral ORPS, ∠ROS + ∠RPS = 180°.
∠ROS = 180° − 65° = 115°.
Answer: ∠ROS = 115°.
OR
(b) Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.
Let AB be the chord and O the centre. Join OA and OB.
OA = OB, so ∠OAB = ∠OBA.
Each tangent is perpendicular to its radius at contact.
Corresponding angles between the chord and tangents are 90° − ∠OAB and 90° − ∠OBA.
These angles are equal.
Answer: The tangents make equal corresponding angles with the chord.
Appeared in: 2022 · Basic · Term II · Main
Q25.In Figure 1, if tangents PA and PB drawn from a point P to a circle with centre O, are inclined to each other at an angle of 70°, then find the measure of ∠POA.
△OAP ≅ △OBP by RHS, so OP bisects ∠APB.
∠OPA = 35°.
OA ⟂ PA, so ∠POA = 180° − 90° − 35° = 55°.
Answer: ∠POA = 55°.
Appeared in: 2022 · Basic · Term II · Main
Q26.In Figure 2, PA and PB are tangents to the circle with centre at O. If ∠APB = 70°, then find m∠AQB.
OA ⟂ PA and OB ⟂ PB.
∠AOB = 180° − 70° = 110°.
Q is on the major arc AB in the figure.
The angle subtended by minor arc AB at the circumference is half its central angle.
∠AQB = 110°/2 = 55°.
Answer: ∠AQB = 55°.
Appeared in: 2022 · Basic · Term II · Main
Q27.In the given figure, O is the centre of the circle. AB and AC are tangents drawn to the circle from point A. If ∠BAC = 65°, then find the measure of ∠BOC.
OB ⟂ AB and OC ⟂ AC.
In quadrilateral OBAC, ∠BOC + ∠BAC = 180°.
∠BOC = 180° − 65° = 115°.
Answer: ∠BOC = 115°.
Appeared in: 2023 · Standard · Main
Q28.PQ is a tangent drawn from an external point P to a circle with centre O and QOR is the diameter of the circle. If ∠POR = 120°, then find the measure of ∠OPQ.
Q, O and R are collinear, so ∠POQ = 60°.
OQ ⟂ PQ, so ∠OQP = 90°.
∠OPQ = 180° − 90° − 60° = 30°.
Answer: ∠OPQ = 30°.
Appeared in: 2026 · Standard · Second board examination
Q29.In the given figure, PA is a tangent to the circle drawn from the external point P and PBC is the secant to the circle with BC as diameter. If ∠AOC = 130°, then find the measure of ∠APB, where O is the centre of the circle.
OP and OC are opposite rays, so ∠AOP = 50°.
OA ⟂ PA, so ∠OAP = 90°.
∠APO = 180° − 90° − 50° = 40°.
P, B and O are collinear, so ∠APB = ∠APO.
Answer: ∠APB = 40°.
Appeared in: 2023 · Standard · Main
Q30.In the adjoining figure, PT is a tangent at T to the circle with centre O. If ∠TPO = 30°, find the value of x.
OT ⟂ PT, so ∠OTP = 90°.
∠TOP = 180° − 90° − 30° = 60°.
The marked angle x is adjacent to ∠TOP on a straight line.
x = 180° − 60° = 120°.
Answer: x = 120°.
Appeared in: 2023 · Basic · Main
Q31.In the given figure, TP and TQ are two tangents. If ∠PTQ = 50°, then find the measure of ∠OPQ.
OP ⟂ TP and OQ ⟂ TQ.
∠POQ = 180° − 50° = 130°.
OP = OQ, so the base angles of △OPQ are equal.
∠OPQ = (180° − 130°)/2 = 25°.
Answer: ∠OPQ = 25°.
Appeared in: 2025 · Basic · Main
Q32.In the given figure, O is the centre of the circle. If ∠AOB = 145°, then find the value of x.
The minor central angle AOB is 145°.
The reflex angle subtended by major arc AB is 360° − 145° = 215°.
C lies on the minor arc, so ∠ACB is subtended by major arc AB.
x = 215°/2 = 107.5°.
Answer: x = 107.5°.
Appeared in: 2024 · Standard · Main
Q33.In the given figure, PAQ and PBR are tangents to the circle with centre O at the points A and B respectively. If T is a point on the circle such that ∠QAT = 45° and ∠TBR = 65°, then find ∠ATB.
By the tangent–chord theorem, ∠ABT = ∠QAT = 45°.
Similarly, ∠BAT = ∠TBR = 65°.
In triangle ATB, ∠ATB = 180° − 45° − 65° = 70°.
Answer: ∠ATB = 70°.
Appeared in: 2024 · Standard · Supplementary
Q34.In the given figure, a circle with centre O is inscribed inside △LMN. A and B are the points of tangency. Find ∠ANB.
The marked reflex angle AOB is 240°.
The minor angle AOB = 360° − 240° = 120°.
OA ⟂ AN and OB ⟂ BN.
Thus ∠ANB = 180° − 120° = 60°.
Answer: ∠ANB = 60°.
Appeared in: 2026 · Standard · Main
Q58.In Figure 1, PQ and PR are tangents to the circle such that ∠QOP = 70°. Find the measure of ∠QPR.
OQ ⟂ PQ.
∠QPO = 180° − 90° − 70° = 20°.
△OQP ≅ △ORP by RHS, so OP bisects ∠QPR.
∠QPR = 2 × 20° = 40°.
Answer: ∠QPR = 40°.
Appeared in: 2022 · Basic · Term II · Supplementary
Q60.In the given figure, O is the centre of circle. Find ∠AQB, given that PA and PB are tangents to the circle and ∠APB = 75°.
OA ⟂ PA and OB ⟂ PB.
The minor angle AOB = 180° − 75° = 105°.
Q lies on the major arc AB in the figure.
∠AQB = 105°/2 = 52.5°.
Answer: ∠AQB = 52.5°.
Appeared in: 2022–23 · Standard · Official sample
Q61.In the given figure, PQ is a chord of the circle centered at O. PT is a tangent to the circle at P. If ∠QPT = 55°, then find ∠PRQ.
By the tangent–chord theorem, the angle between tangent PT and chord PQ equals the angle subtended by PQ in the alternate segment.
Therefore, ∠PRQ = ∠QPT = 55°.
Answer: ∠PRQ = 55°.
Appeared in: 2023 · Standard · Main
Q11.(a) Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
Let chord AB touch the smaller circle at P and let O be the common centre.
OP ⟂ AB, by the tangent–radius theorem.
The perpendicular from the centre of the larger circle to chord AB bisects it.
Hence AP = PB.
Answer: The chord is bisected at the point of contact.
OR
(b) In a right-angled △ABC, right-angled at B, BC = 15 cm and AB = 8 cm. Find the radius of a circle inscribed in the triangle.
AC = √(8² + 15²) = 17 cm.
Let r be the radius. The tangent segments along the two perpendicular sides from B are each r.
Equal tangents give AC = (8 − r) + (15 − r).
17 = 23 − 2r, so r = 3 cm.
Answer: The radius is 3 cm.
Appeared in: 2026 · Standard · Second board examination
Q35.In the given figure, △ABC is circumscribing a circle. Find the length of BC, if AR = 4 cm, BR = 3 cm and AC = 11 cm.
Let the circle touch AB, BC and CA at R, P and Q respectively.
AQ = AR = 4 cm, so CQ = 11 − 4 = 7 cm.
CP = CQ = 7 cm and BP = BR = 3 cm.
BC = BP + PC = 10 cm.
Answer: BC = 10 cm.
Appeared in: 2024 · Standard · Main
Q36.A circle is inscribed in a △ABC touching AB, BC and AC at P, Q and R respectively. If AB = 12 cm, AR = 8 cm and CR = 6 cm, then find the length of BC.
AP = AR = 8 cm.
BP = AB − AP = 4 cm.
BQ = BP = 4 cm and CQ = CR = 6 cm.
BC = BQ + QC = 10 cm.
Answer: BC = 10 cm.
Appeared in: 2025 · Standard · Main
Q37.A quadrilateral circumscribes the circle as shown in the given figure. If AB = 5 cm, BC = 7 cm and CD = 6 cm, then find the length of AD.
Equal tangents in a circumscribed quadrilateral give AB + CD = BC + AD.
5 + 6 = 7 + AD.
AD = 4 cm.
Answer: AD = 4 cm.
Appeared in: 2025 · Basic · Main
Q38.In the given figure, △ABC circumscribes a circle. If AR = 3 cm, BP = 4 cm and QC = 5 cm, find the perimeter of △ABC.
Equal tangents give AR = AQ = 3 cm, BP = BR = 4 cm and CQ = CP = 5 cm.
AB = 7 cm, BC = 9 cm and CA = 8 cm.
Perimeter = 7 + 9 + 8 = 24 cm.
Answer: The perimeter is 24 cm.
Appeared in: 2025 · Basic · Main
Q39.(a) In the given figure, AP, AQ and BC are tangents to the circle with centre O. If AB = 6 cm, AC = 7 cm and BC = 5 cm, then what is the length of AP?
Let BC touch the circle at R.
BP = BR and CQ = CR, by equal tangents.
AP = 6 + BR and AQ = 7 + CR.
AP = AQ gives BR − CR = 1. Also BR + CR = 5.
Thus BR = 3 and CR = 2.
AP = 6 + 3 = 9 cm.
Answer: AP = 9 cm.
OR
(b) In the given figure, TP is tangent to a circle with centre O. Diameter BA when produced meets the tangent at T. If ∠ABP = 35°, then find the measure of ∠PTA.
OB = OP, so ∠BPO = ∠PBO = 35°.
∠BOP = 180° − 70° = 110°.
OA and OB are opposite rays, so ∠AOP = 70°.
OP ⟂ PT, and O, A, T are collinear.
∠PTA = 180° − 90° − 70° = 20°.
Answer: ∠PTA = 20°.
Appeared in: 2026 · Basic · Main
Q41.In the given figure, PQRS is a quadrilateral such that ∠S = 90°. A circle with centre O is inscribed in the quadrilateral. The circle touches PQ, QR, RS and SP at points M, N, T and L respectively. If MQ = 19 cm, RQ = 30 cm and SR = 21 cm, then find the radius of the circle.
QN = QM = 19 cm.
RN = RQ − QN = 11 cm, so RT = RN = 11 cm.
ST = SR − RT = 10 cm.
OT ⟂ SR and OL ⟂ SP; since ∠S = 90°, SLOT is a rectangle.
Its adjacent sides OL and OT are equal radii, so it is a square.
The radius OT = ST = 10 cm.
Answer: The radius is 10 cm.
Appeared in: 2025 · Standard · Supplementary
Q47.A circle is touching the side BC of a △ABC at the point P and touching AB and AC produced at points Q and R respectively. Prove that AQ = (Perimeter of △ABC).
BQ = BP and CR = CP, by equal tangents.
Also AQ = AR.
Perimeter = AB + BP + PC + CA.
Substitution gives AB + BQ + CR + CA = AQ + AR = 2AQ.
Therefore, AQ = (Perimeter of △ABC).
Answer: AQ is half the perimeter of △ABC.
Appeared in: 2023 · Standard · Supplementary
Q51.From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At a point E on the circle, a tangent is drawn to intersect PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of △PCD.
CA = CE and DB = DE, by equal tangents.
Perimeter = PC + CD + PD.
= PC + CE + ED + PD.
= PC + CA + DB + PD = PA + PB.
PA = PB = 10 cm, so the perimeter is 20 cm.
Answer: The perimeter is 20 cm.
Appeared in: 2023–24 · Standard · Official sample
Q52.A △ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 10 cm and 8 cm respectively. Find the lengths of the sides AB and AC, if it is given that ar(△ABC) = 90 cm².
Let AE = AF = x. Equal tangents give BE = BD = 10 and CF = CD = 8.
AB = x + 10, AC = x + 8 and BC = 18 cm.
Join the centre to the vertices: the three triangles each have height 4 cm.
90 = () × 4 × [(x + 10) + (x + 8) + 18].
90 = 4x + 72, so x = 4.5.
AB = 14.5 cm and AC = 12.5 cm.
Answer: AB = 14.5 cm; AC = 12.5 cm.
Appeared in: 2025–26 · Standard · Official sample
Q53.A circle is inscribed in a right triangle ABC, right angled at B. If the lengths of the two sides containing the right angle are 8 cm and 15 cm, find the radius of the incircle.
The hypotenuse is √(8² + 15²) = 17 cm.
Let r be the radius. Tangents from the right-angle vertex each have length r.
Equal tangents on the other sides give 17 = (8 − r) + (15 − r).
2r = 6, so r = 3 cm.
Answer: The radius is 3 cm.
Appeared in: 2026 · Standard · Main
Q54.(a) In Fig. 1, perimeter of △PQR is 20 cm. Find the length of tangent PA.
Let the contact point on QR be C; the other contacts are A and B.
QA = QC and RB = RC, by equal tangents.
PA = PQ + QA and PB = PR + RB.
PA + PB = PQ + PR + QC + CR = 20 cm.
PA = PB, so PA = 10 cm.
Answer: PA = 10 cm.
OR
(b) In Fig. 2, BC is tangent to the circle at point B of circle centred at O. BD is a chord of the circle so that ∠BAD = 55°. Find m∠DBC.
The tangent–chord theorem equates the angle between tangent BC and chord BD with the angle subtended by BD in the alternate segment.
∠DBC = ∠BAD = 55°.
Answer: ∠DBC = 55°.
Appeared in: 2022 · Basic · Term II · Main
Q55.In the given figure, x, y and z are the sides of a right triangle, where z is the hypotenuse. Prove that the radius r of the circle which touches the sides of the triangle is given by r = (x + y − z)/2.
The radii to the contact points on the perpendicular sides form a square with the right-angle vertex.
The two tangent lengths from that vertex are therefore each r.
Equal tangents give the two parts of the hypotenuse as x − r and y − r.
Thus z = x + y − 2r.
Hence r = (x + y − z)/2.
Answer: r = (x + y − z)/2.
Appeared in: 2024 · Standard · Supplementary
Q64.A circle is inscribed in a right-angled triangle ABC, right angled at B. If BC = 7 cm and AB = 24 cm, find the radius of the circle.
AC = √(7² + 24²) = 25 cm.
Let r be the radius. The two tangent segments from B are each r.
By equal tangents, 25 = (7 − r) + (24 − r).
2r = 6, so r = 3 cm.
Answer: The radius is 3 cm.
Appeared in: 2025–26 · Standard · Official sample
For a tangent and radius, state that the radius is perpendicular to the tangent at contact. For two tangents from one external point, state that their lengths are equal. Use the theorem that connects the given measurements to the required result.
Join the centre O to the contact point T and external point P. Since OT is perpendicular to PT, Pythagoras gives PT² = OP² − OT². Take the positive square root and include the unit.
Join the common centre to the contact point. This radius is perpendicular to the chord and bisects it. Use Pythagoras to find half the chord, then double that length.
The two radii at contact are perpendicular to the tangents. The four angles of the resulting quadrilateral total 360°, so the angle between the tangents and the minor angle between those radii total 180°.
Use the printed lengths, angles and geometric conditions. A diagram helps identify points and arcs; its apparent proportions do not establish a length, right angle or midpoint.
For tangents PA and PB to a circle with centre O, triangles OAP and OBP are right triangles. Their hypotenuse OP is common and OA = OB. RHS congruence then proves corresponding angles and tangent lengths equal.
In the examination, answer one alternative according to the paper instructions. Both alternatives are solved on this page for practice, and the original pair is kept together.
For perpendicular sides x and y and hypotenuse z, equal tangent lengths give z = x + y − 2r. Hence r = (x + y − z)/2. Establish the side lengths before substituting.
| Question | Answer |
|---|---|
| Q1 | The tangents are parallel. |
| Q2 | The tangent is perpendicular to the radius at contact. |
| Q3 | The chord is bisected at the point of contact. |
| Q4 | AB + CD + EF = BC + DE + FA. |
| Q5 | The two tangent segments subtend equal angles at the centre. |
| Q6 (a) | The stated angles are supplementary. |
| Q6 (b) | The tangents are parallel. |
| Q7 (a) | Each tangent is 3√3 cm long. |
| Q7 (b) | The tangents are parallel. |
| Q8 (a) | ∠ROS = 115°. |
| Q8 (b) | The tangents make equal corresponding angles with the chord. |
| Q9 (a) | The segment passes through the centre. |
| Q9 (b) | QORP is cyclic. |
| Q10 (a) | Each tangent is 15 cm long. |
| Q10 (b) | The chord is bisected at the point of contact. |
| Q11 (a) | The chord is bisected at the point of contact. |
| Q11 (b) | The radius is 3 cm. |
| Q12 | The radius is 7 cm. |
| Q13 | The radius is 8 cm. |
| Q14 | The radius is 24 m. |
| Q15 | The radius is 3 cm. |
| Q16 | The chord is 2√7 cm long. |
| Q17 | The chord is 6 cm long. |
| Q18 | The chord is 16 cm long. |
| Q19 | The larger radius is 25 cm. |
| Q20 | The bigger radius is 5 cm. |
| Q21 | The smaller radius is 3 cm. |
| Q22 | AC = 10 cm. |
| Q23 | CD = 16 cm. |
| Q24 | PA = cm. |
| Q25 | ∠POA = 55°. |
| Q26 | ∠AQB = 55°. |
| Q27 | ∠BOC = 115°. |
| Q28 | ∠OPQ = 30°. |
| Q29 | ∠APB = 40°. |
| Q30 | x = 120°. |
| Q31 | ∠OPQ = 25°. |
| Q32 | x = 107.5°. |
| Q33 | ∠ATB = 70°. |
| Q34 | ∠ANB = 60°. |
| Q35 | BC = 10 cm. |
| Q36 | BC = 10 cm. |
| Q37 | AD = 4 cm. |
| Q38 | The perimeter is 24 cm. |
| Q39 (a) | AP = 9 cm. |
| Q39 (b) | ∠PTA = 20°. |
| Q40 | The perimeter is 34 cm. |
| Q41 | The radius is 10 cm. |
| Q42 | PX + PY = PO. |
| Q43 | ∠APB = 2∠OAB. |
| Q44 | ORPQ is a square. |
| Q45 | PQOR is cyclic. |
| Q46 | M is the midpoint of AB. |
| Q47 | AQ is half the perimeter of △ABC. |
| Q48 | PA · PB = PC² − AC². |
| Q49 | BC = BD. |
| Q50 | The angles subtended by opposite sides at the centre are supplementary. |
| Q51 | The perimeter is 20 cm. |
| Q52 | AB = 14.5 cm; AC = 12.5 cm. |
| Q53 | The radius is 3 cm. |
| Q54 (a) | PA = 10 cm. |
| Q54 (b) | ∠DBC = 55°. |
| Q55 | r = (x + y − z)/2. |
| Q56 | AB = OT, and they bisect each other. |
| Q57 | Yes, ∠BAC = ∠DCA. |
| Q58 | ∠QPR = 40°. |
| Q59 | The radius is 6.5 cm. |
| Q60 | ∠AQB = 52.5°. |
| Q61 | ∠PRQ = 55°. |
| Q62 | PQ = 4 cm. |
| Q63 | The chord is 8 cm long. |
| Q64 | The radius is 3 cm. |
Selected official questions with TutorVertex explanations in NCERT-style steps; equivalent versions are grouped and original OR pairs retained.
Both OR alternatives are solved for practice. Detailed source references are recorded below; final source review is pending.
Pages are counted from the first PDF page. Confirmed sample marking-scheme pages are shown below. Other scheme-page references remain under review.
2023 · Standard · Main · 30/5/3 · Q24 · Question PDF pp. 13
Official Question paper · MATHEMATICS_STANDARD/30_5_3_Maths Standard.pdf
Official Marking scheme · Maths_Standard/MS 041_30-5-3 Mathematics 2022-23.pdf
2024 · Basic · Main · 430/2/1 · Q25 · Question PDF pp. 13
Official Question paper · MATHEMATICS_BASIC/430-2-1MATHEMATICS (BASIC).pdf
Official Marking scheme · Mathematics/X_241_MS_430_2_1_Unsigned.pdf
2024 · Basic · Main · 430/2/2 · Q23 · Question PDF pp. 13
Official Question paper · MATHEMATICS_BASIC/430-2-2MATHEMATICS (BASIC).pdf
Official Marking scheme · Mathematics/X_241_MS_430_2_2_Unsigned.pdf
2024 · Basic · Main · 430/2/3 · Q22 · Question PDF pp. 11
Official Question paper · MATHEMATICS_BASIC/430-2-3MATHEMATICS (BASIC).pdf
Official Marking scheme · Mathematics/X_241_MS_430_2_3_Unsigned.pdf
2024 · Basic · Main · 430/4/1 · Q22 · Question PDF pp. 11
Official Question paper · MATHEMATICS_BASIC/430-4-1MATHEMATICS (BASIC).pdf
Official Marking scheme · Mathematics/X_241_MS_430_4_1_Unsigned.pdf
2024 · Basic · Main · 430/4/2 · Q24 · Question PDF pp. 13
Official Question paper · MATHEMATICS_BASIC/430-4-2MATHEMATICS (BASIC).pdf
Official Marking scheme · Mathematics/X_241_MS_430_4_2_Unsigned.pdf
2024 · Basic · Main · 430/4/3 · Q25 · Question PDF pp. 13
Official Question paper · MATHEMATICS_BASIC/430-4-3MATHEMATICS (BASIC).pdf
Official Marking scheme · Mathematics/X_241_MS_430_4_3_Unsigned.pdf
2025 · Standard · Main · 30/3/1 · Q25 · Question PDF pp. 13
Official Question paper · 041_Mathematics_Standard/30-3-1_Mathematics Standard.pdf
Official Marking scheme · Math/041 Mathematics Standard/X_MS_041_Mathematics Standard_30-3-1_2024-25.pdf
2025 · Standard · Main · 30/3/2 · Q22 · Question PDF pp. 13
Official Question paper · 041_Mathematics_Standard/30-3-2_Mathematics Standard.pdf
Official Marking scheme · Math/041 Mathematics Standard/X_MS_041_Mathematics Standard_30-3-2_2024-25.pdf
2025 · Standard · Main · 30/3/3 · Q24 · Question PDF pp. 13
Official Question paper · 041_Mathematics_Standard/30-3-3_Mathematics Standard.pdf
Official Marking scheme · Math/041 Mathematics Standard/X_MS_041_Mathematics Standard_30-3-3_2024-25.pdf
2022 · Standard · Term II · Supplementary · 30/B/6 · Q3 · Question PDF pp. 3
Official Question paper · Maths_Std/30-B-6 Maths Std. for VI candidates.pdf
Official Marking scheme · Math standered/30-B-6.pdf
2022 · Standard · Term II · Supplementary · 30/6/3 · Q2 · Question PDF pp. 3
Official Question paper · Maths_Std/30-6-3 Maths Std..pdf
Official Marking scheme · Math standered/30-6-3.pdf
2025 · Basic · Main · 430/2/1 · Q23 · Question PDF pp. 11
Official Question paper · 241_Mathematics_Basic/430-2-1_Mathematics Basic.pdf
Official Marking scheme · Math/241 Mathematics Basic/X_241_Mathematics Basic_MS_430_2_1.pdf
2023 · Basic · Main · 430/B · Q23 · Question PDF pp. 15
Official Question paper · MATHEMATICS_BASIC/430_B_Maths Basic for VI candidates.pdf
Official Marking scheme · Math_Basic/430_VISUALLY IMPAIRED MATHEMATICS BASIC FINAL.pdf
2024 · Standard · Main · 30/B · Q23 · Question PDF pp. 13
Official Question paper · MATHEMATICS_STANDARD/30(B) Mathematics.pdf
Official Marking scheme · Mathematics_Standard/MS 041_30(B) Mathematics 2023-24.pdf
2023 · Standard · Main · 30/B/5 · Q23 · Question PDF pp. 15
Official Question paper · MATHEMATICS_STANDARD/30_B_5_Maths Std. for VI candidates.pdf
Official Marking scheme · Maths_Standard/MS 041_30(B) Mathematics 2022-23.pdf
2025 · Basic · Supplementary · 430/B · Q23 · Question PDF pp. 13
Official Question paper · Maths_Basic/430(B)-S Maths Basic Blind.pdf
Official Marking scheme · MATHEMATICS_BASIC/430_B Final.pdf
2025 · Basic · Main · 430/4/1 · Q24 · Question PDF pp. 9
Official Question paper · 241_Mathematics_Basic/430-4-1_Mathematics Basic.pdf
Official Marking scheme · Math/241 Mathematics Basic/X_241_Mathematics Basic_MS_430_4_1.pdf
2025 · Basic · Main · 430/4/2 · Q22 · Question PDF pp. 9
Official Question paper · 241_Mathematics_Basic/430-4-2_Mathematics Basic.pdf
Official Marking scheme · Math/241 Mathematics Basic/X_241_Mathematics Basic_MS_430_4_2.pdf
2025 · Basic · Main · 430/4/3 · Q21 · Question PDF pp. 9
Official Question paper · 241_Mathematics_Basic/430-4-3_Mathematics Basic.pdf
Official Marking scheme · Math/241 Mathematics Basic/X_241_Mathematics Basic_MS_430_4_3.pdf
2024 · Standard · Main · 30/5/1 · Q21 · Question PDF pp. 13
Official Question paper · MATHEMATICS_STANDARD/30-5-1(Mathematics Standard).pdf
Official Marking scheme · Mathematics_Standard/MS 041_30-5-1 Mathematics 2023-24.pdf
2024 · Standard · Main · 30/5/2 · Q25 · Question PDF pp. 13
Official Question paper · MATHEMATICS_STANDARD/30-5-2(Mathematics Standard).pdf
Official Marking scheme · Mathematics_Standard/MS 041_30-5-2 Mathematics 2023-24.pdf
2024 · Standard · Main · 30/5/3 · Q22 · Question PDF pp. 13
Official Question paper · MATHEMATICS_STANDARD/30-5-3(Mathematics Standard).pdf
Official Marking scheme · Mathematics_Standard/MS 041_30-5-3 Mathematics 2023-24.pdf
2022 · Basic · Term II · Main · 430/B/5 · Q3 · Question PDF pp. 5
Official Question paper · Math_B/430-B-5 Maths Basic for VI candidates.pdf
Official Marking scheme · Mathematics basic/Maths Basic Paper code 430.B.5.pdf
2024 · Standard · Supplementary · 30/B · Q22 · Question PDF pp. 15
Official Question paper · 30(B) Mathematics Standard.pdf
Official Marking scheme · MATHS STANDARD/MS_041_30(B)-S Mathematics 2023-24.pdf
2022 · Basic · Term II · Supplementary · 430/B/6 · Q2 · Question PDF pp. 3
Official Question paper · Maths_Basic/430-B-6 Maths Basic Blind.pdf
Official Marking scheme · Math basic/430.B.6.pdf
2026 · Standard · Second board examination · 30/B · Q22 · Question PDF pp. 13
Official Question paper · Mathmatics_Std/30-B_Maths Std_E2_10_2026.pdf
Official Marking scheme · Mathematics_Standard/MS_X_041_Mathematics_30B_II_Board_2025-26.pdf
2023 · Basic · Main · 430/6/1 · Q25 · Question PDF pp. 15
Official Question paper · MATHEMATICS_BASIC/430_6_1_Maths Basic.pdf
Official Marking scheme · Math_Basic/430_6_1.pdf
2023 · Basic · Main · 430/6/2 · Q22 · Question PDF pp. 13
Official Question paper · MATHEMATICS_BASIC/430_6_2_Maths Basic.pdf
Official Marking scheme · Math_Basic/436 -6-2.pdf
2023 · Basic · Main · 430/6/3 · Q24 · Question PDF pp. 13
Official Question paper · MATHEMATICS_BASIC/430_6_3_Maths Basic.pdf
Official Marking scheme · Math_Basic/430-6-3.pdf
2024 · Basic · Main · 430/5/1 · Q24 · Question PDF pp. 13
Official Question paper · MATHEMATICS_BASIC/430-5-1MATHEMATICS (BASIC).pdf
Official Marking scheme · Mathematics/X_241_MS_430_5_1_Unsigned.pdf
2024 · Basic · Main · 430/5/2 · Q23 · Question PDF pp. 13
Official Question paper · MATHEMATICS_BASIC/430-5-2MATHEMATICS (BASIC).pdf
Official Marking scheme · Mathematics/X_241_MS_430_5_2_Unsigned.pdf
2024 · Basic · Main · 430/5/3 · Q21 · Question PDF pp. 13
Official Question paper · MATHEMATICS_BASIC/430-5-3MATHEMATICS (BASIC).pdf
Official Marking scheme · Mathematics/X_241_MS_430_5_3_Unsigned.pdf
2025 · Standard · Main · 30/1/1 · Q25 · Question PDF pp. 17
Official Question paper · 041_Mathematics_Standard/30-1-1_Mathematics Standard.pdf
Official Marking scheme · Math/041 Mathematics Standard/X_MS_041_Mathematics Standard_30-1-1_2024-25.pdf
2025 · Standard · Main · 30/1/2 · Q22 · Question PDF pp. 15
Official Question paper · 041_Mathematics_Standard/30-1-2_Mathematics Standard.pdf
Official Marking scheme · Math/041 Mathematics Standard/X_MS_041_Mathematics Standard_30-1-2_2024-25.pdf
2025 · Standard · Main · 30/1/3 · Q23 · Question PDF pp. 17
Official Question paper · 041_Mathematics_Standard/30-1-3_Mathematics Standard.pdf
Official Marking scheme · Math/041 Mathematics Standard/X_MS_041_Mathematics Standard_30-1-3_2024-25.pdf
2023–24 · Basic · Official sample · Basic · Q23 · Question PDF pp. 4
Official Question paper · MathsBasic-SQP.pdf
Official Marking scheme · MathsBasic-MS.pdf · PDF p. 3
2022 · Standard · Term II · Main · 30/1/1 · Q6 · Question PDF pp. 5
Official Question paper · Math_S/30-1-1 Maths Standard.pdf
Official Marking scheme · Mathematic_Standard/30_1_1_Mathematics (Standard) Final.pdf
2022 · Standard · Term II · Main · 30/1/2 · Q2 · Question PDF pp. 3
Official Question paper · Math_S/30-1-2 Maths Standard.pdf
Official Marking scheme · Mathematic_Standard/30_1_2_Mathematics (Standard) final.pdf
2022 · Standard · Term II · Main · 30/1/3 · Q5 · Question PDF pp. 5
Official Question paper · Math_S/30-1-3 Maths Standard.pdf
Official Marking scheme · Mathematic_Standard/041_30_1_3_Mathematics (Standard) final.pdf
2026 · Standard · Main · 30/1/1 · Q25 · Question PDF pp. 9
Official Question paper · Mathematics_Standard/30-1-1P-Maths (Std)_X.pdf
Official Marking scheme · 041_MATHEMATICS STANDARD\MS_X_041_Mathematics_30-1-1_2025-26 (1).pdf
2026 · Standard · Main · 30/1/3 · Q23 · Question PDF pp. 7
Official Question paper · Mathematics_Standard/30-1-3P-Maths (Std)_X.pdf
Official Marking scheme · 041_MATHEMATICS STANDARD\MS_X_041_Mathematics_30-1-3_2025-26 (1).pdf
2024 · Standard · Supplementary · 30/S/2 · Q24 · Question PDF pp. 13
Official Question paper · 30-S-2 MATHEMATICS STANDARD.pdf
Official Marking scheme · MATHS STANDARD/MS 041_30-S-2 Mathematics 2023-24.pdf
2025 · Basic · Main · 430/1/1 · Q23 · Question PDF pp. 15
Official Question paper · 241_Mathematics_Basic/430-1-1_Mathematics Basic.pdf
Official Marking scheme · Math/241 Mathematics Basic/X_241_Mathematics Basic_MS_430_1_1.pdf
2025 · Basic · Main · 430/1/2 · Q21 · Question PDF pp. 13
Official Question paper · 241_Mathematics_Basic/430-1-2_Mathematics Basic.pdf
Official Marking scheme · Math/241 Mathematics Basic/X_241_Mathematics Basic_MS_430_1_2.pdf
2025 · Basic · Main · 430/1/3 · Q24 · Question PDF pp. 15
Official Question paper · 241_Mathematics_Basic/430-1-3_Mathematics Basic.pdf
Official Marking scheme · Math/241 Mathematics Basic/X_241_Mathematics Basic_MS_430_1_3.pdf
2022 · Standard · Term II · Main · 30/B/5 · Q5 · Question PDF pp. 5
Official Question paper · Math_S/30-B-5 Maths Std. for VI candidates.pdf
Official Marking scheme · Mathematic_Standard/041_30_B_5_Math (Standard) (For VI).pdf
2024 · Basic · Supplementary · 430/S/2 · Q21 · Question PDF pp. 11
Official Question paper · 430-S-2 MATHEMATICS BASIC.pdf
Official Marking scheme · Maths Basic/X_241_MS_430_S_2.pdf
2024–25 · Basic · Official sample · Basic · Q22 · Question PDF pp. 4
Official Question paper · MathsBasic-SQP.pdf
Official Marking scheme · MathsBasic-MS.pdf · PDF p. 2
2022 · Standard · Term II · Main · 30/4/1 · Q5 · Question PDF pp. 5
Official Question paper · Math_S/30-4-1 Maths Standard.pdf
Official Marking scheme · Mathematic_Standard/041_30_4_1_Mathematics (Standard).pdf
2022 · Standard · Term II · Main · 30/4/2 · Q2 · Question PDF pp. 3
Official Question paper · Math_S/30-4-2 Maths Standard.pdf
Official Marking scheme · Mathematic_Standard/041_30_4_2_Mathematics (Standard).pdf
2022 · Standard · Term II · Main · 30/4/3 · Q6 · Question PDF pp. 5
Official Question paper · Math_S/30-4-3 Maths Standard.pdf
Official Marking scheme · Mathematic_Standard/041_30_4_3_Mathematics (Standard).pdf
2025 · Standard · Main · 30/2/1 · Q25 · Question PDF pp. 17
Official Question paper · 041_Mathematics_Standard/30-2-1_Mathematics Standard.pdf
Official Marking scheme · Math/041 Mathematics Standard/X_MS_041_Mathematics Standard_30-2-1_2024-25.pdf
2025 · Standard · Main · 30/2/2 · Q24 · Question PDF pp. 15
Official Question paper · 041_Mathematics_Standard/30-2-2_Mathematics Standard.pdf
Official Marking scheme · Math/041 Mathematics Standard/X_MS_041_Mathematics Standard_30-2-2_2024-25.pdf
2025 · Standard · Main · 30/2/3 · Q22 · Question PDF pp. 15
Official Question paper · 041_Mathematics_Standard/30-2-3_Mathematics Standard.pdf
Official Marking scheme · Math/041 Mathematics Standard/X_MS_041_Mathematics Standard_30-2-3_2024-25.pdf
2024 · Basic · Supplementary · 430/S/3 · Q24 · Question PDF pp. 13
Official Question paper · 430-S-3 MATHEMATICS BASIC.pdf
Official Marking scheme · Maths Basic/X_241_MS_430_S_3.pdf
2022 · Basic · Term II · Main · 430/1/1 · Q6 · Question PDF pp. 5
Official Question paper · Math_B/430-1-1 Maths Basic.pdf
Official Marking scheme · Mathematics basic/Maths Basic Paper Code 430.1.1..pdf
2022 · Basic · Term II · Main · 430/1/2 · Q3 · Question PDF pp. 5
Official Question paper · Math_B/430-1-2 Maths Basic.pdf
Official Marking scheme · Mathematics basic/Maths Basic paper code 430.1.2.pdf
2022 · Basic · Term II · Main · 430/1/3 · Q3 · Question PDF pp. 3
Official Question paper · Math_B/430-1-3 Maths Basic.pdf
Official Marking scheme · Mathematics basic/Maths Basic Paper Code 430.1.3..pdf
2022 · Basic · Term II · Main · 430/3/1 · Q6 · Question PDF pp. 5
Official Question paper · Math_B/430-3-1 Maths Basic.pdf
Official Marking scheme · Mathematics basic/Maths basic paper code430.3.1.pdf
2022 · Basic · Term II · Main · 430/3/2 · Q2 · Question PDF pp. 3
Official Question paper · Math_B/430-3-2 Maths Basic.pdf
Official Marking scheme · Mathematics basic/Maths Basic Paper code 430.3.2.pdf
2022 · Basic · Term II · Main · 430/3/3 · Q3 · Question PDF pp. 3
Official Question paper · Math_B/430-3-3 Maths Basic.pdf
Official Marking scheme · Mathematics basic/Maths Basic Paper Code 430.3.3.pdf
2023 · Standard · Main · 30/2/1 · Q25 · Question PDF pp. 13
Official Question paper · MATHEMATICS_STANDARD/30_2_1_Maths Standard.pdf
Official Marking scheme · Maths_Standard/MS 041_30-2-1 Mathematics 2022-23.pdf
2023 · Standard · Main · 30/2/2 · Q22 · Question PDF pp. 13
Official Question paper · MATHEMATICS_STANDARD/30_2_2_Maths Standard.pdf
Official Marking scheme · Maths_Standard/MS 041_30-2-2 Mathematics 2022-23.pdf
2023 · Standard · Main · 30/2/3 · Q23 · Question PDF pp. 13
Official Question paper · MATHEMATICS_STANDARD/30_2_3_Maths Standard.pdf
Official Marking scheme · Maths_Standard/MS 041_30-2-3 Mathematics 2022-23.pdf
2026 · Standard · Second board examination · 30/7/2 · Q23 · Question PDF pp. 15
Official Question paper · Mathmatics_Std/30-7-2_Maths Std_E2_10_2026.pdf
Official Marking scheme · Mathematics_Standard/Mathematics Standard-041 E2 (Set 30-7-2).pdf
2023 · Standard · Main · 30/6/1 · Q24 · Question PDF pp. 13
Official Question paper · MATHEMATICS_STANDARD/30_6_1_Maths Standard.pdf
Official Marking scheme · Maths_Standard/MS 041_30-6-1 Mathematics 2022-23.pdf
2023 · Standard · Main · 30/6/2 · Q25 · Question PDF pp. 13
Official Question paper · MATHEMATICS_STANDARD/30_6_2_Maths Standard.pdf
Official Marking scheme · Maths_Standard/MS 041_30-6-2 Mathematics 2022-23.pdf
2023 · Basic · Main · 430/4/1 · Q24 · Question PDF pp. 6
Official Question paper · MATHEMATICS_BASIC/430_4_1 Maths Basic.pdf
Official Marking scheme · Math_Basic/430_4_1.pdf
2023 · Basic · Main · 430/4/3 · Q23 · Question PDF pp. 6
Official Question paper · MATHEMATICS_BASIC/430_4_3 Maths Basic.pdf
Official Marking scheme · Math_Basic/430_4_3.pdf
2025 · Basic · Main · 430/3/1 · Q23 · Question PDF pp. 13
Official Question paper · 241_Mathematics_Basic/430-3-1_Mathematics Basic.pdf
Official Marking scheme · Math/241 Mathematics Basic/X_241_Mathematics Basic_MS_430_3_1.pdf
2025 · Basic · Main · 430/3/2 · Q21 · Question PDF pp. 13
Official Question paper · 241_Mathematics_Basic/430-3-2_Mathematics Basic.pdf
Official Marking scheme · Math/241 Mathematics Basic/X_241_Mathematics Basic_MS_430_3_2.pdf
2025 · Basic · Main · 430/3/3 · Q24 · Question PDF pp. 15
Official Question paper · 241_Mathematics_Basic/430-3-3_Mathematics Basic.pdf
Official Marking scheme · Math/241 Mathematics Basic/X_241_Mathematics Basic_MS_430_3_3.pdf
2024 · Standard · Main · 30/4/1 · Q24 · Question PDF pp. 13
Official Question paper · MATHEMATICS_STANDARD/30-4-1(Mathematics Standard).pdf
Official Marking scheme · Mathematics_Standard/Marking scheme 30 4 1.pdf
2024 · Standard · Main · 30/4/2 · Q25 · Question PDF pp. 13
Official Question paper · MATHEMATICS_STANDARD/30-4-2(Mathematics Standard).pdf
Official Marking scheme · Mathematics_Standard/Marking scheme 30 4 2.pdf
2024 · Standard · Supplementary · 30/S/1 · Q24 · Question PDF pp. 15
Official Question paper · 30-S-1 MATHEMATICS STANDARD.pdf
Official Marking scheme · MATHS STANDARD/MS 041_30-S-1 Mathematics 2023-24.pdf
2026 · Standard · Main · 30/1/2 · Q24 · Question PDF pp. 9
Official Question paper · Mathematics_Standard/30-1-2P-Maths (Std)_X.pdf
Official Marking scheme · 041_MATHEMATICS STANDARD\MS_X_041_Mathematics_30-1-2_2025-26 (1).pdf
2024 · Standard · Main · 30/4/3 · Q21 · Question PDF pp. 11
Official Question paper · MATHEMATICS_STANDARD/30-4-3(Mathematics Standard).pdf
Official Marking scheme · Mathematics_Standard/Marking scheme 30 4 3.pdf
2025 · Standard · Main · 30/B · Q23 · Question PDF pp. 15
Official Question paper · 041_Mathematics_Standard/30 B_Maths Std for Visually Impaired.pdf
Official Marking scheme · Math/041 Mathematics Standard/X_MS_041_Mathematics Standard_30 (B)_2024-25.pdf
2025 · Basic · Main · 430/2/2 · Q21 · Question PDF pp. 11
Official Question paper · 241_Mathematics_Basic/430-2-2_Mathematics Basic.pdf
Official Marking scheme · Math/241 Mathematics Basic/X_241_Mathematics Basic_MS_430_2_2.pdf
2025 · Basic · Main · 430/2/3 · Q24 · Question PDF pp. 13
Official Question paper · 241_Mathematics_Basic/430-2-3_Mathematics Basic.pdf
Official Marking scheme · Math/241 Mathematics Basic/X_241_Mathematics Basic_MS_430_2_3.pdf
2026 · Basic · Main · 430/4/1 · Q24 · Question PDF pp. 13, 15
Official Question paper · Mathematics_Standard/1158-1_430-4-1 Mathematics (Basic).pdf
Official Marking scheme · 241_MATHEMATICS BASIC\X_241_MS_430_4_1_unsigned.pdf
2026 · Basic · Main · 430/4/2 · Q25 · Question PDF pp. 15
Official Question paper · Mathematics_Standard/1158-2_430-4-2 Mathematics (Basic).pdf
Official Marking scheme · 241_MATHEMATICS BASIC\X_241_MS_430_4_2_unsigned.pdf
2026 · Basic · Main · 430/4/3 · Q25 · Question PDF pp. 15
Official Question paper · Mathematics_Standard/1158-3_430-4-3 Mathematics (Basic).pdf
Official Marking scheme · 241_MATHEMATICS BASIC\X_241_MS_430_4_3_unsigned.pdf
2025 · Basic · Supplementary · 430/S/1 · Q24 · Question PDF pp. 13
Official Question paper · Maths_Basic/430-S-1Math Basic.pdf
Official Marking scheme · MATHEMATICS_BASIC/MS_X_Mathematics(Basic)_241_430_S_1.pdf
2025 · Basic · Supplementary · 430/S/2 · Q22 · Question PDF pp. 13
Official Question paper · Maths_Basic/430-S-2Math Basic.pdf
Official Marking scheme · MATHEMATICS_BASIC/MS_X_Mathematics(Basic)_241_430_S_2.pdf
2025 · Basic · Supplementary · 430/S/3 · Q21 · Question PDF pp. 11
Official Question paper · Maths_Basic/430-S-3Math Basic.pdf
Official Marking scheme · MATHEMATICS_BASIC/MS_X_Mathematics(Basic)_241_430_S_3.pdf
2025 · Standard · Supplementary · 30/S/2 · Q24 · Question PDF pp. 17
Official Question paper · Maths_Standard/30-S-2 Maths Standard.pdf
Official Marking scheme · MATHEMATICS_STANDARD/MS_X_041_Mathematics_30-S-2_2024-25.pdf
2025 · Standard · Supplementary · 30/S/1 · Q24 · Question PDF pp. 17
Official Question paper · Maths_Standard/30-S-1 Maths Standard.pdf
Official Marking scheme · MATHEMATICS_STANDARD/MS_X_041_Mathematics_30-S-1_2024-25.pdf
2023 · Basic · Main · 430/4/2 · Q25 · Question PDF pp. 8
Official Question paper · MATHEMATICS_BASIC/430_4_2 Maths Basic.pdf
Official Marking scheme · Math_Basic/430_4_2.pdf
2025 · Standard · Supplementary · 30/S/3 · Q24 · Question PDF pp. 17
Official Question paper · Maths_Standard/30-S-3 Maths Standard.pdf
Official Marking scheme · MATHEMATICS_STANDARD/MS_X_041_Mathematics_30-S-3_2024-25.pdf
2022 · Standard · Term II · Main · 30/3/1 · Q6 · Question PDF pp. 5
Official Question paper · Math_S/30-3-1 Maths Standard.pdf
Official Marking scheme · Mathematic_Standard/marking Scheme _041_30_3_1_.pdf
2022 · Standard · Term II · Main · 30/3/2 · Q5 · Question PDF pp. 5
Official Question paper · Math_S/30-3-2 Maths Standard.pdf
Official Marking scheme · Mathematic_Standard/Marking Scheme 041_30_3_2.pdf
2022 · Standard · Term II · Main · 30/3/3 · Q1 · Question PDF pp. 3
Official Question paper · Math_S/30-3-3 Maths Standard.pdf
Official Marking scheme · Mathematic_Standard/Marking Scheme 041_30_3_3.pdf
2022 · Standard · Term II · Supplementary · 30/6/1 · Q6 · Question PDF pp. 5
Official Question paper · Maths_Std/30-6-1 Maths Std..pdf
Official Marking scheme · Math standered/30-6-1.pdf
2022 · Standard · Term II · Supplementary · 30/6/2 · Q3 · Question PDF pp. 3
Official Question paper · Maths_Std/30-6-2 Maths Std..pdf
Official Marking scheme · Math standered/30-6-2.pdf
2026 · Standard · Main · 30/2/1 · Q25 · Question PDF pp. 17
Official Question paper · Mathematics_Standard/30_2_1_Mathematics Std._cl.10.pdf
Official Marking scheme · 041_MATHEMATICS STANDARD\MS_X_041_Mathematics_30-2-1_2025-26 (1).pdf
2026 · Standard · Main · 30/2/2 · Q23 · Question PDF pp. 17
Official Question paper · Mathematics_Standard/30_2_2_Mathematics Std._cl.10.pdf
Official Marking scheme · 041_MATHEMATICS STANDARD\MS_X_041_Mathematics_30-2-2_2025-26 (1).pdf
2026 · Standard · Main · 30/2/3 · Q22 · Question PDF pp. 17
Official Question paper · Mathematics_Standard/30_2_3_Mathematics Std._cl.10.pdf
Official Marking scheme · 041_MATHEMATICS STANDARD\MS_X_041_Mathematics_30-2-3_2025-26 (1).pdf
2026 · Basic · Second board examination · 430/8/1 · Q22 · Question PDF pp. 13
Official Question paper · Mathmatics_Basic/430-8-1_Maths Basic_E2_10_2026.pdf
Official Marking scheme · Mathematics_Basic/241_430_8_1 Mathematics Basic.pdf
2026 · Basic · Second board examination · 430/8/2 · Q25 · Question PDF pp. 15
Official Question paper · Mathmatics_Basic/430-8-2_Maths Basic_E2_10_2026.pdf
Official Marking scheme · Mathematics_Basic/241_430_8_2 Mathematics Basic.pdf
2026 · Basic · Second board examination · 430/8/3 · Q23 · Question PDF pp. 15
Official Question paper · Mathmatics_Basic/430-8-3_Maths Basic_E2_10_2026.pdf
Official Marking scheme · Mathematics_Basic/241_430_8_3 Mathematics Basic.pdf
2023 · Standard · Supplementary · 30/C/1 · Q24 · Question PDF pp. 13
Official Question paper · Maths_Standard/30_C_1 Mathematics Standard.pdf
Official Marking scheme · Mathematics_Standard/041_30-C-1.pdf
2023 · Standard · Supplementary · 30/C/2 · Q24 · Question PDF pp. 13
Official Question paper · Maths_Standard/30_C_2 Mathematics Standard.pdf
Official Marking scheme · Mathematics_Standard/041_30-C-2.pdf
2023 · Standard · Supplementary · 30/C/3 · Q23 · Question PDF pp. 13
Official Question paper · Maths_Standard/30_C_3 Mathematics Standard.pdf
Official Marking scheme · Mathematics_Standard/041_30-C-3.pdf
2023 · Standard · Main · 30/5/1 · Q22 · Question PDF pp. 13
Official Question paper · MATHEMATICS_STANDARD/30_5_1_Maths Standard.pdf
Official Marking scheme · Maths_Standard/MS 041_30-5-1 Mathematics 2022-23.pdf
2026 · Standard · Second board examination · 30/8/2 · Q24 · Question PDF pp. 17
Official Question paper · Mathmatics_Std/30-8-2_Maths Std_E2_10_2026.pdf
Official Marking scheme · Mathematics_Standard/MS_X_041_Mathematics_30-8-2_2025-26 F (1).pdf
2026 · Standard · Second board examination · 30/8/3 · Q21 · Question PDF pp. 17
Official Question paper · Mathmatics_Std/30-8-3_Maths Std_E2_10_2026.pdf
Official Marking scheme · Mathematics_Standard/MS_X_041_Mathematics_30-8-3_2025-26 F (1).pdf
2023–24 · Standard · Official sample · Standard · Q23 · Question PDF pp. 5
Official Question paper · MathsStandard-SQP.pdf
Official Marking scheme · MathsStandard-MS.pdf · PDF p. 2
2025–26 · Standard · Official sample · Standard · Q25 · Question PDF pp. 4
Official Question paper · MathsStandard-SQP.pdf
Official Marking scheme · MathsStandard-MS.pdf · PDF p. 5
2026 · Standard · Main · 30/B · Q23 · Question PDF pp. 15
Official Question paper · Mathematics_Standard/1164_30(B)_Mathematics Standard.pdf
Official Marking scheme · 041_MATHEMATICS STANDARD\MS_X_041_Mathematics_30(B)_2025-26 (1).pdf
2022 · Basic · Term II · Main · 430/2/1 · Q4 · Question PDF pp. 5
Official Question paper · Math_B/430-2-1 Maths Basic.pdf
Official Marking scheme · Mathematics basic/Maths Basic paper code 430.2.1.pdf
2022 · Basic · Term II · Main · 430/2/2 · Q1 · Question PDF pp. 3
Official Question paper · Math_B/430-2-2 Maths Basic.pdf
Official Marking scheme · Mathematics basic/Maths Basic Paper code 430.2.2.pdf
2022 · Basic · Term II · Main · 430/2/3 · Q2 · Question PDF pp. 3, 5
Official Question paper · Math_B/430-2-3 Maths Basic.pdf
Official Marking scheme · Mathematics basic/Maths Basic Paper code 430.2.3.pdf
2024 · Standard · Supplementary · 30/S/3 · Q24 · Question PDF pp. 15
Official Question paper · 30-S-3 MATHEMATICS STANDARD.pdf
Official Marking scheme · MATHS STANDARD/MS 041_30-S-3 Mathematics 2023-24.pdf
2026 · Standard · Second board examination · 30/8/1 · Q23 · Question PDF pp. 17
Official Question paper · Mathmatics_Std/30-8-1_Maths Std_E2_10_2026.pdf
Official Marking scheme · Mathematics_Standard/MS_X_041_Mathematics_30-8-1_2025-26 F (1).pdf
2026 · Standard · Second board examination · 30/7/1 · Q25 · Question PDF pp. 15
Official Question paper · Mathmatics_Std/30-7-1_Maths Std_E2_10_2026.pdf
Official Marking scheme · Mathematics_Standard/Mathematics Standard-041 E2 (Set 30-7-1).pdf
2026 · Standard · Second board examination · 30/7/3 · Q22 · Question PDF pp. 15
Official Question paper · Mathmatics_Std/30-7-3_Maths Std_E2_10_2026.pdf
Official Marking scheme · Mathematics_Standard/Mathematics Standard-041 E2 (Set 30-7-3).pdf
2024 · Standard · Main · 30/2/1 · Q24 · Question PDF pp. 15
Official Question paper · MATHEMATICS_STANDARD/30-2-1(Mathematics Standard).pdf
Official Marking scheme · Mathematics_Standard/MS 041_30-2-1 Mathematics 2023-24.pdf
2024 · Standard · Main · 30/2/2 · Q21 · Question PDF pp. 13
Official Question paper · MATHEMATICS_STANDARD/30-2-2(Mathematics Standard).pdf
Official Marking scheme · Mathematics_Standard/MS 041_30-2-2 Mathematics 2023-24.pdf
2024 · Standard · Main · 30/2/3 · Q22 · Question PDF pp. 15
Official Question paper · MATHEMATICS_STANDARD/30-2-3(Mathematics Standard).pdf
Official Marking scheme · Mathematics_Standard/MS 041_30-2-3 Mathematics 2023-24.pdf
2022 · Basic · Term II · Supplementary · 430/6/1 · Q2 · Question PDF pp. 3
Official Question paper · Maths_Basic/430-6-1 maths basic.pdf
Official Marking scheme · Math basic/430.6.1.pdf
2022 · Basic · Term II · Supplementary · 430/6/2 · Q4 · Question PDF pp. 5
Official Question paper · Maths_Basic/430-6-2 maths basic.pdf
Official Marking scheme · Math basic/430.6.2.pdf
2022 · Basic · Term II · Supplementary · 430/6/3 · Q4 · Question PDF pp. 5
Official Question paper · Maths_Basic/430-6-3 maths basic.pdf
Official Marking scheme · Math basic/430.6.3.pdf
2022 · Basic · Term II · Main · 430/4/1 · Q5 · Question PDF pp. 5
Official Question paper · Math_B/430-4-1 Maths Basic.pdf
Official Marking scheme · Mathematics basic/Maths Basic Paper code 430.4.1.pdf
2022 · Basic · Term II · Main · 430/4/2 · Q5 · Question PDF pp. 5
Official Question paper · Math_B/430-4-2 Maths Basic.pdf
Official Marking scheme · Mathematics basic/241_430_4_2_Mathematics (Basic).pdf
2022 · Basic · Term II · Main · 430/4/3 · Q2 · Question PDF pp. 3
Official Question paper · Math_B/430-4-3 Maths Basic.pdf
Official Marking scheme · Mathematics basic/241_430_4_3_Mathematics (Basic).pdf
2022–23 · Standard · Official sample · Standard · Q23 · Question PDF pp. 4
Official Question paper · MathsStandard-SQP.pdf
Official Marking scheme · MathsStandard-MS.pdf · PDF p. 2
2023 · Standard · Main · 30/5/2 · Q25 · Question PDF pp. 13
Official Question paper · MATHEMATICS_STANDARD/30_5_2_Maths Standard.pdf
Official Marking scheme · Maths_Standard/MS 041_30-5-2 Mathematics 2022-23.pdf
2026–27 · Basic · Official sample · Basic · Q24 · Question PDF pp. 4
Official Question paper · MathsBasic-SQP.pdf
Official Marking scheme · MathsBasic-MS.pdf · PDF p. 4
2026–27 · Basic · Official sample · Basic · Q24 · Question PDF pp. 4
Official Question paper · MathsBasic-SQP.pdf
Official Marking scheme · MathsBasic-MS.pdf · PDF p. 4
2025–26 · Standard · Official sample · Standard · Q25 · Question PDF pp. 4
Official Question paper · MathsStandard-SQP.pdf
Official Marking scheme · MathsStandard-MS.pdf · PDF p. 5
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