Trigonometry and Pythagoras’ theorem: Edexcel International GCSE Maths questions

Every Edexcel International GCSE Maths exam question on 4.8 Trigonometry and Pythagoras’ theorem, 2019–2025, with its mark scheme and examiner’s report.

All 176 questions on Trigonometry and Pythagoras’ theorem, as a list

June 2025 (R), Paper 1 Foundation, Q24 (3 marks): The diagram shows triangle PQR P Diagram NOT accurately drawn 6.5 cm 24° R Q Work out the length of QR Give your answer correct to 3 significant figures. cm
June 2025 (R), Paper 1 Higher, Q9 (3 marks): The diagram shows triangle PQR P Diagram NOT accurately drawn 6.5 cm 24° R Q Work out the length of QR Give your answer correct to 3 significant figures. cm
June 2025 (R), Paper 1 Higher, Q20 (3 marks): The diagram shows cuboid ABCDEFGH Diagram NOT accurately drawn E H F D G 7 cm 18 cm C A 9 cm B AB = 9 cm AF = 7 cm FC = 18 cm Calculate the length of BC Give yo
June 2025 (R), Paper 1 Higher, Q25 (6 marks): B Diagram NOT accurately drawn A C D BAC is a sector of a circle, centre A BCD is a sector of a circle, centre C Angle BAC = 40° Angle BCD = 130° Area of shaded
June 2025 (R), Paper 2 Foundation, Q27 (5 marks): The diagram shows two triangles, ADE and CDB C Diagram NOT A accurately drawn B D E ABD is a straight line. AE = 28 cm ED = 45 cm AB = 21 cm CD = 35 cm angle AE
June 2025 (R), Paper 2 Higher, Q11 (5 marks): The diagram shows two triangles, ADE and CDB C Diagram NOT A accurately drawn B D E ABD is a straight line. AE = 28 cm ED = 45 cm AB = 21 cm CD = 35 cm angle AE
June 2025 (R), Paper 2 Higher, Q23 (3 marks): The diagram shows a triangular prism, ABCDEF, with a horizontal rectangular base ABCD E F Diagram NOT accurately drawn C B D A M is the midpoint of the line AC
June 2025 (R), Paper 2 Higher, Q24 (6 marks): PQ is a straight line drawn on a square grid, with a scale of 1 cm for 1 unit on each axis. where a > 0 P has coordinates 5, a and Q has coordinates 7 3 , a The
June 2025, Paper 1 Foundation, Q26 (5 marks): A B Diagram NOT accurately drawn 12 cm 60 D C 47 cm ABCD is a trapezium with one line of symmetry. angle ADC = 60° AD = 12 cm DC = 47 cm Work out the area of th
June 2025, Paper 1 Higher, Q9 (5 marks): A B Diagram NOT accurately drawn 12 cm 60 D C 47 cm ABCD is a trapezium with one line of symmetry. angle ADC = 60° AD = 12 cm DC = 47 cm Work out the area of th
June 2025, Paper 1 Higher, Q20 (5 marks): B C 54 9.4 cm A Diagram NOT 72 accurately drawn 12.8 cm 39 D Work out the length of BC Give your answer correct to 3 significant figures. cm
June 2025, Paper 2 Foundation, Q27 (5 marks): ABD and ABC are right‑angled triangles. D Diagram NOT accurately drawn C 12 cm B A 16 cm AB = 16 cm BC = 12 cm AD = 1.5 ×AC Find the length of CD Give your answ
June 2025, Paper 2 Higher, Q10 (5 marks): ABD and ABC are right‑angled triangles. D Diagram NOT accurately drawn C 12 cm B A 16 cm AB = 16 cm BC = 12 cm AD = 1.5 ×AC Find the length of CD Give your answ
June 2025, Paper 2 Higher, Q24 (4 marks): The diagram shows a square-based pyramid ABCDE E Diagram NOT accurately drawn D A C B EA = EB = EC = ED M is the centre of the horizontal square base ABCD Q is
November 2024, Paper 1 Foundation, Q27 (5 marks): Here are two similar triangles. E B Diagrams NOT accurately drawn 7 5. cm 51cm A C x cm D F 24 cm Work out the value of x Show your working clearly. x =
November 2024, Paper 1 Higher, Q10 (5 marks): Here are two similar triangles. E B Diagrams NOT accurately drawn 7 5. cm 51cm A C x cm D F 24 cm Work out the value of x Show your working clearly. x =
November 2024, Paper 1 Higher, Q12 (4 marks): ABC is a right-angled triangle. D is a point on BC A Diagram NOT accurately drawn 47° 24° B D C AB = 4250 m angle BAD 47 angle BCA 24 Work out the length of DC
November 2024, Paper 1 Higher, Q16 (4 marks): OAPB is a sector of a circle, centre O A Diagram NOT accurately drawn P 50° O B Angle AOB 50 Area of triangle OAB = 120 cm 2 Work out the area of the sector OAP
November 2024, Paper 2 Foundation, Q19 (3 marks): The diagram shows triangle PQR P Diagram NOT 8.6 cm accurately drawn 43° Q R x cm Work out the value of x Give your answer correct to one decimal place. x =
November 2024, Paper 2 Higher, Q3 (3 marks): The diagram shows triangle PQR P Diagram NOT 8.6 cm accurately drawn 43° Q R x cm Work out the value of x Give your answer correct to one decimal place. x =
November 2024, Paper 2 Higher, Q24 (6 marks): A, B and C are three points on horizontal ground. AB = 8 4. metres BC = 9 2. metres B is on a bearing of 067° from A C is on a bearing of 129° from B Calculate
November 2024, Paper 2 Higher, Q25 (5 marks): The diagram shows an equilateral triangle ABC and a circle with centre O C Diagram NOT accurately drawn O x cm A B AB, BC and CA are tangents to the circle. The
June 2024 (R), Paper 1 Foundation, Q23 (6 marks): The diagram shows a trapezium, ABCD A B Diagram NOT accurately drawn 15 cm D 14 cm C DAB and ADC are right angles. AD = 15 cm DC = 14 cm The area of the trapezi
June 2024 (R), Paper 1 Higher, Q8 (6 marks): The diagram shows a trapezium, ABCD A B Diagram NOT accurately drawn 15 cm D 14 cm C DAB and ADC are right angles. AD = 15 cm DC = 14 cm The area of the trapezi
June 2024 (R), Paper 1 Higher, Q15 (3 marks): The diagram shows isosceles triangle EFG F Diagram NOT accurately drawn 130° E G EF = GF Angle EFG = 130° The area of triangle EFG is 74 cm² Work out the length
June 2024 (R), Paper 1 Higher, Q22 (6 marks): The diagram shows a cuboid ABCDEFGH with horizontal base ADEH Diagram NOT accurately drawn G F P H E B C 20 cm M 8 cm A 12 cm D AB = 8 cm AD = 12 cm DE = 20 cm
June 2024 (R), Paper 2 Foundation, Q26 (5 marks): The diagram shows a hexagon ABCDEF 11 cm A B Diagram NOT accurately drawn 5 cm 30° F C 4.7 cm E D 23 cm Angle BCF = 30° AB, FC and ED are parallel. Calculate th
June 2024 (R), Paper 2 Higher, Q10 (5 marks): The diagram shows a hexagon ABCDEF 11 cm A B Diagram NOT accurately drawn 5 cm 30° F C 4.7 cm E D 23 cm Angle BCF = 30° AB, FC and ED are parallel. Calculate th
June 2024 (R), Paper 2 Higher, Q15 (3 marks): A D Diagram NOT accurately drawn 6.5 cm B C E 3 cm AB, BC and CD are three sides of a regular pentagon and CDE is a triangle. BCE is a straight line. CD = 6.5 c
June 2024, Paper 1 Foundation, Q15 (4 marks): The diagram shows a shape ABCDE made from a right-angled triangle ABE and a square BCDE 15 cm B C A Diagram NOT accurately drawn 17 cm E D ABC is a straight lin
June 2024, Paper 1 Foundation, Q26 (4 marks): The diagram shows a roof support. C 9 m Diagram NOT accurately drawn A M B 12 m The roof support is made from four lengths of wood, AB, AC, BC and MC AC = BC =
June 2024, Paper 1 Higher, Q11 (4 marks): The diagram shows a roof support. C 9 m Diagram NOT accurately drawn A M B 12 m The roof support is made from four lengths of wood, AB, AC, BC and MC AC = BC =
June 2024, Paper 1 Higher, Q19 (5 marks): Here is quadrilateral ABCD B 15.2 m A x° 12.8 m Diagram NOT accurately drawn 13.4 m 62° 40° C D Work out the value of x Give your answer correct to 3 significan
June 2024, Paper 2 Foundation, Q21 (3 marks): The diagram shows triangle ABC A B 34° Diagram NOT x cm accurately drawn 6.5 cm C Work out the value of x Give your answer correct to one decimal place. x =
June 2024, Paper 2 Higher, Q5 (3 marks): The diagram shows triangle ABC A B 34° Diagram NOT x cm accurately drawn 6.5 cm C Work out the value of x Give your answer correct to one decimal place. x =
June 2024, Paper 2 Higher, Q21 (5 marks): The diagram shows a square ABCD and a circle. A B Diagram NOT accurately drawn D C The sides of the square are tangents to the circle. 2 The total area of the s
November 2023, Paper 1 Foundation, Q24 (5 marks): Here is triangle ABC C Diagram NOT accurately drawn 8 m 40° x° A B 22 m Work out the value of x Give your answer correct to one decimal place. Show your working
November 2023, Paper 1 Higher, Q10 (5 marks): Here is triangle ABC C Diagram NOT accurately drawn 8 m 40° x° A B 22 m Work out the value of x Give your answer correct to one decimal place. Show your working
November 2023, Paper 1 Higher, Q18 (5 marks): The diagram shows the positions of three villages, A, B and C N 132° B 3.6 km N 8.4 km 54° Diagram NOT accurately drawn A C The bearing of B from A is 054° The
November 2023, Paper 1 Higher, Q21 (5 marks): Here is a triangular prism ABCDEF A F Diagram NOT accurately drawn 28 cm 53 cm B E 30° C D AD = 53 cm DF = 28 cm Angle FDE = 30° Work out the volume of the tria
November 2023, Paper 2 Foundation, Q18 (4 marks): The diagram shows triangle ABC and triangle ECD E Diagram NOT accurately drawn 5 cm B w cm 10 cm D A C 14 cm 8 cm ACD and EBC are straight lines. AB = 10 cm AC
November 2023, Paper 2 Higher, Q2 (4 marks): The diagram shows triangle ABC and triangle ECD E Diagram NOT accurately drawn 5 cm B w cm 10 cm D A C 14 cm 8 cm ACD and EBC are straight lines. AB = 10 cm AC
November 2023, Paper 2 Higher, Q20 (4 marks): The diagram shows equilateral triangle ABC with sides of length 10 cm. A circle is drawn inside the triangle. A Diagram NOT 10 cm accurately drawn F D C B E D,
June 2023 (R), Paper 1 Foundation, Q20 (5 marks): The diagram shows a shape made up of three semicircles, enclosing a right‑angled triangle. Diagram NOT A accurately drawn 6 cm 6 cm C B AB, BC and CA are each t
June 2023 (R), Paper 1 Higher, Q4 (5 marks): The diagram shows a shape made up of three semicircles, enclosing a right‑angled triangle. Diagram NOT A accurately drawn 6 cm 6 cm C B AB, BC and CA are each t
June 2023 (R), Paper 1 Higher, Q19 (5 marks): The diagram shows a triangle ABC where A, B and C represent the positions of three towns. C Diagram NOT accurately drawn A B 7 3 → = → = AB BC 2 5 Pru
June 2023 (R), Paper 1 Higher, Q25 (6 marks): Here is a triangle ABC B Diagram NOT C accurately drawn (2x – 1) cm (2x + 1) cm 30° A The area of the triangle is (x2 + x – 3.75) cm2 Find the size of the large
June 2023 (R), Paper 2 Foundation, Q24 (6 marks): The diagram shows a rectangular sheet of metal ABCD A B Diagram NOT accurately drawn 50 cm 32° D C BD = 50 cm and angle BDC = 32° Nasser joins side AD to side B
June 2023 (R), Paper 2 Higher, Q9 (6 marks): The diagram shows a rectangular sheet of metal ABCD A B Diagram NOT accurately drawn 50 cm 32° D C BD = 50 cm and angle BDC = 32° Nasser joins side AD to side B
June 2023 (R), Paper 2 Higher, Q22 (5 marks): Here is a cuboid ABCDEFGH E F Diagram NOT accurately drawn H G 9 cm C D 4 cm A B 15 cm AB = 15 cm BC = 4 cm CF = 9 cm (a) Work out the length of BE Give your an
June 2023, Paper 1 Foundation, Q20 (4 marks): The diagram shows a shaded shape AEBCD made by removing triangle AEB from rectangle ABCD A B Diagram NOT accurately drawn 7.2 cm 5.4 cm 6 cm E D C AE = 7.2 cm B
June 2023, Paper 1 Higher, Q5 (4 marks): The diagram shows a shaded shape AEBCD made by removing triangle AEB from rectangle ABCD A B Diagram NOT accurately drawn 7.2 cm 5.4 cm 6 cm E D C AE = 7.2 cm B
June 2023, Paper 1 Higher, Q22 (6 marks): The diagram shows two circles with centre O and a regular pentagon ABCDE B Diagram NOT accurately drawn A O C E D A, B, C, D and E are points on the larger circ
June 2023, Paper 1 Higher, Q23 (5 marks): A frustum is made by removing a small square-based pyramid from a similar large squared‑based pyramid as shown in the diagram. Diagram NOT accurately drawn 15 c
June 2023, Paper 2 Foundation, Q28 (4 marks): The diagram shows right-angled triangle ABD B Diagram NOT accurately drawn 14 cm C 38° A D 8 cm AB = 14 cm AD = 8 cm C is the point on BD such that angle BAC =
June 2023, Paper 2 Higher, Q12 (4 marks): The diagram shows right-angled triangle ABD B Diagram NOT accurately drawn 14 cm C 38° A D 8 cm AB = 14 cm AD = 8 cm C is the point on BD such that angle BAC =
June 2023, Paper 2 Higher, Q22 (5 marks): The diagram shows a triangle ABC and a flagpole BF F Diagram NOT accurately drawn 10 m B 11 m C 9 m 16 m A A, B and C are points on horizontal ground. BF is ver
January 2023 (R), Paper 1 Foundation, Q24 (4 marks): The diagram shows an isosceles triangle ABC C Diagram NOT accurately drawn y cm y cm A 7 cm B AB = 7 cm AC = BC = y cm The area of the triangle is 42 cm2 Work o
January 2023 (R), Paper 1 Foundation, Q25 (4 marks): R and T are points on a circle, centre O T Diagram NOT M accurately drawn R 52° O RT = 12 cm M is the midpoint of RT Angle ROM = 52° Work out the area of the ci
January 2023 (R), Paper 1 Higher, Q9 (4 marks): The diagram shows an isosceles triangle ABC C Diagram NOT accurately drawn y cm y cm A 7 cm B AB = 7 cm AC = BC = y cm The area of the triangle is 42 cm2 Work o
January 2023 (R), Paper 1 Higher, Q10 (4 marks): R and T are points on a circle, centre O T Diagram NOT M accurately drawn R 52° O RT = 12 cm M is the midpoint of RT Angle ROM = 52° Work out the area of the ci
January 2023 (R), Paper 1 Higher, Q17 (5 marks): C Diagram NOT accurately drawn 8.3 cm A B 4.6 cm AB = 4.6 cm BC = 8.3 cm angle ABC is acute The area of triangle ABC is 12 cm² Work out the perimeter of triangl
January 2023 (R), Paper 1 Higher, Q21 (4 marks): The diagram shows a triangular prism, ABCDEF, with a rectangular base ABCD F Diagram NOT accurately drawn E C 2.2 cm D B 18° 6 cm A AB = 6 cm DE = 2.2 cm angle
January 2023, Paper 1 Foundation, Q23 (5 marks): The diagram shows a triangle ABC inside a semicircle. Diagram NOT accurately drawn C 18 cm 50° A B A, B and C are points on the semicircle. AB is the diameter o
January 2023, Paper 1 Higher, Q8 (5 marks): The diagram shows a triangle ABC inside a semicircle. Diagram NOT accurately drawn C 18 cm 50° A B A, B and C are points on the semicircle. AB is the diameter o
January 2023, Paper 1 Higher, Q16 (5 marks): Here is a shape formed from two triangles ABC and CDE ACD and BCE are straight lines. B D 31 cm 16 cm Diagram NOT C accurately drawn 19 cm 64° E 24 cm A AC = 24
January 2023, Paper 1 Higher, Q21 (5 marks): The diagram shows the cross section of a circular water pipe. Diagram NOT O accurately drawn 4.8 cm 72° A C B OABC is a sector of the circle, centre O The shade
January 2023, Paper 2 Foundation, Q25 (5 marks): The diagram shows an isosceles triangle, with base length 24 cm. Diagram NOT accurately drawn 24 cm The perimeter of the triangle is 54 cm. Work out the area of
January 2023, Paper 2 Higher, Q10 (5 marks): The diagram shows an isosceles triangle, with base length 24 cm. Diagram NOT accurately drawn 24 cm The perimeter of the triangle is 54 cm. Work out the area of
January 2023, Paper 2 Higher, Q23 (5 marks): The diagram shows a solid prism ABCDEFGHIJ J 8 cm 8 cm Diagram NOT accurately drawn F I D G H E C 120° 12 cm x cm A B 2x cm The prism is such that each cross se
June 2022 (R), Paper 1 Foundation, Q27 (6 marks): The diagram shows a quadrilateral ABCD D Diagram NOT accurately drawn A 7.5 cm 6 cm B C In the diagram, ABC and DAC are right‑angled triangles. BC = 6 cm AC = 7
June 2022 (R), Paper 1 Higher, Q11 (6 marks): The diagram shows a quadrilateral ABCD D Diagram NOT accurately drawn A 7.5 cm 6 cm B C In the diagram, ABC and DAC are right‑angled triangles. BC = 6 cm AC = 7
June 2022 (R), Paper 1 Higher, Q17 (5 marks): Here is a parallelogram PQRS, in which angle SPQ is acute. S R Diagram NOT 3.8 cm accurately drawn P 6.1 cm Q PQ = 6.1 cm PS = 3.8 cm 2 The area of the parallel
June 2022 (R), Paper 1 Higher, Q18 (4 marks): The diagram shows a cube ABCDEFGH with sides of length 6 cm. F 6 cm G Diagram NOT accurately drawn T A B E H V D C T is the midpoint of AB and V is the midpoint
June 2022 (R), Paper 2 Foundation, Q27 (5 marks): The diagram shows triangle ABP inside the regular hexagon ABCDEF D E Diagram NOT accurately drawn C F P B A AB = 5 cm BP = 2 cm Angle ABP = 90° Work out the siz
June 2022 (R), Paper 2 Higher, Q10 (5 marks): The diagram shows triangle ABP inside the regular hexagon ABCDEF D E Diagram NOT accurately drawn C F P B A AB = 5 cm BP = 2 cm Angle ABP = 90° Work out the siz
June 2022 (R), Paper 2 Higher, Q15 (3 marks): The diagram shows a kite ABCD D Diagram NOT accurately drawn C A 118° 6 cm 11 cm B AB = 6 cm BC = 11 cm Angle ABC = 118° Calculate the area of the kite. Give yo
June 2022, Paper 1 Foundation, Q25 (4 marks): Two circles, C1 and C2 , are drawn on a centimetre grid, with a scale of 1 cm for 1 unit on each axis. The centre of circle C1 is at the point with coordinates
June 2022, Paper 1 Higher, Q10 (4 marks): Two circles, C1 and C2 , are drawn on a centimetre grid, with a scale of 1 cm for 1 unit on each axis. The centre of circle C1 is at the point with coordinates
June 2022, Paper 1 Higher, Q18 (5 marks): Here is triangle ABC B 12.3 m C 115° x° 9.7 m Diagram NOT accurately drawn A Work out the value of x Give your answer correct to 3 significant figures. x =
June 2022, Paper 1 Higher, Q22 (5 marks): A solid is made from a cone and a hemisphere. 20 cm Diagram NOT accurately drawn The circular plane face of the hemisphere coincides with the circular base of t
June 2022, Paper 2 Foundation, Q22 (3 marks): The diagram shows triangle PQR. P 42° 9.5 cm Diagram NOT x cm accurately drawn Q R Work out the value of x Give your answer correct to one decimal place. x =
June 2022, Paper 2 Higher, Q6 (3 marks): The diagram shows triangle PQR. P 42° 9.5 cm Diagram NOT x cm accurately drawn Q R Work out the value of x Give your answer correct to one decimal place. x =
January 2022 (R), Paper 1 Foundation, Q17 (4 marks): The shaded shape is made using three identical right-angled triangles and a square. Diagram NOT accurately drawn 16 cm 12.8 cm 16 cm 16 cm Work out the perimete
January 2022 (R), Paper 1 Higher, Q3 (4 marks): The shaded shape is made using three identical right-angled triangles and a square. Diagram NOT accurately drawn 16 cm 12.8 cm 16 cm 16 cm Work out the perimete
January 2022 (R), Paper 1 Higher, Q22 (4 marks): The diagram shows triangle ABC C Diagram NOT accurately drawn y° b cm x° A c cm B c = 11.5 correct to one decimal place x = 80 correct to the nearest whole numb
January 2022 (R), Paper 2 Foundation, Q26 (5 marks): In the diagram, ABC is a right-angled triangle and DEF is a semicircular arc. A Diagram NOT E accurately drawn F 3 cm D 30° B C 24 cm In triangle ABC BC = 24 cm
January 2022 (R), Paper 2 Higher, Q9 (5 marks): In the diagram, ABC is a right-angled triangle and DEF is a semicircular arc. A Diagram NOT E accurately drawn F 3 cm D 30° B C 24 cm In triangle ABC BC = 24 cm
January 2022 (R), Paper 2 Higher, Q12 (3 marks): The diagram shows two vertical phone masts, AB and CD, on horizontal ground. D Diagram NOT accurately drawn B 30.7 m 6.2 m A C 244 m AB = 6.2 m AC = 244 m CD =
January 2022 (R), Paper 2 Higher, Q16 (5 marks): The diagram shows quadrilateral ABCD D 28 cm Diagram NOT 45 cm A accurately drawn 19 cm B C 36 cm The angle BCD is acute. Given that the area of triangle BCD =
January 2022 (R), Paper 2 Higher, Q19 (3 marks): ABCD is a horizontal rectangular field. E D C Diagram NOT accurately drawn 12 m 8 m A 18 m B A vertical pole, AE, is placed at the corner A of the field. AE = 1
January 2022, Paper 1 Foundation, Q18 (3 marks): The diagram shows triangle ABC A B Diagram NOT accurately drawn 8.4 cm 65° C Work out the length of the side AB Give your answer correct to 3 significant figure
January 2022, Paper 1 Foundation, Q24 (4 marks): The diagram shows isosceles triangle ABC A Diagram NOT 17.5 cm 17.5 cm accurately drawn B C 28 cm AB = AC = 17.5 cm BC = 28 cm Calculate the area of triangle AB
January 2022, Paper 1 Higher, Q3 (3 marks): The diagram shows triangle ABC A B Diagram NOT accurately drawn 8.4 cm 65° C Work out the length of the side AB Give your answer correct to 3 significant figure
January 2022, Paper 1 Higher, Q9 (4 marks): The diagram shows isosceles triangle ABC A Diagram NOT 17.5 cm 17.5 cm accurately drawn B C 28 cm AB = AC = 17.5 cm BC = 28 cm Calculate the area of triangle AB
January 2022, Paper 1 Higher, Q21 (5 marks): The diagram shows the prism ABCDEFGHJK with horizontal base AEFG J Diagram NOT C accurately drawn H K B D M G F A E ABCDE is a cross section of the prism where
January 2022, Paper 2 Higher, Q14 (3 marks): A zip wire is shown as the dashed line AC in the diagram. A Diagram NOT x accurately drawn C 2.6 m B D 12 m The zip wire is supported by two vertical posts AB a
January 2022, Paper 2 Higher, Q23 (6 marks): The diagram shows triangle PQR R Diagram NOT accurately drawn 18° 4.2 cm P 1.6 cm Q PQ = 1.6 cm PR = 4.2 cm Angle PRQ = 18° Given that angle PQR is obtuse, work
November 2021, Paper 1 Foundation, Q14 (3 marks): Here is a right-angled triangle. 30 cm Diagram NOT accurately drawn h cm 52 cm Calculate the value of h. Give your answer correct to 3 significant figures. h =
November 2021, Paper 1 Higher, Q2 (3 marks): Here is a right-angled triangle. 30 cm Diagram NOT accurately drawn h cm 52 cm Calculate the value of h. Give your answer correct to 3 significant figures. h =
November 2021, Paper 1 Higher, Q12 (6 marks): The diagram shows a vertical cliff with a vertical radio mast on top of the cliff and a buoy in the sea. A Diagram NOT accurately drawn 100 m 20° B d m The heig
November 2021, Paper 1 Higher, Q13 (3 marks): Here is a triangle XYZ. X Diagram NOT accurately drawn 130° 16 cm 25° Y Z The length XZ and the angles YXZ and XYZ are each given correct to 2 significant figur
November 2021, Paper 2 Foundation, Q26 (4 marks): ABC is an isosceles triangle with BA = BC. B Diagram NOT accurately drawn 38° A C N 9.3 cm N is the point on AC such that AN = 9.3 cm and BN is perpendicular to
November 2021, Paper 2 Higher, Q10 (4 marks): ABC is an isosceles triangle with BA = BC. B Diagram NOT accurately drawn 38° A C N 9.3 cm N is the point on AC such that AN = 9.3 cm and BN is perpendicular to
November 2021, Paper 2 Higher, Q18 (5 marks): Here is a quadrilateral ABCD. B 12 cm Diagram NOT 60° accurately drawn C 9 cm 7 cm 84° D A Calculate the area of quadrilateral ABCD. Give your answer correct to
November 2021, Paper 2 Higher, Q22 (6 marks): The diagram shows a sphere of diameter x cm and a pyramid ABCDE with a horizontal rectangular base BCDE. A Diagram NOT accurately drawn 5x cm x cm E D 2x cm O B
June 2021, Paper 1 Higher, Q22 (4 marks): The diagram shows a triangular prism ABCDEF with a horizontal base ABEF. D Diagram NOT accurately drawn C 12 cm 12 cm F E 15 cm A 10 cm B AC = BC = FD = ED = 12
June 2021, Paper 1 Higher, Q25 (6 marks): The diagram shows two circles such that the region R, shown shaded in the diagram, is the region common to both circles. Diagram NOT accurately drawn A 4 cm 5 c
June 2021, Paper 2 Foundation, Q21 (3 marks): Here is a right-angled triangle. Diagram NOT accurately drawn x cm 6.5 cm 42° Work out the value of x. Give your answer correct to one decimal place. x =
June 2021, Paper 2 Foundation, Q24 (5 marks): Here is a triangular prism. Diagram NOT 11.2 cm accurately drawn 15 cm 7.4 cm Work out the volume of the prism. Give your answer correct to 3 significant figure
June 2021, Paper 2 Higher, Q7 (3 marks): Here is a right-angled triangle. Diagram NOT accurately drawn x cm 6.5 cm 42° Work out the value of x. Give your answer correct to one decimal place. x =
June 2021, Paper 2 Higher, Q10 (5 marks): Here is a triangular prism. Diagram NOT 11.2 cm accurately drawn 15 cm 7.4 cm Work out the volume of the prism. Give your answer correct to 3 significant figure
June 2021, Paper 2 Higher, Q18 (6 marks): B Diagram NOT 8 cm accurately drawn A 98° 7.5 cm 35° C D ABCD is a quadrilateral where A, B, C and D are points on a circle. AB = 8 cm BC = 7.5 cm Angle ABC = 9
January 2021 (R), Paper 1 Foundation, Q25 (5 marks): The diagram shows one face of a wall. This face is in the shape of a pentagon with exactly one line of symmetry. Diagram NOT 7 m 7 m accurately drawn 6 m 6 m 10
January 2021 (R), Paper 1 Higher, Q10 (5 marks): The diagram shows one face of a wall. This face is in the shape of a pentagon with exactly one line of symmetry. Diagram NOT 7 m 7 m accurately drawn 6 m 6 m 10
January 2021 (R), Paper 2 Higher, Q13 (3 marks): The diagram shows two hot air balloons. A is a point on the base of one of the balloons and B is a point on the base of the other balloon. Diagram NOT accuratel
January 2021 (R), Paper 2 Higher, Q20 (5 marks): A, B and C are points on a circle with centre O. B Diagram NOT accurately drawn 75° O A C Angle ABC = 75° The area of the shaded segment is 200 cm 2 Calculate t
January 2021 (R), Paper 2 Higher, Q22 (4 marks): ABC is an isosceles triangle in a horizontal plane. The point T is vertically above B. T Diagram NOT accurately drawn 10 cm 8 cm B A 140° 8 cm M C Angle ABC = 1
January 2021, Paper 1 Foundation, Q26 (4 marks): Here is isosceles triangle ABC. A Diagram NOT accurately drawn 65° 16 cm D B C D is the midpoint of AC and DB = 16 cm. Angle DAB = 65° Work out the perimeter of
January 2021, Paper 1 Higher, Q10 (4 marks): Here is isosceles triangle ABC. A Diagram NOT accurately drawn 65° 16 cm D B C D is the midpoint of AC and DB = 16 cm. Angle DAB = 65° Work out the perimeter of
January 2021, Paper 1 Higher, Q16 (5 marks): The diagram shows the positions of three ships, A, B and C. North Diagram NOT accurately drawn B 150 m North 120° A 275 m C Ship B is due north of ship A. The b
January 2021, Paper 2 Foundation, Q22 (5 marks): A, B and C are points on a circle with centre O. C Diagram NOT accurately drawn O 15 cm A 8 cm B AOC is a diameter of the circle. AB = 8 cm BC = 15 cm Angle ABC
January 2021, Paper 2 Higher, Q8 (5 marks): A, B and C are points on a circle with centre O. C Diagram NOT accurately drawn O 15 cm A 8 cm B AOC is a diameter of the circle. AB = 8 cm BC = 15 cm Angle ABC
January 2021, Paper 2 Higher, Q17 (7 marks): The diagram shows a solid prism ABCDEFGH. 28 cm G F Diagram NOT accurately drawn B C H 20 cm E 24 cm A 37 cm D The trapezium ABCD, in which AD is parallel to BC
January 2021, Paper 2 Higher, Q18 (7 marks): A rectangle ABCD is to be drawn on a centimetre grid such that A has coordinates (–4, –2) B has coordinates (1, 10) C has coordinates (19, a) D has coordinates
January 2021, Paper 2 Higher, Q20 (4 marks): Q A P B Diagram NOT accurately drawn R F C T E D The diagram shows a shaded region T formed by removing an equilateral triangle PQR from a regular hexagon ABCDE
January 2021, Paper 2 Higher, Q22 (6 marks): The diagram shows a sector OBC of a circle with centre O and radius (6 + x) cm. O A Diagram NOT 50° 6 cm B accurately drawn D x cm C A is the point on OB and D
November 2020 (R), Paper 1 Higher, Q17 (6 marks): The diagram shows a prism ABCDEFGH with a horizontal base. B 15 cm A Diagram NOT C accurately drawn D 10 cm G H 12 cm F 12 cm E The base of the prism, EFGH, is
November 2020 (R), Paper 2 Foundation, Q20 (4 marks): Markus makes a steel framework. The framework is in the shape of the right‑angled triangle ABC shown in the diagram. A Diagram NOT accurately drawn 4.3 m B C 6.
November 2020 (R), Paper 2 Foundation, Q26 (5 marks): The diagram shows four congruent right‑angled triangles ABJ, BCI, CDH and DEG. The diagram also shows the straight line ABCDEF. Diagram NOT accurately drawn A B
November 2020 (R), Paper 2 Higher, Q7 (4 marks): Markus makes a steel framework. The framework is in the shape of the right‑angled triangle ABC shown in the diagram. A Diagram NOT accurately drawn 4.3 m B C 6.
November 2020 (R), Paper 2 Higher, Q13 (5 marks): The diagram shows four congruent right‑angled triangles ABJ, BCI, CDH and DEG. The diagram also shows the straight line ABCDEF. Diagram NOT accurately drawn A B
November 2020 (R), Paper 2 Higher, Q22 (6 marks): The curve with equation x2 – x + y2 = 10 and the straight line with equation x – y = –4 intersect at the points A and B. Work out the exact length of AB. a Show
November 2020, Paper 1 Higher, Q11 (6 marks): The diagram shows trapezium ABCD in which BC and AD are parallel. 8.4 cm B C Diagram NOT accurately drawn A D 17.6 cm The trapezium has exactly one line of symm
November 2020, Paper 2 Foundation, Q22 (3 marks): The diagram shows a right-angled triangle. Diagram NOT accurately drawn 3.4 cm x° 4.7 cm Calculate the value of x. Give your answer correct to one decimal place
November 2020, Paper 2 Foundation, Q23 (4 marks): The diagram shows an isosceles triangle. Diagram NOT accurately drawn 8.5 cm 8.5 cm 8 cm Work out the area of the triangle. cm2
November 2020, Paper 2 Higher, Q7 (3 marks): The diagram shows a right-angled triangle. Diagram NOT accurately drawn 3.4 cm x° 4.7 cm Calculate the value of x. Give your answer correct to one decimal place
November 2020, Paper 2 Higher, Q8 (4 marks): The diagram shows an isosceles triangle. Diagram NOT accurately drawn 8.5 cm 8.5 cm 8 cm Work out the area of the triangle. cm2
November 2020, Paper 2 Higher, Q18 (5 marks): The diagram shows cuboid ABCDEFGH. E F Diagram NOT accurately drawn H G 4 cm C D A B 5 cm AB = 5 cm AH = 4 cm The size of the angle between CH and the plane ABC
January 2020 (R), Paper 1 Higher, Q15 (4 marks): The diagram shows two right-angled triangles, DEF and EFG. E G 28° Diagram NOT 40° accurately drawn 12 cm D F Work out the length of EG. Give your answer correc
January 2020 (R), Paper 1 Higher, Q21 (6 marks): The diagram shows the prism ABCDEF with cross section triangle ABC. D Diagram NOT C accurately drawn F E A B Angle BEC = 40° and angle ACB is obtuse. AC = 6 cm
January 2020 (R), Paper 2 Foundation, Q19 (3 marks): The diagram shows a rectangle and a diagonal of the rectangle. 8.5 cm Diagram NOT accurately drawn 5.6 cm Work out the length of the diagonal of the rectangle.
January 2020 (R), Paper 2 Higher, Q4 (3 marks): The diagram shows a rectangle and a diagonal of the rectangle. 8.5 cm Diagram NOT accurately drawn 5.6 cm Work out the length of the diagonal of the rectangle.
January 2020, Paper 1 Foundation, Q22 (3 marks): Here is a right-angled triangle. P Diagram NOT accurately drawn 63° 24.3 cm R Q Calculate the length of PQ. Give your answer correct to 3 significant figures. c
January 2020, Paper 1 Higher, Q9 (3 marks): Here is a right-angled triangle. P Diagram NOT accurately drawn 63° 24.3 cm R Q Calculate the length of PQ. Give your answer correct to 3 significant figures. c
January 2020, Paper 1 Higher, Q14 (5 marks): The diagram shows parallelogram EFGH. 14.7 cm F G Diagram NOT accurately drawn 106° 9.3 cm E H EF = 9.3 cm FG = 14.7 cm Angle EFG = 106° (a) Work out the area o
January 2020, Paper 1 Higher, Q19 (4 marks): The diagram shows a cuboid ABCDEFGH. A B Diagram NOT accurately drawn D C 6 cm F G 5 cm E 9 cm H EH = 9 cm, HG = 5 cm and GB = 6 cm. Work out the size of the an
January 2020, Paper 1 Higher, Q22 (6 marks): Triangle HJK is isosceles with HJ = HK and JK = 80 H is the point with coordinates (−4, 1) J is the point with coordinates ( j, 15) where j < 0 K is the point w
January 2020, Paper 2 Foundation, Q27 (5 marks): The diagram shows a shaded shape ABCD made from a semicircle ABC and a right‑angled triangle ACD. B A C Diagram NOT accurately drawn 17 cm 15 cm D AC is the dia
January 2020, Paper 2 Higher, Q11 (5 marks): The diagram shows a shaded shape ABCD made from a semicircle ABC and a right‑angled triangle ACD. B A C Diagram NOT accurately drawn 17 cm 15 cm D AC is the dia
June 2019 (R), Paper 1 Foundation, Q20 (4 marks): The diagram shows isosceles triangle ABC. A Diagram NOT accurately drawn 7.5 cm 7.5 cm 6 cm B C AB = AC = 7.5 cm. The height of the triangle is 6 cm. Calculate
June 2019 (R), Paper 1 Higher, Q7 (4 marks): The diagram shows isosceles triangle ABC. A Diagram NOT accurately drawn 7.5 cm 7.5 cm 6 cm B C AB = AC = 7.5 cm. The height of the triangle is 6 cm. Calculate
June 2019 (R), Paper 1 Higher, Q25 (5 marks): A boat sails from point X to point Y and then to point Z. Y is on a bearing of 280° from X. Z is on a bearing of 220° from Y. The distance from X to Y is 3.5 km
June 2019 (R), Paper 2 Foundation, Q27 (5 marks): B Diagram NOT 42° 3.1m accurately drawn 32°/ A Calculate the length of AB. Show your working clearly. Give your answer correct to 3 significant figures. m
June 2019 (R), Paper 2 Higher, Q12 (5 marks): B Diagram NOT 42° 3.1 m accurately drawn 32° A C D Calculate the length of AB. Show your working clearly. Give your answer correct to 3 significant figures. m
June 2019 (R), Paper 2 Higher, Q19 (6 marks): The diagram shows a sector OAPB of a circle, centre O. P A B Diagram NOT accurately drawn 80° O AB is a chord of the circle. Angle AOB = 80° The area of sector
June 2019 (R), Paper 2 Higher, Q23 (6 marks): The diagram shows a solid pyramid ABCDE with a horizontal base. A Diagram NOT accurately drawn E D O B C 10 cm The base, BCDE, of the pyramid is a square of sid
June 2019, Paper 1 Foundation, Q23 (5 marks): The diagram shows a shape made from a right-angled triangle and a semicircle. Diagram NOT accurately drawn A C 6 cm 6 cm B AC is the diameter of the semicircle.
June 2019, Paper 1 Higher, Q9 (5 marks): The diagram shows a shape made from a right-angled triangle and a semicircle. Diagram NOT accurately drawn A C 6 cm 6 cm B AC is the diameter of the semicircle.
June 2019, Paper 1 Higher, Q18 (3 marks): The diagram shows triangle PQR. Diagram NOT P accurately drawn 17.8 cm 36° R Q 26.3 cm Calculate the length of PR. Give your answer correct to 3 significant fig
June 2019, Paper 2 Foundation, Q21 (4 marks): The diagram shows the positions of three ships A, B and C. North Diagram NOT accurately drawn North 234km A 356km B is 234 km due north of A. C' is 356 km due e
June 2019, Paper 2 Higher, Q12 (4 marks): ABCD is a trapezium. 21.2 cm C B Diagram NOT accurately drawn 16.7 cm 43° A D Calculate the perimeter of the trapezium. Give your answer correct to 3 significan
June 2019, Paper 2 Higher, Q19 (6 marks): ABCD is a quadrilateral. A Diagram NOT accurately drawn 39° 26 cm D 95° B 47° C The area of triangle ACD is 250 cm2 Calculate the area of the quadrilateral ABCD
June 2019, Paper 2 Higher, Q21 (3 marks): The diagram shows cuboid ABCDEFGH. E F Diagram NOT accurately drawn H G C D A B For this cuboid the length of AB : the length of BC : the length of CF = 4 : 2 :
January 2019 (R), Paper 1 Foundation, Q18 (4 marks): Q Diagram NOT accurately drawn 14 cm 5 cm 10 cm P S R In triangle PQR, S is the point on PR such that angle RSQ = 90° RQ = 14 cm RS = 10 cm SP = 5 cm Work out t
January 2019 (R), Paper 1 Higher, Q3 (4 marks): Q Diagram NOT accurately drawn 14 cm 5 cm 10 cm P S R In triangle PQR, S is the point on PR such that angle RSQ = 90° RQ = 14 cm RS = 10 cm SP = 5 cm Work out t
January 2019 (R), Paper 1 Higher, Q20 (4 marks): Here is a cube ABCDEFGH. H E Diagram NOT M accurately drawn F G D C A B M is the midpoint of the edge GH. Find the size of the angle between the line MA and the
January 2019 (R), Paper 1 Higher, Q21 (5 marks): Here is a triangle XYZ. X Diagram NOT accurately drawn 60° 5 cm y cm Y x cm Z The perimeter of the triangle is k cm. Given that x = y − 1 find the value of k. S
January 2019 (R), Paper 2 Foundation, Q22 (4 marks): The diagram shows a trapezium. 37 cm Diagram NOT accurately drawn 125° 15 cm y cm Work out the value of y. Give your answer correct to 1 decimal place. y =
January 2019 (R), Paper 2 Higher, Q7 (4 marks): The diagram shows a trapezium. 37 cm Diagram NOT accurately drawn 125° 15 cm y cm Work out the value of y. Give your answer correct to 1 decimal place. y =
January 2019 (R), Paper 2 Higher, Q19 (5 marks): ABCD is a quadrilateral. A Diagram NOT 97° 9.3 cm accurately drawn D 58° B 47° 11.2 cm C Find the area of quadrilateral ABCD. Give your answer correct to 3 sign
January 2019, Paper 1 Foundation, Q19 (5 marks): A Diagram NOT B accurately drawn 20° 12.6 cm C 19.3 cm D ABC is a straight line. Work out the length of AC. Give your answer correct to 1 decimal place. cm
January 2019, Paper 1 Higher, Q8 (4 marks): The diagram shows an isosceles triangle. Diagram NOT accurately drawn x cm x cm 5 cm The area of the triangle is 12 cm2 Work out the perimeter of the triangle.
January 2019, Paper 1 Higher, Q10 (5 marks): Here is triangle ABD. B Diagram NOT accurately drawn 8 cm C 20° D A 13 cm The point C lies on BD. AD = 13 cm BC = 8 cm angle ADB = 90° angle CAD = 20° Calculate
January 2019, Paper 1 Higher, Q17 (5 marks): Here is triangle ABC. C 5.3 cm Diagram NOT B accurately drawn 110° 4.1 cm x° A Calculate the value of x. Give your answer correct to 3 significant figures.
January 2019, Paper 2 Higher, Q22 (6 marks): The diagram shows a cone. V Diagram NOT accurately drawn A B AB is a diameter of the cone. V is the vertex of the cone. Given that the area of the base of the c

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