Trigonometric functions — Paper 2 · IGCSE Mathematics (9-1) 0980

2 Use your calculator to work out 1 - sin 33° . … [1]

1 marks

Mark scheme: 2 0.839 or 0.8386 to 0.8387 1

This question in 0980/22 May/June 2019

13 11 cm NOT TO 39° SCALE 13 cm Calculate the area of the triangle. … cm2 [2]

2 marks

Mark scheme: 13 45[.0] or 44.99 to 45.00 2 1 M1 for × 13 × 11 × sin 39 oe 2

This question in 0980/21 Oct/Nov 2019

23 Find all the solutions of 4 sinx = 3 for 0° G x G 360 ° . … [2]

2 marks

Mark scheme: 23 48.6 or 48.59… 2 B1 for each and If 0 scored SC1 for two answers with a sum of 180° 131.4 or 131.4…

This question in 0980/22 May/June 2021

18 B NOT TO 800 m SCALE 30° A C 2300 m The diagram shows some land in the shape of a triangle ABC. Houses are built on this land. Each house requires 400 m 2 of land. Find the greatest number of houses that can be built on this land. … [3]

3 marks

Mark scheme: 18 1150 3  1  M2 for  × 800 × 2300 × sin30  ÷ 400 oe  2  1 or M1 for × 800 × 2300 × sin30 oe 2

This question in 0980/21 Oct/Nov 2021

20 Solve 3 ( 2 + cosx) = 5 for 0° G x G 360° . … [3]

3 marks

Mark scheme: 20 109.4 to 109.5 3 B2 for one correct angle and 250.5 to 250.6 5 or M1 for cos x = − 2 or better 3 If 0 scored SC1 for two angles that sum to 360

This question in 0980/21 Oct/Nov 2021

17 (a) Sketch the graph of y = sin x for 0° G x G 360° . y 1 O x 360 – 1 [2] (b) Solve the equation 3 sinx + 1 = 0 for 0° G x G 360° . x = … or x = … [3]

5 marks

Mark scheme: 17(a) 2 Correct sketch to go through B1 for correct sine curve shape through the origin (0, 0), (180, 0) and (360, 0) 17(b) 199.5 or 199.47… 3 B2 for one correct and 340.5 or 340.52 to 340.53… 1 or M1 for sin x =  oe 3 If 0 scored SC1 for two reflex angles with sum of 540 or two non-reflex angles with sum of 180

This question in 0980/22 May/June 2022

22 y 1 0 x 360° – 1 (a) On the diagram, sketch the graph of y = cos x for 0° G x G 360° . [2] 1 (b) Solve the equation cosx =- for 0° G x G 360° . 2 x = … or x = … [2]

4 marks

Mark scheme: 22(a) Correct sketch 2 To go through (0, 1) and close to (360, 1) and reasonably close to (180, –1) 1111 B1 for correct cosine curve shape through 0.50.50.50.5 (0, 1) 0000 0000 50505050 100100100100 150150150150 200200200200 250250250250 300300300300 350350350350 -0.5-0.5-0.5-0.5 -1-1-1-1 Correct sketch to go through (0, 1), (360, 1) and (180, –1) 22(b) 120, 240 2 B1 for each or for two values with sum of 360

This question in 0980/21 Oct/Nov 2022

21 Solve the equation 5 sinx = - 3 for 0° G x G 360° . … [3] Questions 22 and 23 are printed on the next page.

3 marks

Mark scheme: 21 216.9 or 216.86 to 216.87 3 323.1 or 323.13… B2 for one correct angle 3 or M1 for sinx =  or better 5 If M1 or 0 scored SC1 for two reflex angles with a sum of 540 or two non-reflex angles with a sum of 180

This question in 0980/22 May/June 2023

19 (a) y 1 x 0 360° – 1 Sketch the graph of y = cos x for 0° G x G 360 ° . [2] (b) When cosx = 0 .21 , find the reflex angle x. … [2]

4 marks

Mark scheme: 19(a) 2 B1 for correct cosine curve shape through (0,1) Correct sketch to go through (0, 1), close to (360, 1) and reasonably close to (180, –1) 19(b) 282.1 or 282.12… 2 B1 implied by 77.9 or 77.87 to 77.88 or 282.13 or M1 for 360 – their acute angle

This question in 0980/21 Oct/Nov 2023

22 (a) For each sketch, put a ring around the correct type of function shown. (i) y x O linear cubic quadratic reciprocal exponential [1] (ii) y O x linear cubic quadratic reciprocal exponential [1] (b) (i) On the grid, sketch the curve y = sin x for 0° G x G 360 ° . y 1 0 x 180° 360° – 1 [2] (ii) Solve the equation sinx + 0.4 = 0 for 0° G x G 360° . x = … or x = … [3]

7 marks

Mark scheme: 22(a)(i) cubic 1 22(a)(ii) reciprocal 1 22(b)(i) correct sine curve sketch through 2 (0, 0), (180, 0) and (360, 0) M1 for correct sine curve shape through the origin 22(b)(ii) 203.6 and 336.4 3 B2 for one correct or M1 for sin x = −0.4 oe If 0 or M1 scored, SC1 for two reflex angles with a sum of 540 or two non-reflex angles with a sum of 180

This question in 0980/22 May/June 2024

21 Solve the equation 3 tanx + 5 = 1 for 0° G x G 360° . x = … or x = … [3]

3 marks

Mark scheme: 21 126.9 and 306.9 3 B2 for one correct answer 4 or M1 for tan x = – oe 3 If M1 or 0 scored, SC1 for two angles with a difference of 180

This question in 0980/21 Oct/Nov 2024

26 Solve tanx =- for 0° G x G 360° . 3 x = … , x = … [3]

3 marks

Mark scheme: 26 150 and 330 3 B2 for one correct answer or B1 for [tan–1…] = 30 or –30 If 0 scored, SC1 for two answers in range with a difference of 180

This question in 0980/21 Oct/Nov 2025