Pythagoras & TrigonometryCambridge IGCSE Maths: Topic test

20 questions, 52 marks

Cambridge IGCSE Maths

Pythagoras & Trigonometry topic test

Total 52 marks

Name

Class

Date

1
A right-angled triangle has legs 9 cm and 12 cm. A separate triangle DEF has DE = 7 cm, EF = 10 cm and angle DEF = 50 degrees.
(a)
What is the length of the hypotenuse of the right-angled triangle?
[1 mark]
A15 cm
B21 cm
C3 cm
D225 cm
(b)
What is the area of triangle DEF, to 1 decimal place?
[1 mark]
A35.0 cm^2
B22.5 cm^2
C26.8 cm^2
D53.6 cm^2
(c)
What is the exact value of sin 30 degrees?
[1 mark]
Asqrt(2)/2
B1/2
Csqrt(3)/2
D1
Total for question 1: 3 marks
2
A shipping container has internal dimensions 5 m long, 2 m wide and 2 m high.
(a)
Calculate the diagonal distance across the floor of the container, from one corner to the opposite corner, giving your answer to 1 decimal place.
[2 marks]
(b)
Hence calculate the length of the longest straight pole that could fit inside the container, giving your answer to 1 decimal place.
[2 marks]
Total for question 2: 4 marks
3
A triangular sail ABC has AB = 6 m, BC = 9 m and angle ABC = 70 degrees.
(a)
Calculate AC, using the cosine rule, giving your answer to 1 decimal place.
[3 marks]
(b)
Calculate the area of the sail, giving your answer to 1 decimal place.
[3 marks]
Total for question 3: 6 marks
4
A crane's jib is 18 m long and makes an angle of elevation of 35 degrees with the horizontal, lifting a load from ground level to a hook at height h above the point where the jib is anchored. The crane's control software also solves two calibration equations for the swing sensor: 4 sin x - 2 = 0 and tan x = -1, both for 0 degrees <= x <= 360 degrees. Give all answers correct to 1 decimal place where appropriate.
(a)
Calculate the height h, and state whether the hook clears a wall of height 11 m directly below its path.
[4 marks]
(b)
Solve 4 sin x - 2 = 0 for 0 degrees <= x <= 360 degrees, giving all solutions.
[4 marks]
(c)
Solve tan x = -1 for 0 degrees <= x <= 360 degrees, giving all solutions.
[5 marks]
Total for question 4: 13 marks
5
Triangle KLM has KL = 5 cm, LM = 12 cm and angle KLM = 90 degrees. A separate cuboid brick measures 4 cm by 3 cm by 12 cm. In triangle NOP, NO = 8 cm, OP = 10 cm and angle NOP = 60 degrees.
(a)
What is the length of KM?
[1 mark]
A7 cm
B17 cm
C169 cm
D13 cm
(b)
What is the length of the brick's space diagonal (corner to opposite corner)?
[1 mark]
A13 cm
B19 cm
C169 cm
D5 cm
(c)
What is the length of NP, using the cosine rule, to 1 decimal place?
[1 mark]
A15.6 cm
B6.4 cm
C9.2 cm
D84 cm
Total for question 5: 3 marks
6
A Ferris wheel's height above ground varies periodically. Engineers model one part of the cycle using y = cos x for 0 degrees <= x <= 360 degrees, where x is the angle turned by the wheel.
(a)
State the two values of x, with 0 degrees <= x <= 360 degrees, for which y = 0.
[2 marks]
(b)
State the value of x, other than x = 0 degrees, for which y = cos x reaches its maximum value in the range 0 degrees <= x <= 360 degrees.
[2 marks]
Total for question 6: 4 marks
7
A right pyramid has a rectangular base PQRS with PQ = 10 cm and QR = 6 cm, and apex T directly above the centre of the base at a perpendicular height of 9 cm.
(a)
Calculate the distance from the centre of the base to vertex P, giving your answer to 1 decimal place.
[3 marks]
(b)
Hence calculate the length TP, giving your answer to 1 decimal place.
[3 marks]
Total for question 7: 6 marks
8
In triangle XYZ, XY = 14 m, angle XYZ = 48 degrees and angle YXZ = 67 degrees. The perpendicular from Z to XY meets XY at the point W. Give all answers correct to 1 decimal place.
(a)
Calculate angle XZY, and hence use the sine rule to calculate the length XZ.
[4 marks]
(b)
Using the right-angled triangle XWZ and taking XZ = 11.5 m from part (a), calculate the length ZW.
[4 marks]
(c)
Calculate XW, and hence calculate WY (the remaining part of XY). Then calculate the area of triangle XYZ using base XY and height ZW.
[5 marks]
Total for question 8: 13 marks

End of questions