XYZ SECONDARY SCHOOL

Name: _________________ ( ) Date: ____________

Time allowed: min
Class: _______ Marks:
5

Secondary 2 Multiple-Choice Questions

Chapter 6 Phythagoras’ Theorem

1. The lengths of the sides of a right–angled triangle are ( 14 – x ) cm, ( 13 – x )

cm and ( 6 – x ) cm. Calculate the value of x.
(A) 1 (B) 3 (C) 5 (D) 6 (E) 7
( )

2. The lengths of the sides of a right–angled triangle are ( x – 1) cm, x cm and

( x + 1 ) cm. Find the perimeter of the triangle.
(A) 4 cm (B) 3 2 cm (C) 5 cm (D) 12 cm
(E) None of the above ( )

3. The two rectangles PQRS and OLMN overlap as shown . If the area of PQRS is 30
cm², calculate the perimeter of the shaded region in cm.
(A) 22 - 29 (B) 33 - 29
(C) 33 (D) 33 - 21
(E) None of the above ( )

4. A square of sides x cm each is inscribed in a circle of radius 2 cm. Find x.

(A) 2 (B) 2 (C) 2 2 (D) 4
(E) None of the above ( )

Teachers’ Resource NSM 2 © Oxford University Press

5. In the figure ∠ PQR = ∠ HKR = 90°, HR = 8
cm, QH = 4 cm and KR = 6 cm.
Calculate the length of PR in cm.
(A) 16 (B) 12 (C) 18 (D) 34
(E) None of the above
( )

Teachers’ Resource NSM 2 © Oxford University Press

Answers

1. A 2. D 3. B 4. C 5. A

Teachers’ Resource NSM 2 © Oxford University Press

 XYZ SECONDARY SCHOOL
Name: _________________ ( ) Date: ____________
Time allowed: min
Class: _______ Marks:

Secondary 2 Mathematics Test

Chapter 6 Phythagoras’ Theorem

1. A B C D is a square of side 15cm, find the length of the diagonal A C. [2]

2. P Q R S is a rectangle in which PQ = 24cm and QR = 15cm, find the length of the diagonal QS.[2]

3. A B C D is a square in which BD = 16cm, calculate the area of the square ABCD. [2]

4. PQR is a equilateral triangle of side 14cm. Calculate the altitude of the triangle and find its
area. [4]

5. A 5.4m long ladder leans against a vertical wall with its top at a height of 4.2m above the ground.
Find the distance of the base of the ladder from the wall. [2]

6. The length of s triangle ABC are AB = 5cm, BC = 4.8cm and AC = 1.4cm. State with reasons
whether △ ABC is a right-angled triangle. [3]

7. In the right –angled triangle ABC, ∠ABC = 90º, AB = 8cm and AC = 14cm, calculate the
perimeter and area of △ ABC. [4]

8. In the diagram, ∠CKB = 90º, KB = 6cm AC = 18cm and AK = CK = x cm. Calculate

(a) the volume of x and y.
(b) the area of △ CKB. [4]

Teachers’ Resource NSM 2 © Oxford University Press

9. In the figure BD is a perpendicular AC, AB = 14.5cm, BD = 7.8cm, and BC = 10.5cm, calculate
the area of △ ABC. [3]

10. ABCD is a trapezium, calculate the value of x and the area of the trapezium. [4]

11. Calculate the values of x and y in the given diagram. [4]

Teachers’ Resource NSM 2 © Oxford University Press

12. Find the value of the x giving your answers correct to 2 decimal places. [3]

13. Find the values of x and y in the given diagram. [4]

14. Find your values of the x in the given diagram. [3]

Teachers’ Resource NSM 2 © Oxford University Press

15. ABCD is a rectangle of length 15cm and width 9cm. Given that ∠BQR = ∠DPC = 90, calculate
(a) AC
(b) BQ
(c) PQ [6]

16. ABCDEF is a rectangular hexagon of side of side 12 cm. O is the centre of the hexagon and M is
the mid-point of BC. Calculate
(a) ∠BAF,
(b) the length of O M. [4]

17. In the right angle-triangle ABC, AB (x + 3) cm, AC = (y + 7) cm and BC = (x + y) cm. Express x

in terms of y. [3]

18. The width of a rectangle is 21cm. Shorter than its length and its diagonal is 24cm longer than is
24cm longer than its width, find the perimeter and area of the rectangle. [4]

19. ABCD is a rectangle in which AB =3x cm, BC = (x-1)cm and AC = (3x +1)cm. Calculate
(a) the value of x,
(b) the area and perimeter of ABCD. [6]

Teachers’ Resource NSM 2 © Oxford University Press

20. In the diagram, A^PB, = A^QP = 90º, AB= 14cm, AP = 19cm, BP=2x cm and CP = 3xcm.
Calculate (a) the value of x (b) PQ (c) AQ [6]

21. The length of the right-angled triangle ABC where ∠ABC = 90º, AB = (3x +1) cm, 13 C = (x – 4)
and AC = (3x +2)cm. Calculate the value of x and find the area and find the area and perimeter of
△ ABC. [4]

22. In the diagram, ∠ABC = ∠AQP = 90º, AP = 17cm, PC = 14cm, CQ = 10cm and BC = 15cm,
calculate (a) PQ, (b) AC, (c) the area of △ ABC . [6]

23. The side of a right-angled triangle ABC are AB = (x + 3)cm BC = (4x – 1)cm and
AC = (4x +1)cm. Calculate (a) the volume of x, (b) the area of △ ABC, (c) the length of
the perpendicular from B to AC. [6]

24. Which of the following triangles with sides as given below is a right-angled triangle?
(a) 48cm, 50cm, 14cm
(b) 34cm, 30cm, 16cm
(c) 81cm, 75cm, 30cm
(d) 66cm, 23cm, 70cm
(e) 53cm, 45cm, 28cm [5]

25. A rope is tied from the top of a vertical pole to a point 3.2 m from the foot of the pole.
If the pole is 8.2 m high, how long is the rope? [3]

26. In figure, ∠ABC =∠ACD = 90°,

AB = 12 cm, BC = 5 cm and
AD = 24 cm. Calculate the length
of CD. [3]

Teachers’ Resource NSM 2 © Oxford University Press

27. Find the perimeter and area of each of the following figures: [4]

28. The lengths of the sides of a right–angled triangle are (3x – 2) cm, (4x + 5) cm and
(6x – 7) cm. Form an equation in x and solve it. With this value of x, find the perimeter
of the triangle. [4]

29. PQRS is a rectangle in which PQ=6.4 cm, PS=4.8 cm and T is a point on SR

produced such that the area of triangle PST is equal to the area of PQRS. Calculate
the length of ST and PT giving your answer correct to 2 decimal places. [4]

30. PQR is an isosceles triangle in which PQ=PR, PA is perpendicular to QR and QB

is perpendicular to PR. Given that QR=10 cm and PA=14 cm, calculate the length
of PQ and QB giving your answer correct to 2 decimal places. [4]

31. ABCD is a rectangle in which AC meets BD at Q and triangle ADQ is equilateral. P is

a point on AD such that PA=2PD. If BC=12 cm, calculate the length of PC and PQ,
giving your answer correct to 2 decimal places. [4]

Teachers’ Resource NSM 2 © Oxford University Press

Answers

1.Ans: 21.21cm
2.Ans: 28.30cm
3.Ans: 128 cm2
4.Ans: 12.12cm, 84.87cm2
5.Ans: 3.394m
6.Ans: yes, 5 (2) = 4.8 (2) + 1.4 (2)
7.Ans: 33.49cm, 45.96cm2
8.Ans: (a) x = 12.73cm, y = 14.07cm (b) 38.18cm2
2
9.Ans: 75.08cm
10.Ans: 10.95cm, 169.8cm2
11.Ans: x = 30, y = 24
12.Ans: 17.97cm
13.Ans: x = 18.33, y = 16.94
14.Ans: 9.434
15.Ans: (a) 17.49cm (b) 7.72cm (c) 8.23cm
16.Ans: (a) 120° (b) 10.39cm
17.Ans: x = 7y + 29
y - 3
18.Ans: 102cm, 540cm2
19.Ans: (a) x = 8 (b) 168cm2, 62cm
20.Ans: (a) 6.423 (b) 13.53 (c) 13.34
2
21.Ans: x = 13, 180cm , 90cm
22.Ans: (a) 9.798cm, (b) 23.89cm, (c) 139.5cm2
2
23.Ans: (a) x = 9 (b) 210cm (c) 11 13/37cm
24.Ans: (a) Yes (b) Yes (c) No (d) No (e) Yes
25.Ans: 8.80 m
26.Ans: 20.2 cm
27.Ans: (a) 63.1 cm, 180.7 cm² (b) 64.15 cm, 1809 cm²
28.Ans: x = 10; 126 cm
29.Ans: ST=12.8 cm, PT=13.67 cm
30.Ans: PQ=14.87 cm, QB=9.42 cm
31.Ans: PC=21.17 cm, PQ=10.58 cm

Teachers’ Resource NSM 2 © Oxford University Press