Microsoft Word - Revision 2
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MATHEMATICS FORM 5 – REVISION 2
Answer all the questions. 1.
In the diagram, PQ and RS are two vertical poles on the horizontal ground. The angle of elevation of S from P and Q are 30°58' and 21°48'. The height of RS = 12 m. Find (a) the distance of PR, (b) the height of PQ. [6 marks] 2.
In the diagram, ABC and CD are two tangents to the circle with centre O. Find (a) ∠OBA, (b) ∠CDO.
[4 marks]
DES : CHAPTER 8 ,9, 10 FORM 4
MATHEMATICS FORM 5 – REVISION 2
3.
The above diagram shows two circles touching each other externally at U. PUV and WUR are straight lines and XUT is a common tangent to the circles. Given that ∠PQR = 135° and ∠PSU = 37°, find (a) ∠PUR, (b) ∠UWV, [6 marks] (c) ∠WUT. 4.
The diagram above shows two circles with the centres at point Q and point T respectively. Given that PQ = 6 cm and UT = 4 cm. (a) State the total number of common tangents for the two circles. (b) Find the length of PU and RS. (c) Find the value of (i) x, (ii) y. [12 marks]
DES : CHAPTER 8 ,9, 10 FORM 4
MATHEMATICS FORM 5 – REVISION 2
5.
In the diagram shown, CB and CD are two tangents to the circle with centre O. [3 marks] Given that ∠BAO = 38° and ∠AOD = 112°, find ∠CDB. 6.
K and M are two points on horizontal ground and the distance between K and M is 36 m. KL and MN are two vertical poles, where the height of KL is 63 m. If the angle of [4 marks] depression of N from L is 17°, find the height of MN.
7.
The diagram shows a slope. Find the angle at which the slope is inclined to the horizontal.
[3 marks]
DES : CHAPTER 8 ,9, 10 FORM 4
MATHEMATICS FORM 5 – REVISION 2
8.
In the diagram above, ABC is a straight line. Calculate the (a) length of AD, (b) value of cos y. 9.
Given that θ is an angle in quadrant IV and tan θ = − (a) sin θ, (b) cos θ.
[5 marks]
13 , find the value of 84 [4 marks]
10.
In the diagram above, trapezium PQRS is the cross-section of a swimming pool. Find the angle of depression of R from P. [2 marks]
DES : CHAPTER 8 ,9, 10 FORM 4
MATHEMATICS FORM 5 – REVISION 2
11.
In the diagram above, ABC is a straight line. Given that sin x = cos y.
4 , find the value of 5 [3 marks]
12. Two vertical towers, AB and CD, are on the horizontal ground. The horizontal distance between the base of towers A and C is 51 m. The angle of elevation of point D from point B is 48°. If the height of tower AB is 104 m, find the height of tower CD. [4 marks] 13.
In the diagram above, O is the centre of the circle UWV. TU and TV are two tangents to the circle at point U and point V respectively. Given that OU = 9 cm and TV = 19 cm, find (a) the value of y, (b) the area of the shaded region. [6 marks] (Use π = 3.142)
DES : CHAPTER 8 ,9, 10 FORM 4
MATHEMATICS FORM 5 – REVISION 2
14.
The diagram above shows a vertical post MN of height 3 m. Given that the post casts a shadow of 4 m on horizontal ground at a certain time of the day, find the value of θ. [3 marks] 15.
The diagram above shows a boy whose eyes are 0.6 m above the horizontal ground and is 25 m away from a vertical flagpole. The angle of elevation of the top of the flagpole is 29° from the boy's eyes. Find the height of the flagpole. [3 marks]
DES : CHAPTER 8 ,9, 10 FORM 4
MATHEMATICS FORM 5 – REVISION 2
16.
In the diagram, PQ and RQ are two tangents to a circle with centre O, given that ∠PQR = 44°, find the values of (a) ∠QPR, (b) ∠PRO. .
[4 marks]
DES : CHAPTER 8 ,9, 10 FORM 4
MATHEMATICS FORM 5 – REVISION 2
Answers: 1. (a) 20 m (b) 4 m 2. (a) 90° (b) 90° 3. (a) 45° (b) 37° (c) 82° 4. (a) 3 (b) 9.798 cm (c) (i) 78.46° (ii) 101.54° 5. 72° 6. 51.99 m 7. 54.9° 8. (a) 10.89 cm (b) -0.8387 9. 13 (a) − 85 84 85 10. 16.86° or 16°52' 11. 4 − 5 12. 160.64 m 13. (a) 64.65° (b) 79.591 cm2 14. 37.97° 15. 14.46 m 16. (a) 68° (b) 22° (b)
DES : CHAPTER 8 ,9, 10 FORM 4
Answer all the questions. 1.
In the diagram, PQ and RS are two vertical poles on the horizontal ground. The angle of elevation of S from P and Q are 30°58' and 21°48'. The height of RS = 12 m. Find (a) the distance of PR, (b) the height of PQ. [6 marks] 2.
In the diagram, ABC and CD are two tangents to the circle with centre O. Find (a) ∠OBA, (b) ∠CDO.
[4 marks]
DES : CHAPTER 8 ,9, 10 FORM 4
MATHEMATICS FORM 5 – REVISION 2
3.
The above diagram shows two circles touching each other externally at U. PUV and WUR are straight lines and XUT is a common tangent to the circles. Given that ∠PQR = 135° and ∠PSU = 37°, find (a) ∠PUR, (b) ∠UWV, [6 marks] (c) ∠WUT. 4.
The diagram above shows two circles with the centres at point Q and point T respectively. Given that PQ = 6 cm and UT = 4 cm. (a) State the total number of common tangents for the two circles. (b) Find the length of PU and RS. (c) Find the value of (i) x, (ii) y. [12 marks]
DES : CHAPTER 8 ,9, 10 FORM 4
MATHEMATICS FORM 5 – REVISION 2
5.
In the diagram shown, CB and CD are two tangents to the circle with centre O. [3 marks] Given that ∠BAO = 38° and ∠AOD = 112°, find ∠CDB. 6.
K and M are two points on horizontal ground and the distance between K and M is 36 m. KL and MN are two vertical poles, where the height of KL is 63 m. If the angle of [4 marks] depression of N from L is 17°, find the height of MN.
7.
The diagram shows a slope. Find the angle at which the slope is inclined to the horizontal.
[3 marks]
DES : CHAPTER 8 ,9, 10 FORM 4
MATHEMATICS FORM 5 – REVISION 2
8.
In the diagram above, ABC is a straight line. Calculate the (a) length of AD, (b) value of cos y. 9.
Given that θ is an angle in quadrant IV and tan θ = − (a) sin θ, (b) cos θ.
[5 marks]
13 , find the value of 84 [4 marks]
10.
In the diagram above, trapezium PQRS is the cross-section of a swimming pool. Find the angle of depression of R from P. [2 marks]
DES : CHAPTER 8 ,9, 10 FORM 4
MATHEMATICS FORM 5 – REVISION 2
11.
In the diagram above, ABC is a straight line. Given that sin x = cos y.
4 , find the value of 5 [3 marks]
12. Two vertical towers, AB and CD, are on the horizontal ground. The horizontal distance between the base of towers A and C is 51 m. The angle of elevation of point D from point B is 48°. If the height of tower AB is 104 m, find the height of tower CD. [4 marks] 13.
In the diagram above, O is the centre of the circle UWV. TU and TV are two tangents to the circle at point U and point V respectively. Given that OU = 9 cm and TV = 19 cm, find (a) the value of y, (b) the area of the shaded region. [6 marks] (Use π = 3.142)
DES : CHAPTER 8 ,9, 10 FORM 4
MATHEMATICS FORM 5 – REVISION 2
14.
The diagram above shows a vertical post MN of height 3 m. Given that the post casts a shadow of 4 m on horizontal ground at a certain time of the day, find the value of θ. [3 marks] 15.
The diagram above shows a boy whose eyes are 0.6 m above the horizontal ground and is 25 m away from a vertical flagpole. The angle of elevation of the top of the flagpole is 29° from the boy's eyes. Find the height of the flagpole. [3 marks]
DES : CHAPTER 8 ,9, 10 FORM 4
MATHEMATICS FORM 5 – REVISION 2
16.
In the diagram, PQ and RQ are two tangents to a circle with centre O, given that ∠PQR = 44°, find the values of (a) ∠QPR, (b) ∠PRO. .
[4 marks]
DES : CHAPTER 8 ,9, 10 FORM 4
MATHEMATICS FORM 5 – REVISION 2
Answers: 1. (a) 20 m (b) 4 m 2. (a) 90° (b) 90° 3. (a) 45° (b) 37° (c) 82° 4. (a) 3 (b) 9.798 cm (c) (i) 78.46° (ii) 101.54° 5. 72° 6. 51.99 m 7. 54.9° 8. (a) 10.89 cm (b) -0.8387 9. 13 (a) − 85 84 85 10. 16.86° or 16°52' 11. 4 − 5 12. 160.64 m 13. (a) 64.65° (b) 79.591 cm2 14. 37.97° 15. 14.46 m 16. (a) 68° (b) 22° (b)
DES : CHAPTER 8 ,9, 10 FORM 4
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