2009 F4 Mid Firstterm Test
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CHIRADZULU SECONDARY SCHOOL 2009 FORM 4 MID-FIRST-TERM TEST
MATHEMATICS (50 marks) Subject Number: M131 Time Allowed: 1 hr 30 mins 7:00-8:30 pm
Friday, 27 February
Instructions 1. This paper contains 3 pages. Please check. 2. Answer all the six questions.
1.
a.
Simplify , 1 1 ÷ 2 x + x x + 2x + 1
(4 marks)
2
b.
Without using our-figure tables or calculator, evaluate tan 2 60° + tan 2 45°
2.
a.
Simplify
(3marks)
4 without using a calculator or four-figure tables 18 + 2 (3marks) 1
b.
2 Make L the subject of the formula S = 3d ( L − d ) 8
(4 marks)
3
4
a.
Solve the equation a 2 + 3a − 2 = 0 by completing the square
b.
The ratio of the area of two circles is 4 : 9 . (i) Find the ratio of their radii. (ii) If the smaller circle has a radius of 12cm, find the radius of the larger one. (3 marks)
a.
If log10 2 = 0.431 and log10 3 = 0.683 , without using a calculator or four-figure tables evaluate log10 5 (4marks)
b.
Figure 1 shows a circle PQRS with centre O. QP is produced to X. If angle XPS = 77° and angle PSO = 68°,
(5 marks)
X P
77°
Q 68° O
S
R
Figure 1 Find angle PQO. 5
a.
(4 marks)
Find the equation of the line passing through (-2,3) and parallel to 6 x + 2 y − 5 = 0
b.
(4 marks)
2 A function f (x) is given by f ( x ) = ax + bx − 3 where a and b are constant.
2
Given that f (1) = 4 and f (2) = 15 , calculate the values of a and b. (7marks)
3
6
a.
Figure 2, ABC is a circle, centre O. The tangents at A and B meet at T. If angle ATB = 62°,
B
C O 62°
T
A
Figure 2 Calculate angle ACB. b.
(4 marks)
In the TNM football Super League, a win earns a team 3 points, a draw 1 point and a loss 0 points. The results for ESCOM United after playing 20 games are 11 wins, 5 draws and 4 losses, while results for Silver Strikers after playing the same number of games are 7 wins, 9 draws and 4 losses. (i) (ii)
Present this information in two matrices of the orders 3 × 1 and 2×3. Use matrix multiplication to find the number of points each team scored after playing 20 games. (5 marks)
END OF QUESTION PAPER
4
MATHEMATICS (50 marks) Subject Number: M131 Time Allowed: 1 hr 30 mins 7:00-8:30 pm
Friday, 27 February
Instructions 1. This paper contains 3 pages. Please check. 2. Answer all the six questions.
1.
a.
Simplify , 1 1 ÷ 2 x + x x + 2x + 1
(4 marks)
2
b.
Without using our-figure tables or calculator, evaluate tan 2 60° + tan 2 45°
2.
a.
Simplify
(3marks)
4 without using a calculator or four-figure tables 18 + 2 (3marks) 1
b.
2 Make L the subject of the formula S = 3d ( L − d ) 8
(4 marks)
3
4
a.
Solve the equation a 2 + 3a − 2 = 0 by completing the square
b.
The ratio of the area of two circles is 4 : 9 . (i) Find the ratio of their radii. (ii) If the smaller circle has a radius of 12cm, find the radius of the larger one. (3 marks)
a.
If log10 2 = 0.431 and log10 3 = 0.683 , without using a calculator or four-figure tables evaluate log10 5 (4marks)
b.
Figure 1 shows a circle PQRS with centre O. QP is produced to X. If angle XPS = 77° and angle PSO = 68°,
(5 marks)
X P
77°
Q 68° O
S
R
Figure 1 Find angle PQO. 5
a.
(4 marks)
Find the equation of the line passing through (-2,3) and parallel to 6 x + 2 y − 5 = 0
b.
(4 marks)
2 A function f (x) is given by f ( x ) = ax + bx − 3 where a and b are constant.
2
Given that f (1) = 4 and f (2) = 15 , calculate the values of a and b. (7marks)
3
6
a.
Figure 2, ABC is a circle, centre O. The tangents at A and B meet at T. If angle ATB = 62°,
B
C O 62°
T
A
Figure 2 Calculate angle ACB. b.
(4 marks)
In the TNM football Super League, a win earns a team 3 points, a draw 1 point and a loss 0 points. The results for ESCOM United after playing 20 games are 11 wins, 5 draws and 4 losses, while results for Silver Strikers after playing the same number of games are 7 wins, 9 draws and 4 losses. (i) (ii)
Present this information in two matrices of the orders 3 × 1 and 2×3. Use matrix multiplication to find the number of points each team scored after playing 20 games. (5 marks)
END OF QUESTION PAPER
4
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