Second Term Examination
Class : SSS One
Subject : Mathematics
Duration :
Name : __________________________________
Section A : Objective Questions
Instruction : Read the question carefully and pick from the options lettered a – d.
Solve the following equations. Check the results by substitution.
1. (4b – 12)(b – 5) = 0 A. ½, 4 B. 3, 5 C. 4, 6 D. 5, 3
2. (11 – 4x)² = 0. A. 11/3, 3 B. 2 3/4, 3 C. 2 3/4 twice D. 2 4/3 twice
3. (d – 5)(3d – 2) = 0 A. 5, 5 B. 4, 5 C. 5, 9 D. 2/3, 5
Solve the following quadratic equations
4. u2 – 8u – 9 = 0A. – 9, 1 B. -1, 9 C. 1, 8 D. 9 , -1
5. C² = 25 , Find the value of C. A. 5 B. -5 C. +5 D. ± 5
Use the information below to answer question 6 – 8 :
If α and β are the roots of the given equation, 2x² – 7x – 3 = 0. Find the value of:
6. α + β = _______. (a) 2/3 (b) 7/2 (c) 2/5 (d) 5/3
7. α β = _______. (a) -3/2 (b) 2/3 (c) 3/2 (d) – 2/3
8. αβ² + α²β = _______ (a) 21/4 (b) 4/21 (c) – 4/21 (d) -21/4
9. If A={a, b, c} B={a, b, c, e} and C={a, b, c, d, e, f} find A∩B(AƲC) A.{a,b,c,d} B. {a,b,c,d,e} C.{a,b,c,d,e, f} D.{a,b,c}
10. If Q={0<x<30,x is a perfect square}, P={x÷1≤x≤10,x is an odd number} find Q∩P A.{1,3,9} B.{1,9,4} C.{1,9} D.{19,16,25}
Use the following information to answer questions 11 – 13.
Given that set A, B and C are subsets of universal set U such that U={0,1,2,3……..11,12}, A={x:0<x<7}, B={4,6,8,10}, C={1<x<8}
11. Find (A ∪ C)’ A{0,1,9} B.{2,3,4,5} C.{2,3,5,7} D.{0,1,2,9}
12. Find A’ ∩ B ∩C A. { } B. { } C { } D.
13. Find A ∪ B’ ∩ C A.{1,2,3,4,5,6,7} B.{2,3,5,7} C.{6,8,10,12} D.{4,5,7,9,11}
14. If Sin A = 4/5, what is tan A? A 2/5 B. 3/5 C. ¾ D. 1 E. 4/3
15. Use tables to find the value of Cos 77. A. 5.44 B. 6.48 C. 9.12 D 7.57 E. 1.80
16. If cos θ = sin 33°, find tan θ. A. 1.540 B. 2.64 C.0.64 D. 1.16 E. 1.32
17. If the diagonal of a square is 8cm, what is the area of the square? A 16cm² B. 2cm² C. 4cm² D. 20cm² E. 10cm²
18. Calculate the angle which the diagonal in question 17 makes with any of the side of the square. A. 65° B. 45°C. 35° D. 25° E. 75°
19. A town Y is 200 Km from town X in a direction 040°. How far is Y east of X?
a) 125.8km b) 128.6km c) 127km d) 126.8km
20. A boy walks 1260m on a bearing of 120°. How far South is he from his starting point?
a) 630m b) 530m c) 730m d) 630km
21. Calculate the area of a sector of a circle of radius 6cm which subtends an angle of 70o at the centre (π = 22/7) A. 44cm2 B. 22cm2 C. 66cm2 D. 11cm2 E. 16.5cm2
22. What is the angle subtended at the centre of a sector of a circle of radius 2cm if the area of the sector is 2.2cm2? (π = 22/7)A. 120o B. 31 ½o C. 43o D. 58o E. 63o
23. What is the radius of a sector of a circle which subtends 140o at its centre and has an area of 99m2? A. 18m 27m C 9m E. 30m E. 24m
24. A sector of 80o is removed from a circle of radius 12cm What area of the circle is left? A. 253cm2 B. 704cm2C 176cm2D. 125cm2 E. 352cm2π
25. Calculate the area of the shaded segment of the circle shown in the figure below:
( π = 22/7 )
A. 10.45cm2 B. 20.90cm2. C. 5.25cm2 D. 19.0cm2. E. 17.45cm2
THEORY
1. Solve the following equation using the formula method.
a. 6p² – 2p – 7 = 0
b. 3 = 8q – 2q².
2. Prepare a table of values for the graph of y = x² + 3x – 4 for values of x from – 6 to + 3
Use a scale of 1cm to 1 unit on both axes and draw the graph.
Find the least value of y
What are the roots of the equation x2 + 3x – 4 = 0?
Find the values of x when y
3. The universal set U is the set of integers: A,B and C are subsets of U defined as follows
A= {….., -6,-4,-2,0,2,4,6…….}
B= {X: 0 <x < 9}
C= {X: -4 < x < 0}
Write down the set A’, where A’ is the complement of A with respect to U
Find B∩C
Find the members of set :
i. B∪C, ii. A∩B, and
iii. hence show that A∩(B∪C) = (A∩B) ∪(A∩C)
4. The universal set U is the set of all integers and the subsets P,Q,R of U are given by
P={X: X<0}, Q = {……,-5-,3,-1,1,3,5…….}, R= {X: -2<X<7}
Find Q∩ R
Find R’ where R’ is the complement of R with respect to U
Find P’ ∩ R’
List the members of (P∩Q)
5. A chord 30cm long is 20cm from the centre of a circle . Calculate the length of the chord which is 24cm from the centre .
6. Q is 1.4km from P on a bearing 023°. R is 4.4 Km from P on a bearing 113°. Make a sketch of the positions of P, Q and R and hence, calculate QR correct to 2 s.f.
7. The figure below shows the cross section of a tunnel. It is in the shape of a major segment of a circle of radius 1m on a chord of length 1.6m.
Calculate:
i. the angle subtended at the centre of the circle by the major arc correct to the nearest 0.10
ii. the area of the cross section of the tunnel correct to 2d.p.
8. Calculate: (i) the area of the shaded segments in the following diagrams.
(ii) The perimeter
(Take 3.14)
