Sunday 30 December 2012
Thursday 27 December 2012
Wednesday 26 December 2012
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Tuesday 25 December 2012
senior cycle
SECTION A: OBJECTIVES
1.
Simplify 0.63954 ÷ 0.003 giving your
answer correct to two significant figure
[a]
201 [b] 213.18
[c] 213 [d]
21
2. If log 10a = 4 What is a?
[a] 0.4 [b]
10 000 [c] 400
[d] 21
3. If 3y = 243, find the value of y
[a] 2 [b]
3 [c] 5
[d] 7
4. Evaluate, using logarithm table, log (0.65)2
[a] 4.6258 [b]
0.6272 [c] 0.6258
[d] 1.6256
5. In the diagram, PR is a diameter of a circle
centre O. RS is a tangent at R and
QPR =
580. Find < QRS
[a] 1220 [b]
1120 [c] 1480 [d]
1160
6. Evaluate log10
- log10
+ log10
[a] 2 [b]
1/2
[c] 3 [d]
6
7. In the diagram below, O is the centre of the
circle. Calculate the length of
the
chord AB if IOAI = 5cm, IODI = 3cm and <AOD and <BOD
[a] 3cm [b] 5cm [c]
4cm [d] 15cm
8. Simplify 9-½ ÷ 27⅔
[a] 1 [b]
½ [c] 1/9 [d]
1/27
9. In the diagram above, O is the centre of the
circle, if <QRS = 620, find the
Value of
<SQR.
[a] 280 [b] = 140 [c] 310 [d]
900
10. If 5 times
a certain integer is subtracted from twice the square of the integer,
the result is 63. Find the integer.
[a]
21 [b] 7
[c] 4 [d]
3
11. If log ax
= p, express x in terms of a and P.
[a] x
= p [b] x = ap
[c] x = a+p
[d] x = ap
12 In the
diagram, O is the centre of the circle. If <POQ = 800 and <PRQ
=5x, find
the
value of x
.
[a] 160 [b]
320 [c] 200 [d]
80
13. Find the
quadratic whose roots are x = -2 or x = 7
[a] x2+2x-7 [b]
x2+5x-1 [c] x2+5x+1 [d]
x2-5x-14
14. In the
diagram, O is the centre of the circle. If <PAQ = 750, what is
the value of
<PBQ?
[a] 2100 [b]
750 [c] 1500 [d]
1050
15. A sales
girl gave a balance of N 1. 15 to
a customer instead of N 1.25.
Calculate
her percentage error.
[a] 8.7%
[b] 0.10% [c]
2.4% [d] 8.0%
16. If x2
-18x=0 What value of k makes the
given expression a perfect square?
[a] 81 [b]
4 [c] 8
[d] 2
17. If log10q
= 2.7078 what is Q?
[a] 510.2
[b] 849.2 [c]
84.99 [d] 51.02
18. In the diagram,
PQ is a diameter of the circle, centre O and RS meets PQ at S.
If <QPR =
640 and <RSQ = 360 , Calculate <PRS
[a] 100 [b]
180 [c] 220 [d]
160
19. for what value of y is the expression
[a] y = 5
[b] y = 0 [c]
y = 2 [d] y = 3
20. simplify ( 3/x
– 15/2y ) ÷ 6
[a] 2y – 5x/4 [b]
y – 5x/x2 y2 [c]
4/2y-5x
[d] 5x -2y/2
21.
simplify 1/1-x + 1/1+x
[a]
[b]
[c]
[d]
22. The lengths, in cm, of the sides of a right-angled
triangle are x, (x+2) and (x+1)
Where x >
0 find in cm, the length of its hypotenuse.
[a] 6 [b]
4 [c] 5
[6]
23. In the diagram, O is the centre of the circle.
Which of the following is / are not
true?
[a] a = b
[b] b + c = 180 [c]
a + b = c [d] b = 1800
24. Factorise m (2a-b) -2n (b-2a)
[a] (2a-b)(2n-m) [b]
(2a+b)(m-2n) [c] (2a-b)(m+2n) [d]
(2a-b)(m-2n)
25. Three men, Bayo, Ade and Ayo shared N500 in
the ratio 3:2:x respectively. If
Bayo’s
share is N150, find the value of x
[a] 1
[b] 4 [c] 5
[d] 6
26. In ∆
PQR. PQR = 84, QPR = 43 and IPQI = 5cm,
Find IQRI in cm, correct to 1
Decimal
place.
[a] 3.4
[b] 5.9 [c]
4.3 [d] 6.2
27. In the diagram PQS = 650. RPS = 400
and QSR = 200. Find PSQ.
[a] 600 [b] 850 [c]
550 [d] 450
28. Find the value of x which satisfies the equation
5(x-7) = 7-2x
[a] x=2
[b] x=4 [c]
x=6 [d]
x=14
29. The square
root of a number is 2k. What is half of the number.
[a]
[b]
[c]
[d]
[a] 1/3 [b]
-3/2
[c] -1 [d] -3
31. In the diagram, PQ and MN are straight
lines. Find the value of x
[a] 300 [b] 170 [c] 280 [d] 800
32. In the diagram PQRS, is a circle, IPTI = IQTI and
<QPT = 700. What is the size of
<PRS
[a] 1100 [b] 700 [c]
800 [d] 1400
33. Which of
the following is not a measure of centre of tendency?
[a] mean
[b] range [c]
median [d] mode
34. If P=1/2
and 1/p-1 = 2/p+x , find the value
of x.
[a] -21/2 [b]
-11/2
[c] 11/2 [d]
21/2
35. If 2n = 128, find the value of (2n-1)
(5n-2)
[a]
5(106) [b] 2(105) [c]
5(102) [d]
2(106)
36. If (2x+3)3 = 125, find the value
of x
[a] 7
[b] 1 [c]
4 [d] 3
37. In the diagram ISQI = 4cm, IPTI = 7cm, ITRI =
5cm and ST//QR. If ISPI = xcm, find the value of x
[a] 6.5
[b] 5.6 [c] 6.6 [d]
6.8
38. Which shaded region in the following diagrams represents (PUQ) n R?
[a]
[b]
[c] [d]
39. Given that
P = {x:1≤ x ≤ 6 } and Q = { x: 2 < x < 10 } where x is an integer. Find
n( P n Q )
[a]
6 [b] 4
[c] 8 [d] 10
40. Given that
T = { x: -2 < x ≤ 9 } where x is an integer. What is n(T) ?
[a] 10
[b] 11 [c] 9
[d] 12
41. In the diagram, PQ is the tangent to the
circle RST at T. ISTI = ISRI and < RTQ =
680
find <PTS.
[a]
680 [b] 620 [c]
610 [d] 560
42. Given that
2p-m = 6 and 2p +4m = 1, find the value of (4p-3m)
[a] 1
[b] 3 [c]
9 [d] 7
The table below
shows the masses to the nearest kilogram of 40 students in a
University
Mass(kg)
|
65
|
66
|
67
|
68
|
69
|
70
|
No of students
|
4
|
5
|
11
|
8
|
7
|
5
|
Use
the information to answer question 43 and 44
43. The median of the distribution is
[a] 9.5kg [b]
11kg [c] 67kg
[d] 68kg
44. The
percentage of the students with mass less than 69kg is
[a] 56%
[b] 8% [c] 5% [d} 70%
45. If cos Ѳ = 5/13, what is the
value of tan Ѳ for 00 < Ѳ < 900 ?
[a] 13/15 [b]
13 [c] 5 [d] 12/5
46.The value of 2100 is
[a]
[b]
[c] 1/2 [d]
-1/2
47.
Which of the sketches
above gives correct method for
constructing an angle of
1200
at point P
[a] ii and iii [b]
ii only [c] iii only [d]
i and ii
48. Given that
4p45 = 11910 find the value of P.
[a] 1
[b] 2 [c]
4 [d]
3
49. Which of the following is not a measure of
dispersion?
[a] standard deviation [b]
mean deviation [c] range
[d] mea
THEORY – PART
A (answer all in this part)
1a. Without using Tables or Calculator, Simplify:
log
- 2log
+ log
b. Simplify
(-
-
2/3
2a. Prove that the angle which an arc of a
circle subtend at the centre is twice that which it subtend
at any point on the remaining part
of the circumference.
b.
In the diagram below, RST is a tangent to circle VSU centre O. <SVU =
500 and UV is a diameter.
Calculate <RSV
3a. Construct a
quadratic equation whose roots are – ½
and 2
b. Solve the equation 3x2 +25x – 18 = 0
4a. the sum of the
interior angles of a regular polygon is 1440⁰, calculate:
(i)
b. Solve
the simultaneous equations 3y – 2x = 21; 4y + 5x = 5
PART B (ANSWER
ANY FOUR FROM THIS PART)
5a. Copy and complete the table for y = x2
-2x – 2 for -4
X
|
-4
|
-3
|
-2
|
-1
|
0
|
1
|
2
|
3
|
4
|
Y
|
22
|
-2
|
1
|
6
|
(b) Using a scale of 2 cm to 1 unit on the
x-axis and 2 cm to 5 units on the y- axis, draw the graph of
Y = x2 – 2x – 2 for -4
(c) Use your graph to find:
(i) the roots of the equation x2 – 2x -2 = 0;
(ii) the values of x for which x2
-2x -4 ½ = 0
6a. Given that Ų = {1, 2, 3,…, 10},P ={x: x is prime} and {y: y is
odd},find P n Q
b. .
A money lender collects #200 simple interest on a capital after 2 years
at 5%.
Calculate the capital
invested
7a. Using logarithm table evaluate correct to 3
significant figures.
b. without
using mathematical tables, find the value of
8a. A point on the ground is 5m away from the
foot of a vertical wall 7m high.
Calculate, correct to the nearest
degree, the angle of depression of the point from
the top of the wall
b. In
the diagram below, O is the centre of
the circle, radius 7 cm. If
the length of
the minor
arc
XY is 18 cm,
calculate the area
of the minor
sector OXY. [Take π = 22/7]
9a. A string is 4.8m. A boy measured it to be
4.95. Find the percentage error.
b. A regular plot measures 12m by 5m. A path
of constant width runs along one side and end. If the
Total area of the plot and the path is 120m2;
find the width of the path.
10a. Use tables to find the values of the following:
(i)
tan 2360 (ii)
sin 3080
(iii) sin(-219)0
b. draw a
line PQ 8cm long. Construct a point X on PQ such that IPXI : IXQI = 4:3
Measure
IPXI.
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