There are 250 boys and 150 girls in a school, if 60% of the boys and 40% of the girls play football, what percentage of the school play football?
Απάντηση
(D)
52.5%
7
If \(\log_{10}\)(6x - 4) - \(\log_{10}\)2 = 1, solve for x.
Απάντηση
(C)
4
8
If F = \(\frac{9}{5}\)C + 32, find C when F = 98.6
Απάντηση
(B)
37
9
If y + 2x = 4 and y - 3x = -1, find the value of (x + y)
Απάντηση
(A)
3
10
If x : y : z = 3 : 3 : 4, evaluate \(\frac{9x + 3y}{6z - 2y}\)
Απάντηση
(A)
1\(\frac{1}{2}\)
11
Simplify; \(\frac{2 - 18m^2}{1 + 3m}\)
Απάντηση
(C)
\(2(1 - 3m)\)
12
A curve is such that when y = 0, x = -2 or x = 3. Find the equation of the curve.
Απάντηση
(D)
y = \(x^2 - x - 6\)
13
The volume of a cylindrical tank, 10m high is 385 m\(^2\). Find the diameter of the tank. [Take \(\pi = \frac{22}{7}\)]
Απάντηση
(C)
7m
14
The surface area of a sphere is \(\frac{792}{7} cm^2\). Find, correct to the nearest whole number, its volume. [Take \(\pi = \frac{22}{7}\)]
Απάντηση
(A)
113\(cm^3\)
15
The angles of a polygon are x, 2x, 2x, (x + \(30^o\)), (x + \(20^o\)) and (x - \(10^o\)). Find the value of x
Απάντηση
(C)
\(84^o\)
16
If M and N are the points (-3, 8) and (5, -7) respectively, find |MN|
Απάντηση
(D)
17 units
17
The equation of the line through the points (4,2) and (-8, -2) is 3y = px + q, where p and q are constants. Find the value of p.
Απάντηση
(A)
1
18
The mean of 1, 3, 5, 7 and x is 4. Find the value of x
Απάντηση
(B)
4
19
The table shows the distribution of goals scored by 25 teams in a football competition. Calculate the probability that a team selected at randon scored either 4 or 7 goals.
Απάντηση
(A)
\(\frac{9}{25}\)
20
The table shows the distribution of goals scored by 25 teams in a football competition. Calculate the probability that a team selected at random scored at most 3 goals.
Απάντηση
(D)
\(\frac{2}{5}\)
21
The total surface area of a hemispher is 75\(\pi cm^2\). Find the radius.
Απάντηση
(A)
5.0 cm
22
Find the value of x for which \(\frac{x - 5}{x(x - 1)}\) is undefined.
Απάντηση
(D)
0 or 1
23
Solved the equation \(2x^2 - x - 6\) = 0
Απάντηση
(A)
x = \(\frac{-3}{2}\) or 2
24
Factorise completely the expression
\((x + 2)^2\) - \((2x + 1)^2\)
Απάντηση
(D)
3(x + 1)(1 - x)
25
Find the \(n^{th}\) term of the sequence 2 x 3, 4 x 6, 8 x 9, 16 x 12...
Απάντηση
(B)
2\(^n\) x 3n
26
If 3x\(^o\) 4(mod 5), find the least value of x
Απάντηση
(C)
3
27
Find the inter-quartile range of 1, 3, 4, 5, 8, 9, 10, 11, 12, 14, 16
Απάντηση
(C)
8
28
If x : y = \(\frac{1}{4} : \frac{3}{8}\) and y : z = \(\frac{1}{3} : \frac{4}{9}\), find x : z
Απάντηση
(D)
1:2
29
Expression 0.612 in the form \(\frac{x}{y}\), where x and y are integers and y \(\neq\) 0
Απάντηση
(A)
\(\frac{153}{250}\)
30
The angle of elevation of the top of a tree from a point 27m away and on the same horizontal ground as the foot of the tree is 30\(^o\). Find the height of the tree.
Απάντηση
(D)
9\(\sqrt{3m}\)
31
In the diagram, which of the following ratios is equal to \(\frac{|PN|}{|PQ|}\)?
Απάντηση
(C)
\(\frac{|PM|}{|PR|}\)
32
If P and Q are two statements, under what condition would p|q be false?
Απάντηση
(B)
If p is true and q is false
33
Find the median of 2, 1, 0, 3, 1, 1, 4, 0, 1 and 2
Απάντηση
(C)
1.0
34
Find the mean deviation of 20, 30, 25, 40, 35, 50, 45, 40, 20 and 45
Απάντηση
(B)
9
35
Find the value of t in the diagram
Απάντηση
(C)
126\(^o\)
36
In the diagram, PR is a tangent to the circle at Q, QT//RS, < SQR = 35º and < RSQ = 50º. Find the value of <QST
Απάντηση
(D)
95\(^o\)
37
In the diagram, WXYZ is a rectangle with dimension 8cm by 6cm. P, Q, R and S are the midpoints of the sides of the rectangle as shown. Using this information, what type of quadrilateral is the shaded region?
Απάντηση
(D)
Rhombus
38
In the diagram, PS and RS are tangents to the circle centre O. ∠PSR = 70°, ∠POR = m, and ∠PSR =n. Find ( m + n ).
Απάντηση
(C)
165\(^o\)
39
In the diagram, WXYZ is a rectangle with diamension 8cm by 6cm. P, Q, R and S are the midpoints of the rectangle as shown. Using this information calculate the area of the part of the rectangle that is not shaded
Απάντηση
(B)
24cm\(^2\)
40
The solution of x + 2 \(\geq\) 2x + 1 is illustrated
Απάντηση
(A)
i
41
The diagram shows a trapezium inscribed in a semi-circle. If O is the mid-point of WZ and |WX| = |XY| = |YZ|, calculate the value of m
Απάντηση
(B)
60\(^o\)
42
In the diagram, PQ//RS. Find x in terms of y and z
Απάντηση
(D)
x = 360\(^o\) - y - z
43
In the diagram, PQ is a straight line, (m + n) = 110\(^o\) and (n + r) = 130\(^o\) and (m + r) = 120\(^o\). Find the ratio of m : n : r
Απάντηση
(D)
5 : 6 : 7
44
Donations during the launching of a church project were sent in sealed envolopes. The table shows the distribution of the amount of money in the envelope. How much was the donation?
Απάντηση
(D)
N62,972.00
45
A piece of thread of length 21.4cm is used to form a sector of a circle of radius 4.2cm on a piece of cloth. Calculate, correct to the nearest degree, the angle of the sector. [Take \(\pi = \frac{22}{7}\)]
