WAEC - Mathematics (2013)

1
Multiply 2.7 x 10^-4 by 6.3 x 10⁶ and leave your answers in standard form
Răspuns
(C)
1.701 x 10³
2
If 9^{(2 - x)} = 3, find x
Răspuns
(B)
\(\frac{3}{2}\)
3
In what number base is the addition 465 + 24 + 225 = 1050?
Răspuns
(D)
seven
4
Simplify \(\frac{1\frac{7}{8} \times 2\frac{2}{5}}{6\frac{3}{4} \div \frac{3}{4}}\)
Răspuns
(D)
\(\frac{1}{2}\)
5
If Un = n(n² + 1), evaluate U5 - U4
Răspuns
(C)
62
6
If \(\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}\), find K
Răspuns
(D)
2
7
A sales boy gave a change of N68 instead of N72. Calculate his percentage error
Răspuns
(B)
5\(\frac{5}{9}\)%
8
Four oranges sell for Nx and three mangoes sell for Ny. Olu bought 24 oranges and 12 mangoes. How much did he pay in terms of x and y?
Răspuns
(B)
N(6x + 4y)
9
Simplify: \(\frac{x^2 - y^2}{(x + y)^2} \div \frac{(x - y)^2}{(3x + 3y)}\)
Răspuns
(C)
\(\frac{3}{x - y}\)
10
Solve the inequality: \(\frac{2x - 5}{2} < (2 - x)\)
Răspuns
(D)
x < 2\(\frac{1}{4}\)
11
If x = 64 and y = 27, evaluate: \(\frac{x^{\frac{1}{2}} - y^{\frac{1}{3}}}{y - x^{\frac{2}{3}}}\)
Răspuns
(C)
\(\frac{5}{11}\)
12
If \(\frac{1}{2}\)x + 2y = 3 and \(\frac{3}{2}\)x - 2y = 1, find (x + y)
Răspuns
(A)
3
13
Given that \(p^{\frac{1}{3}}\) = \(\frac{\sqrt[3]{q}}{r}\), make q the subject of the equation
Răspuns
(C)
q = pr³
14
A chord is 2cm from the centre of a circle. If the radius of the circle is 5cm, find the length of the chord
Răspuns
(A)
2\(\sqrt{21}\)cm
15
A cube and cuboid have the same base area. The volume of the cube is 64cm\(^3\) while that of the cuboid is 80cm\(^3\). Find the height of the cuboid
Răspuns
(C)
5cm
16
If sin x = \(\frac{5}{13}\) and 0^o \(\leq\) x \(\leq\) 90^o, find the value of (cos x - tan x)
Răspuns
(C)
\(\frac{79}{156}\)
17
An object is 6m away from the base of a mast. The angle of depression of the object from the top pf the mast is 50^o, Find, correct to 2 decimal places, the height of the mast
Răspuns
(C)
7.15m
18
The bearing of Y from X is 060º and the bearing of Z from Y = 060º. Find the bearing of X from Z
Răspuns
(B)
240^o
19
Which of the following is not a probability of Mary scoring 85% in a mathematics test?
Răspuns
(D)
1.01
20
If 2 log x (3\(\frac{3}{8}\)) = 6, find the value of x
Răspuns
(A)
\(\frac{3}{2}\)
21
If p = (y : 2y \(\geq\) 6) and Q = (y : y -3 \(\leq\) 4), where y is an integer, find p\(\cap\)Q
Răspuns
(C)
{3, 4, 5, 6, 7}
22
Find the values of k in the equation 6k² = 5k + 6
Răspuns
(B)
{\(\frac{-2}{3}, \frac{3}{2}\)}
23
If y varies directly as the square root of (x + 1) and y = 6 when x = 3, find x when y = 9
Răspuns
(A)
8
24
The graph of the relation y = x2 + 2x + k passes through the point (2, 0). Find the values of k
Răspuns
(D)
-8
25
What is the locus of the point X which moves relative to two fixed points P and M on a plane such that < PXM = 30^o
Răspuns
(B)
an arc of a circle with PM as a chord
26
When a number is subtracted from 2, the result equals 4 less than one-fifth of the number. Find the number
Răspuns
(C)
5
27
Express \(\frac{2}{x + 3} - \frac{1}{x - 2}\) as a simple fraction
Răspuns
(A)
\(\frac{x - 7}{x^2 + x - 6}\)
28
An interior angle of a regular polygon is 5 times each exterior angle. How many sides has the polygon?
Răspuns
(B)
12
29
Given that P = x² + 4x - 2, Q = 2x - 1 and Q - p = 2, find x
Răspuns
(B)
-1
30
A pyramid has a rectangular base with dimensions 12m by 8m. If its height is 14m, calculate the volume
Răspuns
(B)
448m³
31
The slant height of a cone is 5cm and the radius of its base is 3cm. Find, correct to the nearest whole number, the volume of the cone. ( Take \(\pi = \frac{22}{7}\))
Răspuns
(C)
38cm³
32
The distance between two towns is 50km. It is represented on a map by 5cm. Find the scale used
Răspuns
(A)
1: 1,000,000
33
Given that (x + 2)(x2 - 3x + 2) + 2(x + 2)(x - 1) = (x + 2) M, find M
Răspuns
(D)
x² - x
34
An open cone with base radius 28cm and perpendicular height 96cm was stretched to form sector of a circle. calculate the arc of the sector (Take \(\pi = \frac{22}{7}\))
Răspuns
(A)
8800cm²
35

In the diagram, PRST is a square. If |PQ| = 24cm. |QR| = 10cm and < PQR = 90o, find the perimeter of the polygon PQRST.
Răspuns
(A)
112cm
36
in the diagram, the height of a flagpole |TF| and the length of its shadow |FL| re in the ratio 6:8. Using k as a constant of proportionality, find the shortest distance between T and L
Răspuns
(B)
10K units
37
In the diagrams, |XZ| = |MN|, |ZY| = |MO| and |XY| = |NO|. Which of the following statements is true?
Răspuns
(D)
\(\bigtriangleup\) XYZ= \(\bigtriangleup\) NOM
38

In the diagram, PQRS is a rhombus and < PSQ = 35º. Calculate the size of < PRQ
Răspuns
(B)
55^o
39
Find the value of m in the diagram
Răspuns
(D)
17^o
40

In the diagram, O is the centre of the circle. OM||XZ and < ZOM = 25º. Calculate ∠XYZ
Răspuns
(D)
65^o
41

Using the histogram, estimate the mode of distribution
Răspuns
(C)
53.5
42

Using the histogram, what is the median class?
Răspuns
(C)
40.5 - 50.5
43

The pie chart shows the distribution of 600 mathematics textbooks for Arts, Business, Science and Technical Classes. How many textbooks are for the technical class?
Răspuns
(D)
250
44

The pie chart shows the distribution of 600 mathematics textbooks for Arts, Business, Science and Technical Classes. What percentage of the total number of textbooks belongs to science?
Răspuns
(A)
12\(\frac{1}{2}\)%
45
In the diagram, PQRST is a regular polygon with sides QR and TS produced to meet at V. Find the size of < RVS
Răspuns
(A)
36^o