2003 - WAEC Mathematics Past Questions and Answers - page 2
11
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
correct option: c
5(x - 7) = 7 - 2x
5x - 35 = 7 - 2x
5x + 2x = 7 + 35
7x = 42
x = \(\frac{42}{7}\)
= 6
12
Evaluate \(\frac{log8}{log\left(\frac{1}{4}\right)}\)
A
-2
B
\(\frac{-3}{2}\)
C
\(\frac{1}{2}\)
D
4
correct option: b
\(\frac{log8}{log\frac{1}{4}}=\frac{log2^3}{log2^{-2}}=\frac{3log2}{-2log2}=-\frac{3}{2}\)
Users' Answers & Comments13
A pyramid of volume 120cm3 has a rectangular base which measures 5cm by 6cm. Calculate the height of the pyramid
A
5cm
B
9cm
C
12cm
D
15cm
correct option: c
\(V= \frac{1}{2}\hspace{1mm}base\hspace{1mm}area\hspace{1mm}\times\hspace{1mm}height\
120=\frac{1}{3}\times 5 \times 6 \times h; h = \frac{120}{10}=12cm\)
Users' Answers & Comments120=\frac{1}{3}\times 5 \times 6 \times h; h = \frac{120}{10}=12cm\)
14
PQRS is a cyclic quadrilateral. If ∠QPS = 75°, what is the size of ∠QRS?
A
180o
B
150o
C
105o
D
75o
correct option: c
< QPS = 75°
< QRS = 180° - 75° = 105° (opposite angles of a cyclic quadrilateral)
15
In the diagram, ZM is a straight line. Calculate the value of x.
A
27o
B
30o
C
35o
D
37o
correct option: c
The sum of angles in a triangle is 180o
2xo + (2x -21)o + ∠ZYP = 180o
Also ∠ZYP = 180o - (3x+14)o
∴2xo + (2x-21)o + 180o - (3x+14)o = 180
x = 35o
Users' Answers & Comments2xo + (2x -21)o + ∠ZYP = 180o
Also ∠ZYP = 180o - (3x+14)o
∴2xo + (2x-21)o + 180o - (3x+14)o = 180
x = 35o
16
Find the value of x in the equation 3x\(^2\) - 8x - 3 = 0
A
\(\frac{1}{3},-3\)
B
\(-\frac{1}{3},-3\)
C
\(-\frac{1}{3},3\)
D
\(\frac{1}{3},3\)
correct option: c
3x\(^2\) - 8x - 3 = 0
3x\(^2\) - 9x + x - 3 = 0
3x(x - 3) + 1(x - 3) = 0
(3x + 1)(x - 3) = 0
3x = -1 \(\implies\) x = \(-\frac{1}{3}\)
or x = 3.
17
In\( ∆ PQR, P\hat{Q}P = 84^°, |Q\hat{P}R |= 43^°\) and |PQ| = 5cm. Find /QR/ in cm, correct to 1 decimal place.
A
3.4
B
4.3
C
5.9
D
6.2
correct option: b
Using the sine rule
\(\frac{|QR|}{sinP}=\frac{|PQ|}{sinR}\
\frac{x}{sin43^o}=\frac{5}{sin53^o}\
x = \frac{5\times sin43^o}{sin53^o}\
=\frac{5\times 0.6820}{0.7986}\
=4.3\)
Users' Answers & Comments\(\frac{|QR|}{sinP}=\frac{|PQ|}{sinR}\
\frac{x}{sin43^o}=\frac{5}{sin53^o}\
x = \frac{5\times sin43^o}{sin53^o}\
=\frac{5\times 0.6820}{0.7986}\
=4.3\)
18
Given, that \(4P4_5 = 119_{10}\), find the value of P
A
1
B
2
C
3
D
4
correct option: c
\(4P4_5 = 119_{10}\)
\(4 \times 5^2 + P \times 5^1 + 4 \times 5^0 = 119\)
\(100 + 5P + 4 = 119\)
\(5P = 119 - 104 = 15\)
\(P = 3\)
19
A ladder, 6m long, leans against a vertical wall at an angle 53o to the horizontal. How high up the wall does the ladder reach?
A
3.611m
B
4.521m
C
4.792m
D
7.962m
correct option: c
Sin 53 = \(\frac {h}{6} \)
h = 6 sin 53 = 6 x 0.7986
= 4.792m
Users' Answers & Commentsh = 6 sin 53 = 6 x 0.7986
= 4.792m
20
What is the size of angle x in the diagram
A
15o
B
30o
C
45o
D
60o
correct option: b
\(Sin\theta^{\circ} = \frac{opp}{hyp}\
Sin X^{\circ}=\frac{5}{10}=0.5000\SinX^{\circ}\
X^{\circ} = sin^{-1}0.5000\
X^{\circ}=30^{\circ}\)
Users' Answers & CommentsSin X^{\circ}=\frac{5}{10}=0.5000\SinX^{\circ}\
X^{\circ} = sin^{-1}0.5000\
X^{\circ}=30^{\circ}\)