WAEC Mathematics Past Questions & Answers - Page 101

502.

If sin x = \(\frac{5}{13}\) and 0o \(\leq\) x \(\leq\) 90o, find the value of (cos x - tan x)

A.

\(\frac{7}{13}\)

B.

\(\frac{12}{13}\)

C.

\(\frac{79}{156}\)

D.

\(\frac{209}{156}\)

Correct answer is C

Sin x = \(\frac{5}{13}\)

0o \(\leq\) x \(\leq\) 90o, (cos x - tan x)

AC2 = AB2 + BC2

132 = 52 + BC2

169 - 25 + BC2

169 - 25 = BC2

144 = BC2

Cos x = \(\frac{Adj}{Hyp}\) = \(\frac{12}{13}\)

BC = \(\sqrt{144}\)

BC = 12

tan x = \(\frac{opp}{adj} = \frac{5}{12}\)

BC = 12

cos x - tan x = \(\frac{12}{13} - \frac{5}{12}\)

\(\frac{144 - 65}{156} = \frac{79}{156}\)

503.

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

A.

1cm

B.

3cm

C.

5cm

D.

6cm

Correct answer is C

Volume of a cube with side a cm = a\(^3\)

a\(^3\) = 64 \(\implies\) a = 4cm

Base area of a cube = a\(^2\)

= 4\(^2\)

= 16 cm\(^2\)

\(\implies\) Base area of the cuboid = 16 cm\(^2\)

Volume of cuboid = Base area x height

80 = 16 x h

h = \(\frac{80}{16}\)

= 5 cm

504.

A chord is 2cm from the centre of a circle. If the radius of the circle is 5cm, find the length of the chord

A.

2\(\sqrt{21}\)cm

B.

\(\sqrt{42}\)cm

C.

2\(\sqrt{19}\)cm

D.

\(\sqrt{21}\)cm

Correct answer is A

From \(\bigtriangleup\) OMQ find /MQ/ by Pythagoras OQ2 = OM2 + MQ2

52 = 22 + MQ2

25 = 4 + MQ2

25 - 4 = MQ2

21 - MQ2

MQ2 = 21

MQ2 = \(\sqrt{21}\)

Length of chord = 2 x \(\sqrt{21}\) = 2\(\sqrt{21}\)cm

505.

Given that p\(\frac{1}{3}\) = \(\frac{3\sqrt{q}}{r}\), make q the subject of the equation

A.

q = p\(\sqrt{r}\)

B.

q = p3r

C.

q = pr3

D.

q = pr\(\frac{1}{3}\)

Correct answer is D

p\(\frac{1}{3}\) = \(\frac{3\sqrt{q}}{r}\)(cross multiply)

3\(\sqrt{q}\) = r x 3\(\frac{\sqrt{q}}{r}\)(cross multiply)

3\(\sqrt{q}\) = r x 3\(\sqrt{p}\) cube root both side

q = 3\(\sqrt{r}\) x p

q = r\(\frac{1}{3}\)p = pr\(\frac{1}{3}\)