# Waecmaths

Title waecmaths question
Question 1

Express, correct to three significant figures, 0.003597

Question 2

Evaluate ${{(0.064)}^{-\tfrac{1}{3}}}$

Question 3

Solve $\frac{y+1}{2}-\frac{2y-1}{3}=4$

Question 4

Simplify, correct to three significant figures, ${{(27.63)}^{2}}-{{(12.37)}^{2}}$

Question 5

If  7 + y = 4(mod 8). Find the least value if $10\le y\le 30$

Question 6

If T ={ Prime numbers} and

M = {odd numbers} are subsets of

$\mu =\{x:0<x\le 10\text{ and }x\text{ is an integer }\!\!\}\!\!\text{ }$find $(T'\cap M')$

Question 7

Evaluate $\frac{{{\log }_{3}}9-{{\log }_{2}}8}{{{\log }_{3}}9}$

Question 8

If 25y = 1111two ,find the value of y

Question 9

If 6, P and 14 are consecutive terms in an Arithmetic Progression (A.P), find the value of P.

Question 10

Evaluate $2\sqrt{28}-3\sqrt{50}+\sqrt{72}$

Question 11

If m : n = 2 : 1, evaluate $\frac{3{{m}^{2}}-2{{n}^{2}}}{{{m}^{2}}+mn}$

Question 12

H varies directly as p and inversely as the square of y. If H =1, P =8 and y =2, find H in terms of p and y

Question 13

Solve $4{{x}^{2}}-16x+15=0$

Question 14

Evaluate $\frac{0.42\div 2.5}{0.5\times 2.05}$ leaving the answer in standard form

Question 15

Simplify ${{\log }_{10}}6-3{{\log }_{10}}3+\tfrac{2}{3}{{\log }_{10}}27$

Question 16

Bala sold an article for N6,900.00 and made a profit of 15%. Calculate his percentage profit if he had sold it for N6,600

Question 17

If $3p=4q$ and $9p=8q-12$ find the value of pq

Question 18

If ${{(0.25)}^{y}}=32$ . Find the value of y

Question 19

There are 8 boys and 4 girls in a lift, What is the probability that the first person who steps out of the lift will be a boy

Question 20

Simplify $\frac{{{x}^{2}}-5x-14}{{{x}^{2}}-9x+14}$

Question 21

Which of these values would make $\frac{3p-1}{{{p}^{2}}-p}$ undefined

Question 22

The total surface area of a solid cylinder is 165cm2. If the base diameter is 7cm, calculate its height [Take $\pi =\tfrac{22}{7}$]

Question 23

If ${{2}^{a}}=\sqrt{64}$ and $\frac{b}{a}=3$, evaluate ${{a}^{2}}+{{b}^{2}}$

Question 24

In $\Delta XYZ$, $\left| YZ \right|=32cm$, $\angle YXZ=52{}^\circ$ and $\angle XZY=90{}^\circ$ Find, correct to the nearest centimetre, $\left| XZ \right|$

Question 25

If ${{\log }_{x}}2=0.3$ evaluate ${{\log }_{x}}8$

Question 26

An arc subtends an angle of 72o at the centre of a circle. Find the length of the arc if the radius of the circle is 3.5cm [Take $\pi=\frac{22}{7}$

Question 27

Make b the subject of the relation$lb=\tfrac{1}{2}(a+b)h$

Question 28

Eric sold his house through an agent who charged 8% commission on the selling price.
If Eric received $117,760.00 after the sale, what was the selling price of the house? Question 29 . Find the angle which an arc of length 22cm subtends at the centre of a circle of radius 15cm [Take$\pi =\tfrac{22}{7}$] Question 30 A rectangular board has length 15cm and width xcm. If its sides are doubled, find its new area. Question 31 In the diagram, POS and ROT are straight lines. OPQR is a parallelogram,$\left| OS \right|=\left| OT \right|$and$\angle OST=50{}^\circ $. Calculate the value of$\angle OPQ$Question 32 Factorize completely$(2x+2y)(x-y)+(2x-2y)(x+y)$Question 33 The interior angles of a polygon are 3xo, 2xo, 4xo, 3xo and 6xo. Find the size of the smallest angle of the polygon Question 34 A box contains 2 white and 3 blue identical balls. If two balls are picked at random from the box, one after the other with replacement, what is the probability that they are of different colors? Question 35 Find the equation of a straight line passing through the point (1, −5) and having gradient$\tfrac{3}{4}$Question 36 The foot of a ladder is 6m from the base of an electric pole. The top of the ladder rest against the pole at a point 8 m above the ground. How long is the ladder Question 37 If$\tan x=\frac{3}{4}$,$0{}^\circ <x<90{}^\circ $evaluate$\frac{\cos x}{2\sin x}$Question 38 From the top of a vertical cliff 20m high, a boat at sea can sighted 75 m away and on the same horizontal position as the foot of the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff Question 39 In the diagram O is the centre of the circle of radius 18cm . If$\angle ZXY=70{}^\circ $, Calculate the length of arc ZY [Take$\pi =\tfrac{22}{7}$] Question 40 In the diagram, RT is a tangent to the circle at R,$\angle PQR=70{}^\circ $,$\angle QRT=52{}^\circ $,$\angle QSR=y$and$\angle PRQ=x\$.

Find the value of y