WAEC SSCE - General Mathematics - 2019 (Objective)

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.

Factorize completely; (2x + 2y)(x - y) + (2x - 2y)(x + y) 

The total surface area of a solid cylinder 165cm\(^2\). Of the base diameter is 7cm, calculate its height. [Take \(\pi = \frac{22}{7}\)]

A box contains 5 red, 6 green and 7 yellow pencils of the same size. What is the probability of picking a green pencil at random?

In the diagram, RT is a tangent to the circle at R, < PQR = 70\(^o\), < QRT = 52\(^o\), < QSR and < PRQ = x.  Calculate the variance of 2, 4, 7, 8 and 9 

From the top of a vehicle cliff 20m high, a boat at sea can be sighted 75m away and on the same horizontal position as the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff. 

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

Solve 4x^{2}\) - 16x + 15 = 0.

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

In the diagram, PQ is parallel to RS, < QFG = 105\(^o\) and < FEG = 50\(^o\). Find the value of n

If 23\(_y\) = 1111\(_{\text{two}}\), find the value of y

If tan x = \(\frac{3}{4}\), 0 < x < 90\(^o\), evaluate \(\frac{\cos x}{2 sin x}\) 

Find the angle at which an arc of length 22 cm subtends at the centre of a circle of radius 15cm.  [Take \(\pi = \frac{22}{7}\)]

Simplify: \(\log_{10}\) 6 - 3 log\(_{10}\)  3 + \(\frac{2}{3} \log_{10} 27\)

The fourth term of an Arithmetic Progression (A.P) is 37 and the first term is -20. Find the common difference.
 

In the diagram, POS and ROT re straight lines. OPOR is a parallelogram, |OS| = |OT| and

Which of these values would make \(\frac{3p^-}{p^{2-}}\) undefined? 

The following are scores obtained by some students in a test. Find the median score

Evaluate: \(\frac{0.42 + 2.5}{0.5 \times 2.95}\), leaving the answer in the standard form.

In the diagram, O is the centre of the circle of radius 18cm. If < zxy = 70\(^o\), calculate the length of arc ZY. [Take \(\pi = \frac{22}{7}\)]
 

A box contains 3 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 colours?

Simplify: \(\frac{x^2 - 5x - 14}{x^2 - 9x + 14}\) 

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? 

If (0.25)\(^y\) = 32, find the value of y.

Evaluate: 2\(\sqrt{28} - 3\sqrt{50} + \sqrt{72}\)  

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

Simplify, correct to three significant figures, (27.63)\(^2\) - (12.37)\(^2\) 

8, 18, 10,14, 18, 11, 13, 14, 13, 17, 15, 8, 16, and 13

The following are scores obtained by some students in a test. How many students scored above the mean score? 

In XYZ, |YZ| = 32cm, < YXZ 53\(^o\) and XZY = 90\(^o\). Find, correct to the nearest centimetre, |XZ|

The interior angles of a polygon are 3x\(^o\), 2x\(^o\), 4x\(^o\), 3x\(^o\) and 6\(^o\). Find the size of the smallest angle of the polygon.

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 8m above the ground. How long is the ladder? 

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

Solve: \(\frac{y + 1}{2} - \frac{2y - 1}{3}\) = 4

Evaluate: (0.064) - \(\frac{1}{3}\) 

If 7 + y = 4 (mod 8), find the least value of y, 10 \(\leq y \leq 30\) 

Bala sold an article for #6,900.00 and made a profit of 15%. Calculate his percentage profit if he had sold it for N6,600.00. 

If log\(_x\) 2 = 0.3, evaluate log\(_x\) 8.

A rectangular board has a length of 15cm and width x cm. If its sides are doubled, find its new area.

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

The following are scores obtained by some students in a test, Find the mode of the distribution

Evaluate; \(\frac{\log_3 9 - \log_2 8}{\log_3 9}\) 

Find the equation of a straight line passing through the point (1, -5) and having gradient of \(\frac{3}{4}\) 

If T = {prime numbers} and M = {odd numbers} are subsets of \(\mu\)  = {x : 0 < x ≤ 10} and x is an integer, find (T\(^{\prime}\) n M\(^{\prime}\)). 

In the diagram, PQ is parallel to RS, < QFG = 105\(^o\) and < FEG = 50\(^o\). Find the value of m.

In the diagram, RT is a tangent to the circle at R, < PQR = 70\(^o\), < QRT = 52\(^o\), < QSR and < PRQ = x. Find the value of y. 

Express, correct to three significant figures, 0.003597. 

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? 

The pie chart represents fruits on display in a grocery shop. If there are 60 oranges on display, how many apples are there?  
 

In the diagram, RT is a tangent to the circle at R, < PQR = 70\(^o\), < QRT = 52\(^o\), < QSR and < PRQ = x. Calculate the value of x.

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