WAEC SSCE - General Mathematics - 2019 (Objective)

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. 

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

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

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. 

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

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

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

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

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

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

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 \(\pi = \frac{22}{7}\)]

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

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

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

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.

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

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

Express, correct to three significant figures, 0.003597. 

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

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

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 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 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\(^{\prime}\)). 

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

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

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? 

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

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

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

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

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

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? 

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

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

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?

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

Evaluate: (0.064) - \(\frac{1}{3}\) 

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

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

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

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

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

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?

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

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. 

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

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