Mathematics JAMB, WAEC, NECO AND NABTEB Official Past Questions

(a)  In the diagram, /PQ/ = 6 cm, /QR/ = 13 cm, /RS/ = 5 cm and < RSQ is a right- angled triangle. Calculate, correct to one decimal place, /PS/.

(b)  The diagram show a wooden structure in the form of a cone mounted on a hemispherical base. The vertical height of the cone is 24 cm and the base radius 7 cm. Calculate, correct to 3 significant figures, the surface area of the structure. [Take \(\pi = \frac{22}{7}\)].

(a) Copy and complete the table of values for \(y = 1 – 4\cos x\).

(b) Using a scale of 2cm to 30° on the x- axis and 2cm to 1 unit on the y- axis, draw the graph of \(y = 1 – 4\cos x\) for \(0° \leq x \leq 360°\).

(c) Use the graph to : (i) solve the equation \(1 – 4\cos x = 0\) ; (ii) find the value of y when x = 105° ; (iii) find x when y = 1.5.

(a)  

In the diagram, ABCD is a rectangular garden (3n – 1)m long and (2n + 1)m wide. A wire mesh 135m long is used to mark its boundary and to divide it into 8 equal plots. Find the value of n.

(b) A cylinder with base radius 14 cm has the same volume as a cube of side 22 cm. Calculate the ratio of the total surface area of the cylinder to that of the cube. [Take \(\pi = \frac{22}{7}\)]

The table shows the distribution of marks scored by students in an examination. Calculate, correct to 2 decimal places, the

(a) mean ; (b) standard deviation of the distribution.

Three towns X, Y and Z are such that Y is 20 km from X and 22 km from Z. Town X is 18 km from Z. A health centre is to be built by the government to serve the three towns. The centre is to be located such that patients from X and Y travel equal distance to access the health centre while patients from Z will travel exactly 10 km to reach the Health centre.

(a) Using a scale of 1 cm to 2 km, find the construction, using a pair of compasses and ruler only, the possible positions the Health centre can be located.

(b) In how many possible locations can the Health centre be built?

(c) Measure and record the distances of the location from town X.

(d) Which of these locations would be convenient for all three towns?

A point H is 20 m away from the foot of a tower on the same horizontal ground. From the point H, the angle of elevation of the point P on the tower and the top (T) of the tower are 30° and 50° respectively. Calculate, correct to 3 significant figures :

(a) /PT/; (b) the distance between H and the top of the tower

(c) The position of H if the angle of depression of H from the top of the tower is to be 40°.

(a) (i) Using a scale of 2 cm to 1 unit on both axes, on the same graph sheet, draw the graphs of \(y – \frac{3x}{4} = 3\) and \(y + 2x = 6\).

(ii) From your graph, find the coordinates of the point of intersection of the two graphs.

(iii) Show, on the graph sheet, the region satisfied by the inequality \(y – \frac{3}{4}x \geq 3\).

(b) Given that \(x^{2} + bx + 18\) is factorized as \((x + 2)(x + c)\). Find the values of c and b.

(a)  A boy had M Dalasis (D). He spent D15 and shared the remainder equally with his sister. If the sister’s share was equal to \(\frac{1}{3}\) of M, find the value of M.

(b) A number of tourists were interviewed on their choice of means of travel. Two- thirds said that they travelled by road, \(\frac{13}{30}\) by air and \(\frac{4}{15}\) by both air and road. If 20 tourists did not travel by either air or road ; (i) represent the information on a Venn diagram ; (ii) how many tourists (1) were interviewed ; (2) travelled by air only?

In the diagram, O is the centre of the circleand XY is a chord. If the radius is 5 cm and /XY/ = 6 cm, calculate, correct to 2 decimal places, the :

(a) angle which XY subtends at the centre O ;

(b) area of the shaded portion.

(a) A box contains 40 identical discs which are either red or white. If the probability of picking a red disc is \(\frac{1}{4}\); Calculate the number of (i) white discs ; (ii) red discs that should be added such that the probability of picking a red disc will be \(\frac{1}{3}\).

(b) A salesman bought some plates at N50.00 each. If he sold all of them for N600.00 and made a profit of 20% on the transaction, how many plates did he buy?

(a)  In the diagram, TU is tangent to the circle. < RVU = 100° and < URS = 36°. Calculate the value of angle STU.

(b) In triangle XYZ, |XY| = 5 cm, |YZ| = 8 cm and |XZ| = 6 cm. P is a point on the side XY such that |XP| = 2 cm and the line through P, parallel to YZ meets XZ at Q. Calculate |QZ|.

Sonny is twice as old as Wale. Four years ago, he was four times as old as Wale. When will the sum of their ages be 66?

(a) Simplify : \(\frac{1\frac{1}{4} + \frac{7}{9}}{1\frac{4}{9} – 2\frac{2}{3} \times \frac{9}{64}}\)

(b) Given that \(\sin x = \frac{2}{3}\), evaluate, leaving your answer in surd form and without using tables or calculator, \(\tan x – \cos x\).

The diagram is a polygon. Find the largest of its interior angles

The graph is that of y = 2x² – 5x – 3. For what value of x will y be negative? For what value of x will y be negative?

In the diagram, |SR| = |QR|. < SRP = 65^o and < RPQ = 48^o, find < PRQ

The diagram is a circle of radius |QR| = 4cm. \(\bar{R}\) is a tangent to the circle at R. If TPO = 120^o, find |PQ|.

The diagram is a circle with centre P. PRST are points on the circle. Find the value of < PRS

In the diagram, MN//PO, < PMN = 112º, < PNO = 129º, < NOP = 37º and < MPN = yo. Find the value of y

The graph is that of y = 2x² – 5x – 3. For what value of x will y be negative? What is the gradient of y = 2x² – 5x – 3 at the point x = 4?

The bar chart shows the frequency distribution of marks scored by students in a class test. What is the median of the distribution?