Mathematics JAMB, WAEC, NECO AND NABTEB Official Past Questions

The table shows the marks scored by some candidates in an examination.

(a) Construct a cumulative frequency table for the distribution and draw a cumulative frequency curve.

(b) Use the curve to estimate, correct to one decimal place, the :

(i) Lowest mark for distinction if 5% of the candidates passed with distinction ; (ii) probability of selecting a candidate who scored at most 45%.

A water reservoir in the form of a cone mounted on a hemisphere is built such that the plane face of the hemisphere fits exactly to the base of the cone and the height of the cone is 6 times thr radius of its base.

(a) Illustrate this information in a diagram.

(b) If the volume of the reservoir is \(333\frac{1}{3}\pi m^{3}\), calculate, correct to the nearest whole number, the :

(I) volume of the hemisphere ; (II) Total surface area of the reservoir. [Take \(\pi = \frac{22}{7}\)].

(a) Make m the subject of the relations \(h = \frac{mt}{d(m + p)}\).

(b)  

In the diagram, WY and WZ are straight lines, O is the centre of circle WXM and < XWM = 48°. Calculate the value of < WYZ.

(c) An operation \(\star\) is defind on the set X = {1, 3, 5, 6} by \(m \star n = m + n + 2 (mod 7)\) where \(m, n \in X\).

(i) Draw a table for the operation.

(ii) Using the table, find the truth set of : (I) \(3 \star n = 3\) ; (II) \(n \star n = 3\).

(a) Without using Mathematical tables or calculators, simplify : \(\frac{2\tan 60° + \cos 30°}{\sin 60°}\)

(b) From an aeroplane in the air and at a horizontal distance of 1050m, the angles of depression of the top and base of a control tower at an instance are 36° and 41° respectively. Calculate, correct to the nearest meter, the :

(i) height of the control tower ; (ii) shortest distance between the aeroplane and the base of the control tower.

(a) The first term of an Arithmetic Progression (AP) is 8, the ratio of the 7th term to the 9th term is 5 : 8, find the common difference of the AP.

(b) A trader bought 30 baskets of pawpaw and 100 baskets of mangoes for N2,450.00. She sold the pawpaw at a profit of 40% and the mangoes at a profit of 30%. If her profit on the entire transaction was N855.00, find the (i) cost price of a basket of pawpaw ; (ii) selling price of the 100 baskets of mangoes.

(a) Using ruler and a pair of compasses only, construct a :

(i) Trapezium WXYZ such that |WX| = 8 cm, |XY| = 5.5 cm, |YZ| = 8.3 cm, < WXY = 60° and WX // ZY;

(ii) rectangle PQYZ where P and Q are on WX 

(b) Measure : (i) |QX| ; (ii) < XWZ.

The table is for the relation \(y = px^{2} – 5x + q\).

(a)(i) Use the table to find the values of p and q.

(ii) Copy and complete the table.

(b) Using scales of 2cm to 1 unit on the x- axis and 2 cm to 5 units on the y- axis, draw the graph of the relation for \(-3 \leq x \leq 5\).

(c) Use the graph to find : 

(i) y when x = 1.8  ; (ii) x when y = -8.

(a) (i) Illustrate the following statements in a Venn diagram : All good Literature students in a school are in the General Arts class. 

(ii) Use ths diagram to determine whether or not the following are valid conclusions from the given statement.

(1) Vivian is in the General Arts class therefore she is a good Literature student.

(2) Audu is not a good Literature student therefore he is not in the General Arts class;

(3) Kweku is not in the General Arts class therefore he is not a good Literature student.

(b) The cost (c) of producing n bricks is the sum of a fixed amount, h, and a variable amount, y, where y varies directly as n. If it costs GH¢950.00 to produce 600 bricks and GH¢ 1,030.00 to produce 1000 bricks,

(i) Find the relationship between c, h and n ; (ii) Calculate the cost of producing 500 bricks.

A trapezium PQRS is such that PQ // RS and the perpendicular P to RS is 40 cm. If |PQ| = 20 cm, |SP| = 50 cm and |SR| = 60 cm. Calculate, correct to 2 significant figures, the

(a) Area of the trapezium ; (b) < QRS.

(a) By how much is the sum of \(3\frac{2}{3}\) and \(2\frac{1}{5}\) less than 7?

(b) The height, h m, of a dock above sea level is given by \(h = 6 + 4\cos (15p)°, 0 < p < 6\). Find :

(i) the value of h when p = 4 ; (ii) correct to two significant figures, the value of p when h = 9 m.

(a) The ratio of the interior angle to the exterior angle of a regular polygon is 5 : 2, Find the number of sides of the polygon.

(b) 

The diagram shows a circle PQRS with centre O, < UQR = 68°, < TPS = 74° and < QSR = 40°. Calculate the value of < PRS.

(a) Solve the inequality : \(4 + \frac{3}{4}(x + 2) \leq \frac{3}{8}x + 1\)

(b) 

The diagram shows a rectangle PQRS from which a square of side x cm has been cut. If the area of the shaded portion is 484\(cm^{2}\), find the values of x.

(a)  Without using Mathematical tables or calculators, simplify:

\(3\frac{4}{9} \div (5\frac{1}{3} – 2\frac{3}{4}) + 5\frac{9}{10}\)

(b) A number is selected at random from each of the sets {2, 3, 4} and {1, 3, 5}. Find the probability that the sum of the two numbers is greater than 3 and less than 7.

In the diagram, \(\bar{OX}\) bisects < YXZ and \(\bar{OZ}\) bisects < YZX. If < XYZ = 68^o, calculate the value of < XOZ

In a circle radius rcm, a chord 16\(\sqrt{3}cm\) long is 10cmfrom the centre of the circle. Find, correct to the nearest cm, the value of r

A letter is selected from the letters of the English alphabet. What is the probability that the letter selected is from the word MATHEMATICS?

Two angles of a pentagon are in the ratio 2:3. The others are 60^o each. Calculate the smaller of the two angles

In the diagram, the shaded part is carpet laid in a room with dimensions 3.5m by 2.2m leaving a margin of 0.5m round it. Find area of the margin

Calculate the mean deviation of 5, 3, 0, 7, 2, 1

Find the value of p if \(\frac{1}{4}\)p + 3q = 10 and 2p – q = 7

Describe the shaded portion in the diagram