Mathematics JAMB, WAEC, NECO AND NABTEB Official Past Questions

(a) Find the equation of a straight line which passes through the point (2, -3) and is parallel to the line \(2x + y = 6\).

(b) The operation \(\Delta\) is defined on the set T = {2, 3, 5, 7} by \(x \Delta y = (x + y + xy) mod 8\).

(i) Construct modulo 8 table for the operation \(\Delta\) on the set T.

(ii) Use the the table to find: (a) \(2 \Delta (5 \Delta 7)\) ; (b) \(2 \Delta n = 5 \Delta 7\).

(a) Copy and complete the table of values, correct to one decimal place, for the relation \(y = 3\sin x + 2\cos x\) for \(0° \leq x \leq 360°\).

(b) Using scales of 2cm to 30°mon the x- axis and 2cm to 1 unit on the y- axis, draw the graph of the relation \(y = 3\sin x + 2\cos x\) for \(0°\leq x \leq 360°\).

(c) Use the graph to solve :

(i) \(3\sin x + 2\cos x = 0\)

(ii) \(2 + 2\cos x + 3\sin x = 0\).

(a) If \(\frac{3p + 4q}{3p – 4q} = 2\), find \(p : q\).

(b)  

The diagram shows the cross section of a bridge with a semi-circular hollow in the middle. If the perimeter of the cross section is 34 cm, calculate the :

(i) length PQ; (ii) area of the cross section. 

[Take \(\pi = \frac{22}{7}\)].

Using ruler and a pair of compasses only, 

(a) construct : 

(i) \(\Delta\)XYZ such that |XY| = 10cm, < XYZ = 30° and < YXZ = 45°.

(ii) locus, \(l_{1}\), of points equidistant from Y and Z.

(iii) locus, \(l_{2}\), of points parallel to XY through Z.

(b) Locate M, the point of intersection of \(l_{1}\) and \(l_{2}\).

(c) Measure < ZMY.

The weight (in kg) of 50 contestants at a competition is as follows:

65 66 67 66 64 66 65 63 65 68 64 62 66 64 67 65 64 66 65 67 65 67 66 64 65 64 66 65 64 65 66 65 64 65 63 63 67 65 63 64 66 64 68 65 63 65 64 67 66 64.

(a) Construct a frequenct table for the discrete data.

(b) Calculate, correct to 2 decimal places, the;

(i) mean ; (ii) standard deviation of the data.

(a) 

In the diagram, < KLM = x, < LMK = y, < KJH = r and < KGF = 110°. If 2x = r = y, find the value of x.

(b) Ten boys and twelve girls collected donations for a project. The total amount collected by the boys was N600.00 gretaer than that collected by the girls. If the average collection of the boys was N100.00 greater than the average collection of the girls, how much was collected by the two groups?

(a) Using the method of completing the square, solve, correct to 2 decimal places, \(\frac{x – 2}{4} = \frac{x + 2}{2x}\).

(b) 

In the diagram, PQRST is a circle with centre O. If PS is a diameter, RS//QT, and < QTS = 52°, find :

(i) < SQT ; (ii) < PQT.

(a) Find the sum of the Arithmetic Progression (AP) 1, 3, 5,…, 101.

(b) Out of the 95 travellers interviewed, 7 travelled by bus and train only, 3 by train and car only and 8 travelled by all 3 means of transport. The number, x, of travellerswho travelled by bus only was equal to the number who travelled by bus and car only. If 47 people travelled by bus and 30 by train :

(i) represent this information in a Venn diagram;

(ii) calculate the 

(1) value of x ; (2) number who travelled by at least two means.

(a)  

In the diagram, PQST is a parallelogram, PR is a straight line, |TS| = 8cm, |SM| = 6cm and area of triangle PSR = \(36 cm^{2}\). Find the value of |QR|.

(b) A tree and a flagpole are on the same horizontal ground. A bird on top of the tree observes the top and bottom of the flagpole below it at angle of 45° and 60° respectively. If the tree is 10.65m high, calculate, correct to 3 significant figures, the height of the flagpole.

The table shows the outcome when a die is thrown a number of times. If the probability of obtaining a 3 is 0.225;

(a) How many times was the die thrown?

(b) Calculate the probability that a trial chosen at random gives a score of an even number or a prime number.

(a) 

In the diagram, < RTS = 28°, < VRM = 46°, MQ is a tangent to the circle VRSTU at the point R. Find < VUS.

(b) A cylinder tin, 7cm high, is closed at one end. If its total surface area is 462\(cm^{2}\), calculate its radius. [Take \(\pi = \frac{22}{7}\)].

(a) Solve : \(7(x + 4) – \frac{2}{3}(x – 6) \leq 2[x – 3(x + 5)]\)

(b) A transport company has a total of 20 vehicles made up of tricycle and taxicabs. Each tricycle carries 2 passengers while each taxicab carries four passengers. If the 20 vehicles carry a total of 66 passengers at a time, how many tricycles does the company have?

(a) Without using Mathematical tables or calculators, evaluate \(\frac{0.09 \times 1.21}{3.3 \times 0.00025}\), leaving the answer in standard form (Scientific Notation).

(b) A principal of GH¢5,600 was deposited for 3 years at compound interest. If the interest earned was GH¢1,200, find, correct to 3 significant figures, the interest rate per annum.

From the diagram, which of the following is true?

An object is 6m away from the base of a mast. If the angle of depression of the object from the top of the mast is 50^o, find, correct to 2 decimal places, the height of the mast.

In the diagram MN is a chord of a circle KMN centre O and radius 10cm. If < MON = 140^o, find, correct to the nearest cm, the length of the chord MN.

Halima is n years old. Her brother’s age is 5 years more than half of her age. How old is her brother?

The ratio of the exterior angle to the interior angle of a regular polygon is 1:11. How many sides has the polygon?

Find the lower quartile of the distribution illustrated by the cumulative frequency curve

Find the next three terms of the sequence; 0, 1, 1, 2, 3, 5, 8…

The relation y = x² + 2x + k passes through the point (2,0). Find the value of k