Mathematics JAMB, WAEC, NECO AND NABTEB Official Past Questions

The table below shows the mark distribution of candidates in an aptitude test for selection into the public service.

(a) Make a cumulative frequency for the distribution

(b) Draw the cumulative frequency curve.

(c) From your graph, estimate the median mark.

(d) The cut-off mark was 63%. What percentage of the candidates was selected?

(a)  PQRST is a circle with centre C. PCS is a straight line, RS // QT, |QR| = |RS| and < QTS = 56°. Find (i) SQT (ii) PQT.

(b)    In the diagram, points B and C are on a horizontal plane and |BC| = 30cm. A and D are points vertically above B and C respectively. |DC| = 40 cm and |AB| = 26 cm. Calculate the angles of depression of : (i) B from D ; (ii) A from D ; correct to the nearest degree.

Above is the graph of the quadratic function \(y = ax^{2} + bx + c\) where a, b and c are constants. Using the graph, find :

(a)(i) the scales on both axes ; (ii) the equation of the line of symmetry of the curve ; (iii) the roots of the quadratic equation \(ax^{2} + bx + c = 0\)

(b) Use the coordinates of D, E and G to find the values of the constants a, b and c hence write down the quadratic function illustrated in the graph.

(c) Find the greatest value of y within the range \(-3 \leq x \leq 5\).

  The solid is a cylinder surmounted by a hemispherical bowl. Calculate its

(a) total surface area ;

(b) volume (Take \(\pi = \frac{22}{7}\))

(a) Solve the simultaneous equation : \(\log_{10} x + \log_{10} y = 4\)

                                                            \(\log_{10} x + 2\log_{10} y = 3\)

(b) The time, t, taken to buy fuel at a petrol station varies directly as the number of vehicles V on queue and jointly varies inversely as the number of pumps P available in the station. In a station with 5 pumps, it took 10 minutes to fuel 20 vehicles. Find :

(i) the relationship between t, P and V ; (ii) the time it will take to fuel 50 vehicles in the station with 2 pumps ; (iii) the number of pumps required to fuel 40 vehicles in 20 minutes.

(a) Using a ruler and a pair of compasses only, construst \(\Delta\) ABC in which |AB| = 7cm, |BC| = 5cm and < ABC = 75°. Measure |AC|.

(b) In (a) above, locate by construction, a point D such that CD is parallel to AB and D is equidistant from points A and C. Measure < BAD.

(a) Use logarithm tables to evaluate \(\frac{15.05 \times \sqrt{0.00695}}{6.95 \times 10^{2}}\).

(b) The first 5 students to arrive in a school on a Monday morning were 2 boys and 3 girls. Of these, two were chosen at random for an assignment. Find the probability that :

(i) both were boys ; (ii) the two were of different sexes.

(a) Given that \(\frac{5y – x}{8y + 3x} = \frac{1}{5}\), find the value of \(\frac{x}{y}\) to two decimal places.

(b) If 3 is a root of the quadratic equation \(x^{2} + bx – 15 = 0\), determine the value of b. Find the other root.

The table below shows how a company’s sales manager spent his 1995 annual salary.

(a) Represent this information on a pie chart.

(b) Find his savings at the end of the year if his annual salary was N60,000.00.

(a) Given that \(\sin x = \frac{5}{13}, 0° \leq x \leq 90°\), find \(\frac{\cos x – 2 \sin x }{2\tan x}\).

(b) 

 The diagram represents the vertical cross-section of a mountain with height NQ standing on a horizontal ground PRN. If the angles of elevation of the top of the mountain from P and R are 30° and 70° respectively and PR = 500m, calculate, correct to 3 significant figures :

(i) |QP| ; (ii) the height of the mountain.

(a) The 6th term of an A.P is 35 and the 13th term is 77. Find the 20th term.

(b)  

The Venn diagram represents three subsets P, Q and R of the universal set U. Copy the Venn diagram. Shade and indicate the regions represented by (i) \(P \cap Q’ \cap R\) ; (ii) \(P’ \cap Q \cap R’\).

(a) Copy and complete the binary multiplication table:

(b) Convert \(11.011_{two}\)  to a number in base ten.

(c) Simplify \(\frac{9.6 \times 10^{18}}{0.24 \times 10^{5}}\) and express your answer in the form \(P \times 10^{m}\) where 1 < P < 10 and m is an integer.

A bag contains 3 white, 6 red, 5 blue identical balls. A ball is picked at random from bag. What is the probability that is either white or blue?

What is the probability of having an odd number in a single throw of a fair die with the faces numbered 1,2,3,4,5,6?

The table shows the scores of a group of students in a test. If the average score is 3.5, find the value of x

A bag contains red, black and green identical balls. A ball is picked and replaced. The table shows the result of 100 trials. Find the experimental probability of picking a green ball.

The graph is the cumulative frequency curve for the weight distribution of 100 workers in a factory. Which of the points P,Q,R,S and T indicates the median weight?

Two sides of a triangle are perpendicular. If the two sides are 8cm and 6cm, calculate correct to the nearest degree, the smallest angle of the triangle.

Cos 65^o has the same value as

lf sin θ= \(\frac{-1}{2}\), find all the values of θ between 0° and 360°.

Express the true bearing of 250° as a compass bearing