Mathematics JAMB, WAEC, NECO AND NABTEB Official Past Questions

P and Q are two points on latitude 55°N and their longitudes are 33°W and 20°E respectively. Calculate the distance between P and Q measured along 

(a) the parallel of latitude ;

(b) a great circle. 

[Take \(\pi = \frac{22}{7}\) and radius of the earth = 6400km].

The table below shows the frequency distribution of the marks scored by fifty students in an examination.

(a) Draw the cumulative frequency curve for the distribution.

(b) Use your curve to estimate the : (i) upper quartile; (ii) pass mark if 60% of the students passed.

(a) Copy and complete the following table of values for \(y = 3\sin 2\theta – \cos \theta\).

(b) Using a scale of 2cm to 30° on the \(\theta\) axis and 2cm to 1 unit on the y- axis, draw the graph of \(y = 3 \sin 2\theta – \cos \theta\) for \(0° \leq \theta \leq 180°\).

(c) Use your graph to find the : (i) solution of the equation \(3 \sin 2\theta – \cos \theta = 0\), correct to the nearest degree; (ii) maximum value of y, correct to one decimal place.

(a) What is the 25th term of 5, 9, 13,… ?

(b) Find the 5th term of \(\frac{8}{9}, \frac{-4}{3}, 2, …\).

(c) The 3rd and 6th terms of a G.P are \(48\) and \(14\frac{2}{9}\) respectively. Write down the first four terms of the G.P.

(a) Prove that the angle which an arc of a circle subtends at the centre is twice that which it subtends at any point on the remaining part of the circumference.

(b) 

In the diagram, O is the centre of the circle ACDB. If < CAO = 26° and < AOB = 130°. Calculate : (i) < OBC ; (ii) < COB.

(a) 

In the diagram, BA is parallel to DE. Find the value of x.

(b) Illustrate graphically and shade the region in which inequalities \(y – 2x < 5 ; 2y + x \geq 4 ; y + 2x \leq 10\) are satisfied.

(a)(i) Given that \(\log_{10} 5 = 0.699\) and \(\log_{10} 3 = 0.477\), find \(\log_{10} 45\), without using Mathematical tables.

(ii) Hence, solve \(x^{0.8265} = 45\).

(b) Use Mathematical tables to evaluate \(\sqrt{\frac{2.067}{0.0348 \times 0.538}}\)

A box contains identical balls of which 12 are red, 16 white and 8 blue. Three balls are drawn from the box one after the other without replacement. Find the probability that :

(a) three are red;

(b) the first is blue and the other two are red;

(c) two are white and one is blue.

(a) Simplify \(\frac{3}{m + 2n} – \frac{2}{m – 3n}\)

(b) A number is made up of two digits. The sum of the digits is 11. If the digits are interchanged, the original number is increased by 9. Find the number.

A simple measuring device is used at points X and Y on the same horizontal level to measure the angles of elevation of the peak P of a certain mountain. If X is known to 5,200m above sea level, /XY/ = 4,000m and the measurements of the angles of elevation of P at X and Y are 15° and 35° respectively, find the height of the mountain. (Take \(\tan 15 = 0.3\) and \(\tan 35 = 0.7\))

The universal set \(\varepsilon\) is the set of all integers and the subset P, Q, R of \(\varepsilon\) are given by:

\(P = {x : x < 0} ; Q = {… , -5, -3, -1, 1, 3, 5} ; R = {x : -2 \leq x < 7}\)

(a) Find \(Q \cap R\).

(b) Find \(R’\) where R’ is the complement of R with respect to \(\varepsilon\).

(c) Find \(P’ \cup R’\)

(d) List the members of \((P \cap Q)’\).

(a) Simplify, without using Mathematical tables: \(\log_{10} (\frac{30}{16}) – 2 \log_{10} (\frac{5}{9}) + \log_{10} (\frac{400}{243})\)

(b) Without using Mathematical tables, calculate \(\sqrt{\frac{P}{Q}}\) where \(P = 3.6 \times 10^{-3}\) and \(Q = 2.25 \times 10^{6}\), leaving your answer in standard form.

A die rolled 200 times. The outcome obtained are shown in the table above.

What is the probability of obtaining a number less than 3 ?

A die is rolled 200 times the outcomes obtained are shown in the table below.

Find the probability of obtaining 2.

What is the probability that the total sum of seven would appear in toss of a fair die?

What is the probability of having an even number in a single toss of a fair die?

A fair die is rolled once. What is the probability of obtaining a number less than 3?

What is the probability that an integer selected from the set of integers (20, 21, …., 30) is a prime number?

How many students scored less than 7 marks?

How many student took the examination

The distribution by state of 840 students in the Faculty of Science of a Nigerian University in a certain session is as follows:

In a pie chart drawn to represent this distribution, the angle subtended by Ondo is