2013 Mathematics Jamb Past Questions CBT

Convert 27₁₀ to another number in base three.

3 girls share a number of apples in the ratio 5:3:2. If the highest share is 40 apples, find the smallest share.

Evaluate \(  \frac{1.25 \: \times \: 0.025}{0.05} \)

correct to 1 decimal place.

Calculate the time taken for ₦ 3000 to earn ₦ 600 if invested at 8% simple interest.

Simplify \( \frac{3^{-5n}}{9^{1\:-\:n}} \scriptsize \: \times \: 27^{n\: +\:1}\)

If log₁₀4 = 0.6021

Evaluate \( \scriptsize \log 4^{\frac{1}{3}} \)

Simplify \(\frac{\sqrt{5}\left(\sqrt{147} \: – \: \sqrt{12} \right)}{\sqrt{15}}\)

P, Q and R are subsets of the universal set U. The Venn diagram showing the relationship \( \scriptsize (P \cap Q) \cup R \: is \)

If P = {x: x is odd, – 1 < x ≤ 20} and Q = {y: y is prime; -2< y < 25}, find P n Q

If \( \scriptsize S = \sqrt{t^2 \: – \: 4t \: + \: 4} \)

find t in terms of S

If x – 4 is a factor of \( \scriptsize x^2 \: -\: x \: – \: k \)

then k is

The remainder when 6p³ – p² – 47p + 30 is divided by p – 3 is

P varies jointly as m and u, and varies inversely as q. Given that p = 4, m = 3 and u = 2 and q = 1, find the value of p when m = 6, u = 4 and q = ⁸/₅

If r varies inversely as the square root of s and t, how does s vary with r and t?

Evaluate 3(x + 2) > 6(x + 3)

The graph shown is correctly represented by

Solve for x : |x – 2|<3

If the sum of the first two terms of a G.P. is 3 and the sum of the second and the third terms is -6. Find the sum of the first term and the common ratio.

The nth term of the progression \( \normalsize\frac{4}{2} \scriptsize, \: \normalsize\frac{7}{3} \scriptsize, \: \normalsize\frac{10}{4} \scriptsize, \: \normalsize\frac{13}{5} \scriptsize, \:  is \)

If a binary operation * is defined by x * y = x + 2y, find 2*(3*4)

If P = \( \scriptsize \begin{pmatrix} 5 & 3 \\ 2 & 1 \end{pmatrix} \)

and Q = \( \scriptsize \begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix} \)

Find 2P + Q

Find the inverse of \( \scriptsize \begin{pmatrix} 5 & 3 \\ 6 & 4 \end{pmatrix} \)

In the diagram given, find the value of x.

The value x in the figure given is

If the angles of a quadrilateral are (3 y + 10)°, (2 y +30)°, (y + 20)° and 4y°, find the value of y.

A square tile has side 30cm. How many of these tiles will cover a rectangular floor of length 7.2m and width 4.2m?

Find the length of a chord which subtends an angle of 90° at the centre of a circle whose radius is 8 cm.

A chord of a circle subtends an angle of 120° at the centre of a circle of diameter 4√3 cm. Calculate the area of the major sector.

The locus of the points which is equidistant from the line PQ forms a

If the midpoint of the line PQ is (2, 3) and the point P is (-2, 1), find the coordinate of the point Q.

Find the equation of the perpendicular bisector of the line joining P(2, -3) to Q(-5, 1)

In triangle PQR, q = 8 cm, r = 6 cm and cos P = \( \frac{1}{12} \)

Calculate the value of p.

If tanθ = \( \frac{3}{4} \)

find the value of \( \scriptsize sin \theta \: + \: cos \theta \)

If y = x sin x

Find \( \frac{dx}{dy} \)

If y = (2x + 2)³

Find \( \frac{dx}{dy} \)

What is the probability that an integer x (1≤ x ≤ 25) chosen at random is divisible by both 2 and 3?

The radius of a circle is increasing at the rate of 0.02 cms^-1. Find the rate at which the area is increasing when the radius of the circle is 7 cm.

Integrate \(\frac{1\:+\:x}{x^3} \scriptsize dx \)

Evaluate \(\scriptsize \int_{0} ^{\frac{\pi}{2}} \sin x \mathrm d x \)

The bar chart above shows the allotment of time (in minutes) per week for selected subjects in a certain school. What is the total time allocated to the six subjects per week?

In how many ways can a student select 2 subjects from 5 subjects

The pie chart above shows the statistical distribution of 80 students in five subjects in an examination. Calculate how many students offer Mathematics.

Find the mean of t + 2, 2t – 4, 3t + 2 and 2t.

The mean of seven numbers is 10. If six of the numbers are 2, 4, 8, 14, 16 and 18, find the mode.

\( \scriptsize \begin{array}{c|c}Age & 20 & 25 & 30 & 35 & 40 & 45 \\ \hline \text{No. of people} & 3 & 5 & 1 & 1 & 2 & 3 \end{array} \)

Calculate the median age of the frequency distribution in the table above

If the variance of 3 + x, 6. 4,  x, and 7 – x is 4 and the mean is 5. Find the standard deviation.

\(\scriptsize \begin{array}{c|c} Score & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline Frequency & 1 & 0 & 7 & 5 & 2 & 3 & 1 & 1 \end{array} \)

The table above shows the scores of 20 students in further mathematics test. What is the range of the distribution?

In how many ways can three seats be occupied if 5 people are willing to sit?

A basket contains 9 apples, 8 bananas, and 7 oranges. A fruit is picked from the basket, find the probability that it is neither an apple nor orange.