JAMB Mathematics 2012 Past Questions

Convert 72₆ to a number in base three

Simply \(\frac{2\frac{2}{3} \times 1\frac{1}{2}}{4\frac{4}{5}}\)

Evaluate \(\frac{21}{9}\) to 3 significant figures

A man earns N3,500 per month out of which he spends 15% on his children's education. If he spends additional N1,950 on food, how much does he have left?

If 27^{x + 2} \(\div\) 9^{x + 1} = 3^2x, find x

If log₃x² = -8, what is x?

Simplify \((\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2\)

If P is a set of all prime factors of 30 and Q is a set of all factors of 18 less than 10, find P \(\cap\) Q

In a class of 46 students, 22 play football and 26 play volleyball. If 3 students play both games, how many play neither?

Make 'n' the subject of the formula if w = \(\frac{v(2 + cn)}{1 - cn}\)

Find the remainder when 2x³ - 11x² + 8x - 1 is divided by x + 3

Solve for x and y in the equations below
x² - y² = 4
x + y = 2

If y varies directly as \(\sqrt{n}\) and y = 4 when n = 4, find y when n = 1\(\frac{7}{9}\)

U is inversely proportional to the cube of V and U = 81 when V = 2. Find U when V = 3

The value of y for which \(\frac{1}{5}y + \frac{1}{5} < \frac{1}{2}y + \frac{2}{5}\) is

Find the range of values of m which satisfy (m - 3)(m - 4) < 0

The nth term of a sequence is n² - 6n - 4. Find the sum of the 3rd and 4th terms.

The sum to infinity of a geometric progression is \(-\frac{1}{10}\) and the first term is \(-\frac{1}{8}\). Find the common ratio of the progression.

The binary operation * is defined on the set of integers such that p * q = pq + p - q. Find 2 * (3 * 4)

The binary operation on the set of real numbers is defined by m*n = \(\frac{mn}{2}\) for all m, n \(\in\) R. If the identity element is 2, find the inverse of -5

If \(\begin{vmatrix} 5 & 3 \\ x & 2 \end{vmatrix}\) = \(\begin{vmatrix} 3 & 5 \\ 4 & 5 \end{vmatrix}\), find the value of x

Given that I₃ is a unit matrix of order 3, find |I₃|

The angles of a polygon are given by x, 2x, 3x, 4x and 5x respectively. Find the value of x.

Calculate the volume of a cuboid of length 0.76cm, breadth 2.6cm and height 0.82cm.

The locus of a point equidistant from the intersection of lines 3x - 7y + 7 = 0 and 4x - 6y + 1 = 0 is a

The gradient of the straight line joining the points P(5, -7) and Q(-2, -3) is

The distance between the point (4, 3) and the intersection of y = 2x + 4 and y = 7 - x is

Find the equation of the line through the points (-2, 1) and (-\(\frac{1}{2}\), 4)

If angle \(\theta\) is 135^o, evaluate cos\(\theta\)

If y = x² - \(\frac{1}{x}\), find \(\frac{\delta y}{\delta x}\)

Evaluate \(\int^2_1(x^2 - 4x)dx\)

Evaluate \(\int^{\frac{\pi}{4}}_0sec^2 \theta d \theta\)

The mean of seven numbers is 96. If an eighth number is added, the mean becomes 112. Find the eighth number.

Find the median of 2,3,7,3,4,5,8,9,9,4,5,3,4,2,4 and 5

Find the range of 4,9,6,3,2,8,10 and 11

Find the standard deviation of 2,3,8,10 and 12

Evaluate ⁿ⁺¹C_n-2 If n =15

In how many ways can the letters of the word TOTALITY be arranged?

The probability that a student passes a physics test is \(\frac{2}{3}\). If he takes three physics tests, what is the probability that he passes two of the tests?

The probabilities that a man and his wife live for 80 years are \(\frac{2}{3}\) and \(\frac{3}{5}\) respectively. Find the probability that at least one of them will live up to 80 years

The shaded region above is represented by
the equation

In diagram above, QR//TU, < PQR = 80^o and
< PSU = 95^o. Calculate < SUT.

In the diagram above, PQR is a circle centre
O. If < QPR is XO, find < QRP.

Find the area of the trapezium above.

The grades of 36 students in a class test are
as shown in the pie chart above. How many
students have excellent?

The bar chart above shows the distribution
of marks in a class test. If the pass mark is 5,
what percentage of students failed the
test?