2009 Mathematics Jamb Past Questions CBT

Subtract 16418₉ from 18630₉

If 55_X + 52_X = 77₁₀, find x

Simplify \(\scriptsize 7 \frac {1}{12} \; – \;  4 \frac {3}{4} \; + \; 2 \frac {1}{2}\)

Evaluate \( \frac {81.81 \; + \;  99.44}{20.09 \; + \; 36.16} \)

Correct to 3 Significant figures

A man bought a second-hand photocopying machine for ₦34,000.

He serviced it at a cost of N2,000 and then sold it at a profit of 15%.

What was the selling price?

A student spent ¹/₅  of his allowance on books, ¹/₃  of the remainder on food, and kept the rest for contingencies. What fraction was kept?

Solve \(\scriptsize 5^{2(x \: -\:  1)}\:  \times \:  5^{x \: +\:  1} = 0.04\)

If log₁₀2 = 0.3010 and log₁₀7 = 0.8451,

evaluate log₁₀280.

Simplify \( \normalsize \frac {5 \: + \:\sqrt{7}}{3\: +\:\sqrt{7}}\)

If X = {n² + 1 : n is a positive integer and 1 ≤ n ≤ 5},
Y = {5n : n is a positive integer and 1 ≤ n ≤ 5},

find x ∩ y

I. S∩T∩W = S

II. S∪T∪W = W

III. T∩W = S

If S⊂T⊂W,

Which of the above statements are true?

If  \( p=\sqrt{\frac{rs^3}{t}}\),express r in terms of p, s and t

A polynomial in x whose roots are ⁴/₃  and  – ³/₅  is

Which of the following equations represents the graph above?

W is directly proportional to U. If W = 5 when U = 3, find when W = ²/₇

Determine the value of x for which (x² – 1) > 0.

Find the range of values of x for which 3x – 7  ≤ 0 and x + 5 > 0

The sum of the first n terms of the arithmetic

progression 5, 11, 17, 23, 29, 35…. is

Find to infinity, the sum of the sequence \(\scriptsize 1,\: \normalsize \frac{9}{10},\: \left(\frac{9}{10}\right)^2,\: \left(\frac{9}{10}\right)^3,…..\)

If m ∗ n = n-(m + 2) for any real numbers m and n, find the value of 3 ∗ (-5)

A binary operation ⊗ defined on the set of integers

is such that m ⊗ n = m + n + mn for all integers m and n.

Find the inverse of -5 under this operation. If the identity element is 0.

If Q is \( \scriptsize \left[ \begin{array}{cc} 9 & -2 \\-7 & 4 \\\end{array} \right]\)

Then |Q| is

If P \(=\scriptsize\left[\begin{array}{cc}x+3 & x+2\\
x+1 & x-1\end{array}\right]\)

evaluate x if |P| = -10

Find the acute angle between the straight lines y = x and y = \( \scriptsize \sqrt{3x} \)

A regular polygon has 150° as the size of each interior angle.

How many sides does it have?

In the figure above , TS//YZ and XY = TY, ∠SYZ = 34^o, ∠TXY = 47^o, find the angle marked x

If the hypotenuse of a right-angled isosceles triangle is 2 cm, what is the area of the triangle?

A chord is drawn 5 cm away from the centre of a circle of radius 13 cm. Calculate the length of the chord

Find the radius of a sphere whose surface area is 154 cm² 

(\( \scriptsize \pi = \normalsize \frac{22}{7}\))

Find the locus of a particle which moves in the first quadrant so that it is equidistant from the lines x= 0 and y= 0 (where k is a constant)

What it is the locus of the mid-point of all chords of length 6cm with a circle of radius 5cm and with center O?

What is the value of p if the gradient of the line joining (-1, p) and (p, 4) is  ²/_3?

What is the value of r if the distance between the points (4, 2) and(1, r) is 3 units?

Find the value of sin 45° – cos 30°

A cliff on the bank of a river is 300 meters high. If the angle of depression of a point on the opposite side of the river is 60^o, find the width of the river.

If y = 3 cos 4x

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

If s = (2 + 3t)(5t – 4), find \(\frac{ds}{dt}\) when t = \(\frac{4}{5}\scriptsize \: secs\)

What value of x will make the function, x(4 – x) a maximum?

The distance traveled by a particle from a fixed point is given as s = (t³ – t² – t + 5) cm. Find the minimum distance that the particle can cover from the fixed point.

Evaluate \( \scriptsize \int sec^2 \theta \: d\theta \)

The distribution above shows the number of days a group of 260 students were absent from school in a particular term. How many students were absent for at least four days in the term?

The histogram above represents the number of candidates that sat for Mathematics examination in a school. How many candidates scored more than 50 marks?

The pie chart above represents 400 fruits on display in a grocery store. How many apples are in the store?

The cumulative frequency curve above shows the distribution of the scores of 50 students in an examination. Find the 36th percentile score.

5, 8, 6 and k occur with frequencies 3, 2, 4, and 1 respectively and have a mean of 5.7. Find the value of k.

What is the mean deviation of x, 2x, x + 1 and 3x, if their mean is 2?

In how many ways can a delegation of 3 be chosen from 5 men and 3 women, if at least 1 man and 1 woman must be included?

In how many ways can 9 people be seated if 3 chairs are available?

The probability of a student passing any examination is \( \frac{2}{3}\). If the student takes three examinations, what is the probability that he will not pass any of them

The table above shows the distribution of marks of students in a test. Find the probability of passing the test if the pass mark is 5.