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Question 1 of 40
The pie chart above represents 400 fruits on display in a grocery store. How many apples are in the store?
Question 2 of 40
The cumulative frequency curve above shows the distribution of the scores of 50 students in an examination. Find the 36th percentile score.
Question 3 of 40
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.
Question 4 of 40
What is the mean deviation of x, 2x, x + 1 and 3x, if their mean is 2?
Question 5 of 40
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?
Question 6 of 40
In how many ways can 9 people be seated if 3 chairs are available?
Question 7 of 40
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?
Question 8 of 40
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.
Question 9 of 40
Determine the value of x for which
\( \scriptsize (x^2\: -\: 1) > 0 \)
Question 10 of 40
Find the range of values of x for which 3x – 7 ≤ 0 and x + 5 > 0.
Question 11 of 40
The sum of the first n terms of the arithmetic progression 5, 11, 17, 23, 29, 35,… is
Question 12 of 40
Find to infinity, the sum of the sequence \( \scriptsize 1, \normalsize \frac{9}{10}\scriptsize, \normalsize\left( \frac{9}{10} \right)^2 \scriptsize, \normalsize\left( \frac{9}{10} \right)^ 3 \scriptsize \: ,………\)
Question 13 of 40
If m*n = n – m + 2 for any real numbers m and n, find the value of 3 * -5.
Question 14 of 40
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.
Question 15 of 40
If Q = \( \scriptsize \left[ \begin{array}{cc} 9 & -2 \\ -7 & 4 \\ \end{array} \right],\)
then |Q| is
Question 16 of 40
If P = \( \scriptsize\begin{pmatrix} x + 3 & x + 2 \\ x + 1 & x \:- \:1 \end{pmatrix}\)
Evaluate x if |P| = -10
Question 17 of 40
What is the size of each interior angle of a 12-sided regular polygon?
Question 18 of 40
A circle of perimeter 28 cm is opened to form a square. What is the maximum possible area of the square?
Question 19 of 40
A chord of a circle of radius 7 cm is 5 cm from the centre of the circle. What is the length of the chord?
Question 20 of 40
A solid metal cube of side 3 cm is placed in a rectangular tank of dimensions 3, 4 and 5 cm. What volume of water can the tank now hold?
Question 21 of 40
The perpendicular bisector of a line XY is the locus of a point _______
Question 22 of 40
The midpoint of P(x, y) and Q(8, 6) is (5, 8). Find x and y.
Question 23 of 40
Find the equation of a line perpendicular to line 2y = 5x + 4 which passes through (4, 2).
Question 24 of 40
In a right-angled triangle, if tan θ = \( \frac{3}{4} \).
What is cos θ – sin θ?
Question 25 of 40
A man walks 100 m due West from a point X to Y, he then walks 100 m due North to a point Z. Find the bearing of X from Z.
Question 26 of 40
The derivative of (2x + 1)(3x + 1) is
Question 27 of 40
The 3rd term of an A.P. is 4x – 2y and the 9th term is 10x – 8y. Find the common difference.
Question 28 of 40
If (x – 1), (x + 1) and (x – 2) are factors of the polynomial ax3 + bx2 + cx – 1
find a, b, c respectively.
Question 29 of 40
Find the inverse of p under the binary operation * defined by p * q = p + q – pq, where p and q are real numbers and zero is the identity.
Question 30 of 40
3y = 4x – 1 and Ky = x + 3 + 3 are equations of two straight lines. If the two lines are perpendicular to each other, find K.
Question 31 of 40
If P and Q are fixed points and X is a point which moves so that XP = XQ, the locus of X
Question 32 of 40
A predator moves in a circle of radius 2 centre (0, 0), while a prey moves along the line y = x.
If 0 ≤ x ≤ 2, at which point(s) will they meet?
Question 33 of 40
Find the minimum value for the function
f(θ) = \( \frac{2}{3\:-\:cos \theta} \)
for \( \scriptsize 0 \leq \theta \leq 2 \pi \)
Question 34 of 40
P is a point on one side of the straight line UV and P moves in the same direction as UV. If the straight line ST is on the locus of P and ΔVUS = 50º, find ΔUST.
Question 35 of 40
In the diagram, EFGH is a circle with centre O. FH is a diameter and GE is a chord which meets FH at right angle at the point N; if NH = 8 cm and EG = 24 cm, calculate FH.
Question 36 of 40
A ship sails a distance of 50 km in the direction S50ºE and then sails a distance of 50 km in the direction N40ºE. Find the bearing of the ship from its original position.
Question 37 of 40
Simplify \(\scriptsize 3\frac{1}{3} \: -\: \left(2 \frac{1}{3} \: \times \: 1\frac{1}{4} \right) \: + \: \frac{3}{5} \)
Question 38 of 40
A father decided to give 20% of his monthly income to his three children as their monthly allowance. The eldest child got 45% of the allowance and the youngest got 25%. How much was the father’s monthly income, if the second child got ₦
Question 39 of 40
If the interest on ₦ ₦ ₦
Question 40 of 40
Three boys shared some oranges. The first received 1 /3 of the oranges and the second received 2 /3 of the remaining. If the third boy received the remaining 12 oranges, how many oranges did they share?
