If \(E \subseteq G \subseteq U\), where U is the universal set, then the shaded venn diagram representing \(U – E\) or \(E^{c}\) is
- A. I
- B. II
- C. III
- D. IV
The response of 160 pupils in a school asked to indicate their favourite subjects is given in the bar chart above. What percentage of the pupils have English and Health education as the their favourite subjects?
- A. 55%
- B. 52%
- C. 36%
- D. 22%
Find the roots of x\(^3\) – 2x\(^2\) – 5x + 6 = 0
- A. 1, -2, 3
- B. 1, 2, -3,
- C. -1, -2, 3
- D. -1, 2, -3
If x = \(\begin{pmatrix} 1 & 0 & 1 \\ 2 & -1 & 0 \\ -1 & 0 & 1\end{pmatrix}\) and y = \(\begin{pmatrix} -1 & 1 & 2 \\ 0 & -1 & -1 \\ 2 & -1 & 1\end{pmatrix}\)
find 2x – y
- A. \(\begin{pmatrix} 3 & -1 & 0 \\ 4 & -3 & -1 \\ -4 & 1 & 1\end{pmatrix}\)
- B. \(\begin{pmatrix} 3 & -1 & 0 \\ 4 & -1 & 1 \\ -4 & 1 & 1\end{pmatrix}\)
- C. \(\begin{pmatrix} 3 & -1 & 0 \\ 4 & -3 & 1 \\ -4 & 1 & 1\end{pmatrix}\)
- D. \(\begin{pmatrix} 3 & -1 & 0 \\ 4 & 1 & 1 \\ -4 & -1 & 1\end{pmatrix}\)
Find p, q for which \(\begin{pmatrix} 2p & 8 \\ 3 & -5q \end{pmatrix}\)\(\begin{pmatrix} 1 \\ 2\end{pmatrix}\) = \(\begin{pmatrix}24 \\ -17\end{pmatrix}\)
- A. -4
- B. 45
- C. 4,2
- D. 2
How many terms of the series 3, -6, +12, – 24, + ….. are needed to make a total of 1 – 2\(^8\)?
- A. 12
- B. 10
- C. 9
- D. 8
If y = x\(^2\) – x – 12, find the range of values of x for which y \( \geq \) 0
- A. x < -3 0r x > 4
- B. x \( \leq \) -3 or x \( \geq \) 4
- C. -3 < x \( \geq \) 4
- D. -3 \( \leq \) x \( \leq \) 4
If \(T = 2\pi \sqrt{\frac{l}{g}}\), make g the subject of the formula
- A. (4π l2) / T
- B. (4π2l) / T2
- C. (4π2l2) / T2
- D. (2π√l) / T
The sum of the first n positive integers is
- A. 1/2 n(n-1)
- B. n(n+1)
- C. n(n-1)
- D. 1/2 n(n+1)
The cost of renovating a 6 m square room is N540. What is the cost of renovating a 9 m square room?
- A. N1215
- B. N720
- C. N1620
- D. N810
Solve the inequalities for which \(\frac{x+4}{3}-\frac{x-3}{2} < 4\)
- A. x < 7
- B. x > -7
- C. x < -7
- D. x > 7
Find the value of k if the expression kx3 + x2 – 5x – 2 leaves a remainder 2 when it is divided by 2x + 1
- A. 10
- B. 8
- C. -10
- D. -8
A binary operation * on the set of rational numbers is defined as \(x \ast y = \frac{x^2 – y^2}{2xy}\). Find \(-5 \ast 3\)
- A. \(\frac{-8}{15}\)
- B. \(\frac{8}{15}\)
- C. \(\frac{17}{15}\)
- D. \(\frac{-17}{15}\)
If p varies inversely as the cube of q and q varies directly as the square of r, what is the relationship between p and r?
- A. p varies directly as r3
- B. p varies inversely as r6
- C. p varies inversely as 6√P
- D. p varies directly as r6
A binary operation \(\oplus\) defined on the set of real number is such that x\(\oplus\)y = xy/6 for all x, y ∈ R. Find the inverse of 20 under this operation when the identity element is 6
- A. 1/12
- B. 10/3
- C. 1/20
- D. 9/5
The solution set of the shaded area above is
- A. y ≥ 0, y ≥ x and y + x ≤ 4
- B. y ≤ x, y + x ≤ 4
- C. y + x ≥ 4, y ≤ x
- D. y ≤ x, y + x ≤ 4 and y ≥ 0
In the diagram above, PQ = 10 cm, PS = 8 cm and ∠PSR is 60o while ∠SRQ is a right angle. Find SR
- A. 14 cm
- B. 14√3 cm
- C. 10 cm
- D. 10√3 cm
If the locus of the points which are equidistant from point P and Q meets line PQ at point N, then PN equals
- A. NQ
- B. 1/4NQ
- C. 2NQ
- D. 1/2NQ
PQRSTW is a regular hexagon and QS intersects RT at V. Calculate ∠TVS
- A. 120o
- B. 90o
- C. 30o
- D. 60o
What is the locus of points equidistant from the lines ax + by + c = 0?
- A. A line bx - ay +q = 0
- B. A line ax - by +q = 0
- C. A line bx + ay +q = 0
- D. A line ax + by +q = 0
In the diagram above, POQ is a diameter of the circle PQRS. If ∠PSR = 145°, find x°
- A. 55o
- B. 45o
- C. 35o
- D. 25o