Find the area bounded by the curve y = x(2-x). The x-axis, x = 0 and x = 2.
- A. 4 sq units
- B. 2 sq units
- C. \(\frac{4}{3}sq\hspace{1 mm}units\)
- D. \(\frac{1}{3}sq\hspace{1 mm}units\)
Find the equation of the locus of a point P(x,y) such that PV = PW, where V = (1,1) and W = (3,5)
- A. 2x + 2y = 9
- B. 2x + 3y = 8
- C. 2x + y = 9
- D. x + 2y = 8
From a point P, the bearings of two points Q and R are N670W and N230E respectively. If the bearing of R from Q is N680E and PQ = 150m, calculate PR
- A. 120m
- B. 140m
- C. 150m
- D. 160m
Find the tangent to the acute angle between the lines 2x + y = 3 and 3x – 2y = 5.
- A. -7/4
- B. 7/8
- C. 7/4
- D. 7/2
In ∆MNO, MN = 6 units, MO = 4 units and NO = 12 units. If the bisector of angle M meets NO at P, calculate NP.
- A. 4.8 units
- B. 7.2 units
- C. 8.0 units
- D. 18.0 units
A man 1.7m tall observes a bird on top of a tree at an angle of 30°. if the distance between the man’s head and the bird is 25m, what is the height of the tree?
- A. 26.7m
- B. 14.2m
- C. \(1.7+(25\frac{\sqrt{3}}{3}m\)
- D. \(1.7+(25\frac{\sqrt{2}}{2}m\)
Find a positive value of \(\alpha\) if the coordinate of the centre of a circle x\(^2\) + y\(^2\) – 2\(\alpha\)x + 4y – \(\alpha\) = 0 is (\(\alpha\), -2) and the radius is 4 units.
- A. 1
- B. 2
- C. 3
- D. 4
Divide 4x\(^3\) – 3x + 1 by 2x – 1
- A. 2x2-x+1
- B. 2x2-x-1
- C. 2x2+x+1
- D. 2x2+x-1
The first term of a geometric progression is twice its common ratio. Find the sum of the first two terms of the G.P if its sum to infinity is 8.
- A. 8/5
- B. 8/3
- C. 72/25
- D. 56/9
Express \(\frac{1}{x^{3}-1}\) in partial fractions
- A. \(\frac{1}{3}(\frac{1}{x - 1} - \frac{(x + 2)}{x^{2} + x + 1})\)
- B. \(\frac{1}{3}(\frac{1}{x - 1} - \frac{x - 2}{x^{2} + x + 1})\)
- C. \(\frac{1}{3}(\frac{1}{x - 1} - \frac{(x - 2)}{x^{2} + x + 1})\)
- D. \(\frac{1}{3}(\frac{1}{x - 1} - \frac{(x - 1)}{x^{2} - x - 1})\)
Three consecutive positive integers k, l and m are such that l\(^2\) = 3(k+m). Find the value of m.
- A. 4
- B. 5
- C. 6
- D. 7
Factorize completely \(x^{2} + 2xy + y^{2} + 3x + 3y – 18\).
- A. (x+y+6)(x+y-3)
- B. (x-y-6)(x-y+3)
- C. (x-y+6)(x-y-3)
- D. (x+y-6)(x+y+3)
A binary operation * is defined by a*b = ab+a+b for any real number a and b. if the identity element is zero, find the inverse of 2 under this operation.
- A. 2/3
- B. 1/2
- C. -1/2
- D. -2/3
The sum of two numbers is twice their difference. If the difference of the numbers is P, find the larger of the two numbers
- A. p/2
- B. 3p/2
- C. 5p/2
- D. 3p
If \(m*n = (\frac{m}{n} – \frac{n}{m}\)) for m, n belong to R, evaluate -3*4
- A. \(\frac{-25}{12}\)
- B. \(\frac{-7}{12}\)
- C. \(\frac{7}{12}\)
- D. \(\frac{25}{12}\)
Simplify \(\sqrt{\frac{(0.0023 \times 750)}{(0.00345 \times 1.25)}}\)
- A. 15
- B. 20
- C. 40
- D. 75
If 2\(_9\) x (Y3)\(_9\) = 3\(_5\) x (Y3)\(_5\), find the value of Y.
- A. 4
- B. 3
- C. 2
- D. 1
What is the answer when 2434\(_6\) is divided by 42\(_6\)?
- A. 236
- B. 356
- C. 526
- D. 556
A trader bought 100 oranges at 5 for N1.20, 20 oranges got spoilt and the remaining were sold at 4 for N1.50. Find the percentage gain or loss.
- A. 30% gain
- B. 25% gain
- C. 30% loss
- D. 25% loss
If \(\frac{({a^2b^{-3}c})^{3/4}}{a^{-1}b^4c^5}\) = \(a^p b^q c^r\); what is the value of p+2q?
- A. (5/2)
- B. -(5/4)
- C. -(25/4)
- D. -10
If \(\frac{(a^2 b^{-3}c)^{\frac{3}{4}}}{a^{-1}b^{4}c^{5}}=a^{p} b^{q} c^{r}\) What is the value of p+2q?
- A. (5/2)
- B. -(5/4)
- C. -(25/4)
- D. -10