Teams P and Q are involved in a game of football. What is the probability that the game ends in a draw?
- A. 2/3
- B. 1/2
- C. 1/3
- D. 1/4
Given the scores: 4, 7, 8, 11, 13, 8 with corresponding frequencies: 3, 5, 2, 7, 2, 1 respectively. The mean score is
- A. 7.0
- B. 8.7
- C. 9.5
- D. 11.0
Given the scores: 4, 7, 8, 11, 13, 8 with corresponding frequencies: 3, 5, 2, 7, 2, 1 respectively. Find the square of the mode.
- A. 49
- B. 121
- C. 25
- D. 64
Find the dimensions of a rectangle of greatest area which has a fixed perimeter p.
- A. square of sides p
- B. square of sides 2p
- C. square of sides (p/2)
- D. square of sides (p/4)
If y = x sinx, find dy/dx when x = ฯ/2.
- A. -ฯ/2
- B. -1
- C. 1
- D. ฯ/2
Find the rate of change of the volume, V of a sphere with respect to its radius, r when r = 1.
- A. 12ฯ
- B. 4ฯ
- C. 24ฯ
- D. 8ฯ
Find the area bounded by the curves y = 4 – x2 and y = 2x + 1
- A. 20(1/3) sq. units
- B. 20(2/3) sq. units
- C. 10(2/3) sq. units
- D. 10(1/3) sq. units
Differentiate \((2x+5)^{2} (x-4)\) with respect to x.
- A. 4(2x+5)(x-4)
- B. 4(2x+5)(4x-3)
- C. (2x+5)(2x-13)
- D. (2x+5)(6x-11)
Evaluate \(\int 2(2x – 3)^{\frac{2}{3}} \mathrm d x\)
- A. 3/5(2x-3)5/3 + k
- B. 6/5(2x-3)5/3 + k
- C. 2x-3+k
- D. 2(2x-3)+k
If the gradient of the curve y = 2kx2 + x + 1 at x = 1 is 9, find k.
- A. 4
- B. 3
- C. 2
- D. 1
The chord ST of a circle is equal to the radius, r, of the circle. Find the length of arc ST.
- A. ฯr/6
- B. ฯr/2
- C. ฯr/12
- D. ฯr/3
Find the locus of a point which moves such that its distance from the line y = 4 is a constant, k.
- A. y = 4 \(\pm\) k
- B. y = k \(\pm\) 4
- C. y = 4 + k
- D. y = k - 4
A cylindrical tank has a capacity of 3080 m3. What is the depth of the tank if the diameter of its base is 14 m?
(Take pi = 22/7)
- A. 23 m
- B. 25 m
- C. 20 m
- D. 22 m
The bearings of P and Q from a common point N are 020ยฐ and 300ยฐ respectively. If P and Q are also equidistant from N, find the bearing of P from Q.
- A. 040ยฐ
- B. 070ยฐ
- C. 280ยฐ
- D. 320ยฐ
P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius.
- A. 6.5 units
- B. 13.0 units
- C. 3.5 units
- D. 7.0 units
Find the number of sides of a regular polygon whose interior angle is twice the exterior angle.
- A. 6
- B. 2
- C. 3
- D. 8
Find the value of P if the line joining (P, 4) and (6, -2) is perpendicular to the line joining (2, P) and (-1, 3).
- A. 4
- B. 6
- C. 3
- D. 0
A straight line makes an angle of 30ยฐ with the positive x-axis and cuts the y-axis at y = 5. Find the equation of the straight line.
- A. y = (x/10) + 5
- B. y = x + 5
- C. โ3y = - x + 5โ3
- D. โ3y = x + 5โ3
A point P moves such that it is equidistant from Points Q and R. Find QR when PR = 8cm and angle PRQ = 30ยฐ
- A. 4โ3cm
- B. 8cm
- C. 8โ3cm
- D. 4cm
A sector of a circle of radius 7.2cm which subtends an angle of 300ยฐ at the centre is used to form a cone. What is the radius of the base of the cone?
- A. 8cm
- B. 6cm
- C. 9cm
- D. 7cm