Find the rate of change of the volume, V of a sphere with respect to its radius, r when r = 1.
- A. 12π
- B. 4π
- C. 24π
- D. 8π
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. πr/6
- B. πr/2
- C. πr/12
- D. πr/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 020° and 300° respectively. If P and Q are also equidistant from N, find the bearing of P from Q.
- A. 040°
- B. 070°
- C. 280°
- D. 320°
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 30° 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. √3y = - x + 5√3
- D. √3y = x + 5√3
A point P moves such that it is equidistant from Points Q and R. Find QR when PR = 8cm and angle PRQ = 30°
- A. 4√3cm
- B. 8cm
- C. 8√3cm
- D. 4cm
A sector of a circle of radius 7.2cm which subtends an angle of 300° 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
Factorize 4x2 – 9y2 + 20x + 25
- A. (2x -3y + 5)(2x - 3y - 5)
- B. (2x - 3y)(2x + 3y)
- C. (2x - 3y +5)(2x + 3y + 5)
- D. (2x + 5)(2x - 9y +5)
The sixth term of an A.P is half of its twelfth term. The first term of the A.P is equal to
- A. zero
- B. half of the common difference
- C. double the common difference
- D. the common difference
An operation * is defined on the set of real numbers by a*b = a + b + 1. If the identity elements is -1, find the inverse of the element 2 under *.
- A. 4
- B. zero
- C. -2
- D. -4
Solve the equations
m2 + n2 = 29
m + n = 7
- A. (2, 3) and ( 3, 5)
- B. (2, 5) and (5, 2)
- C. (5, 2) and ( 5, 3)
- D. (5, 3) and (3, 5)
If two graphs y = px\(^2\) + q and y = 2x\(^2\) -1 intersect at x = 2, find the value of p in terms q.
- A. \(\frac{q-8}{7}\)
- B. \(\frac{7-q}{4}\)
- C. \(\frac{8-q}{2}\)
- D. \(\frac{7+q}{8}\)