The gradient of a curve is given by 3x\(^2\) – 8x + 2. If the curve passes through P(0, 4), find the equation of the curve.
- A. y = x\(^3\) - 4x\(^2\) + 2x + 4
- B. y = x\(^3\) - 4x\(^2\) + 2x + 2
- C. y = 3x\(^3\) - 4x\(^2\) + 2x + 4
- D. y = 3x\(^3\) - 4x\(^2\) + 2x - 2
Find, correct to the nearest degree, the acute angle between 3x – y – 5 = 0, and 7x – y – 3 = 0
- A. 10\(^0\)
- B. 11\(^0\)
- C. 24\(^0\)
- D. 27\(^0\)
The mean of four numbers is 5 and the mean of another three numbers is 12. Find the mean of the seven numbers.
- A. 10
- B. 9
- C. 8
- D. 7
If y\(^2\) + 2xy – 8 = 0, find \(\frac{dy}{dx}\)
- A. \(\frac{- y}{y + x}\)
- B. \(\frac{2y + y}{y}\)
- C. \(\frac{2y - x}{-y}\)
- D. \(\frac{y}{2y - x}\)
In triangle XYZ, |XY| = 10cm, |YZ| = 9 cm and |XZ| = 7 cm. If XZY = \(\alpha\), find the value of cos \(\alpha\).
- A. \(\frac{11}{15}\)
- B. \(\frac{17}{35}\)
- C. \(\frac{5}{21}\)
- D. \(\frac{7}{32}\)
In how many ways can 12 people be seated on a bench if only 5 spaces are available?
- A. 95040
- B. 11880
- C. 792
- D. 495
A body of mass 80 kg moving with a velocity of 25 ) ms\(^{-1}\) collides with another moving in the opposite direction at 10 ms\(^{-1}\). After collision, both bodies moved with a common velocity of 12.8 ms\(^{-1}\). Calculate, correct to the nearest whole number, the mass of the second body.
- A. 33 kg
- B. 38 kg
- C. 43 kg
- D. 47 kg
If \(\begin{pmatrix} 6 & 4 \\ 7 & 5 \end{pmatrix}\) \(\begin{pmatrix} 2 \\ m \end{pmatrix}\) = 2\(\begin{pmatrix} 12 \\ 14.5 \end{pmatrix}\), find the value of m.
- A. 5
- B. 4
- C. 3
- D. 2
How many three-digit numbers can be formed from the digits 2, 3, 4, 5, 6, 7, and 8 if repetition is not allowed?
- A. 420
- B. 210
- C. 120
- D. 35
Given that f(x) = x\(^2\) + 3x + 1, find the value of x at the turning point.
- A. 2
- B. 1\(\frac{1}{2}\)
- C. -1\(\frac{1}{2}\)
- D. -2
Find the coefficient of y\(^2\) in the binomial expansion of (y – 2x)\(^5\).
- A. 80x\(^3\)
- B. 80x\(^2\)
- C. - 80x\(^2\)
- D. - 80x\(^3\)
The point P(-3, 5) lies on a line which is perpendicular to 2x – 4y + 3 = 0. Find the equation of the line.
- A. y - 2x - 11 = 0
- B. y - 2x - 1 = 0
- C. y + 2x + 1 = 0
- D. y + 2x + 11 = 0
A particle of mass 40 kg is kept on a smooth plane inclined at an angle of 30º to the horizontal by a force up the plane. find, correct to one decimal place, the magnitude of the normal reaction of the plane of the particle.[Take g = 10 ms\(^{-2}\)]
- A. 146.0N
- B. 200.6N
- C. 346.4N
- D. 400.3N
Find the range of values of x for which 9x – 1 > 14x\(^2\)
- A. \(\frac{1}{7}\) < x < \(\frac{1}{2}\)
- B. -\(\frac{1}{7}\) < x < \(\frac{1}{2}\)
- C. x \(\leq\) -\(\frac{1}{7}\) or x \(\geq\) \(\frac{1}{2}\)
- D. x \(\leq\) \(\frac{1}{7}\) or x \(\geq\) \(\frac{1}{2}\)
A particle starts from rest accelerates at 4ms\(^{-2}\). Find the distance covered after 4 seconds.
- A. 12 m
- B. 14 m
- C. 18 m
- D. 32 m
Given that M and N are two sets. Which of the following is the same as (M ∩ N)‘?
- A. M' ∩ N'
- B. M' U N
- C. M ∩ N'
- D. M' U N'
A body of mass 42 kg increases its speed from 15 ms\(^{-1}\) to 43 ms\(^{-1}\) in 12 seconds. Find the force acting on the body.
- A. 203N
- B. 150N
- C. 98N
- D. 52N
A fair dice is thrown twice. Find the probability that the sum obtained will be a factor of 12.
- A. \(\frac{1}{3}\)
- B. \(\frac{5}{18}\)
- C. \(\frac{1}{9}\)
- D. \(\frac{7}{18}\)
If kx\(^2\) is a term in the binomial expansion of (1 – 2x)\(^4\), find the value of k.
- A. -24
- B. -8
- C. 8
- D. 24
The gradient of the curve y = mx\(^2\) + 3x – 1 at the point (-1, 1) is 9. Find the value of m
- A. - 3
- B. 3
- C. \(\frac{-5}{4}\)
- D. \(\frac{5}{4}\)
If r = i + 2j and n = -i + 3j, find |2n – r|.
- A. 3.6
- B. 4.0
- C. 5.0
- D. 8.5