Find the value of the derivative of y = 3x\(^2\) (2x +1) with respect to x at the point x = 2.
- A. 72
- B. 84
- C. 96
- D. 120
Find the equation of the normal to the curve y= 2x\(^2\) – 5x + 10 at P(1, 7).
- A. y+x-3 =0
- B. y-x+6=0
- C. y - x - 6=0
- D. y -x+ 3 =0
The gradient ofy= 3x\(^2\) + 11x + 7 at P(x.y) is -1. Find the coordinates of P.
- A. (-3, -2)
- B. (-2,-3)
- C. (-2,3)
A bag contains 8 red, 4 blue and 2 green identical balls. Two balls are drawn randomly from the bag without replacement. Find the probability that the balls drawn are red and blue.
A. 12/91 B. C. D.
- A. 12/91
- B. 16/91
- C. 30/91
- D. 32/91
Consider the following statements:
X: Benita is polite
y: Benita is neat
z: Benita is intelligent
Which of the following symbolizes the statement: “Benita is neat if and only if she is neither polite nor intelligent”?
- A. y⟺ ~x v z
- B. y⟺ ~x v ~z
- C. y⟺ ~x ^ ~z
- D. y⟺ ~x ^ z
If 2i +pj and 4i -2j are perpendicular, find the value of p.
- A. 2
- B. 3
- C. 4
- D. 5
If √5 cosx + √15sinx = 0, for 0° < x < 360°, find the values of x.
- A. 30° and 150°
- B. 150° and 210°
- C. 150° and 330°
- D. 210° and 330°
A committee consists of 6 boys and 4 girls. In how many ways can a sub-committee consisting of 3 boys and 2 girls be formed if one particular boy and one particular girl must be on the sub-committee?
- A. 120
- B. 80
- C. 56
- D. 30
The first term of an AP is 4 and the sum of the first three terms is 18. Find the product of the first three terms
- A. 292
- B. 272
- C. 192
- D. 172
If sin x = \(\frac{12}{13}\) and sin y = \(\frac{4}{5}\), where x and y are acute angles, find cos (x + y)
- A. \(\frac{48}{65}\)
- B. \(\frac{13}{15}\)
- C. \(\frac{-33}{65}\)
- D. \(\frac{-48}{65}\)
If ( 1- 2x)\(^4\) = 1 + px + qx\(^2\) – 32x\(^3\) + 16\(^4\), find the value of (q – p)
- A. -32
- B. -16
- C. 16
- D. 32
A stone is thrown vertically upward and distance, S metres after t seconds is given by S = 12t + \(\frac{5}{2t^2}\) – t\(^3\).
Calculate the distance travelled in the third second.
- A. 5.5m
- B. 14.5m
- C. 26.0m
- D. 30.0m
A stone is thrown vertically upward and distance, S metres after t seconds is given by S = 12t + \(\frac{5}{2t^2}\) – t\(^3\).
Calculate the maximum height reached.
- A. 418.5m
- B. 56.0m
- C. 31.5m
- D. 30.0m
In △PQR, \(\overline{PQ}\) = 5i – 2j and \(\overline{QR}\) = 4i + 3j. Find \(\overline{RP}\).
- A. -i - 5j
- B. -9 - j
- C. i + 5j
- D. -9i + j
Three forces, F\(_1\) (8N, 030°), F\(_2\) (10N, 150° ) and F\(_3\) ( KN, 240° )are in equilibrium. Find the value of N
- A. 5√3
- B. 6√2
- C. 6√3
- D. 9√3
If 2y\(^2\) + 7 = 3y – xy, find \(\frac{dy}{dx}\)
- A. \(\frac{-y}{4x+y-3}\)
- B. \(\frac{y}{4x+y-3}\)
- C. \(\frac{y}{4x+x-3}\)
- D. \(\frac{ -y}{4y+ x -3}\)
A fair die is tossed 60 times and the results are recorded in the table
| Number of die | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 15 | 10 | 14 | 2 | 8 | 11 |
Find the probability of obtaining a prime number.
- A. \(\frac{7}{30}\)
- B. \(\frac{1}{6}\)
- C. \(\frac{7}{15}\)
- D. \(\frac{8}{15}\)
A body of mass 15kg is placed on a smooth plane which is inclined at 60° to the horizontal. If the box is at rest,
calculate the normal reaction to the plane. [ Take g = 10m/s\(^2\) ]
- A. 129.9N
- B. 75N
- C. 60.0N
- D. 7.5N
Given that P = { x: 0 ≤ x ≤ 36, x is a factor of 36 divisible by 3} and Q = { x: 0 ≤ x ≤ 36, x is an even number and a perfect square}, find P n Q.
- A. {1,4,9,36}
- B. {3,9.36}
- C. {9,36}
- D. {36}
Find the inverse of \(\begin{pmatrix} 4 & 2 \\ -3 & -2 \end{pmatrix}\)
- A. \(\begin{pmatrix} 1 & 1 \\ -1.5 & -2 \end{pmatrix}\)
- B. \(\begin{pmatrix} 1 & -1 \\ 1.5 & -2 \end{pmatrix}\)
- C. \(\begin{pmatrix} -2 & 1 \\ 1.5 & 1 \end{pmatrix}\)
- D. \(\begin{pmatrix} -2 & -1 \\ 1.5 & 1 \end{pmatrix}\)
A binary operation * is defined on the set of real numbers, R, by
P * q = \(\frac{q^2 – p^2}{2pq}\). Find 3 * 2
- A. \(\frac{13}{12}\)
- B. \(\frac{5}{12}\)
- C. -\(\frac{5}{12}\)
- D. \(\frac{-1}{2}\)