For what value of k is 4x\(^2\) – 12x + k, a perfect square?
- A. -9
- B. \(\frac{-9}{4}\)
- C. \(\frac{9}{4}\)
- D. 9
If f(x) = 4x\(^3\) + px\(^2\) + 7x – 23 is divided by (2x -5), the remainder is 7. find the value of p
- A. -7.0
- B. -8.0
- C. -9.6
- D. 9
If α and β are the roots of 3x\(^2\) – 7x + 6 = 0, find \(\frac{1}{α}\) + \(\frac{1}{β}\)
- A. \(\frac{7}{6}\)
- B. \(\frac{7}{3}\)
- C. \(\frac{14}{5}\)
- D. \(\frac{14}{3}\)
In how many ways can 8 persons be seated on a bench if only three seats are available?
- A. 100
- B. 125
- C. 336
- D. 427
Using binomial expansion of ( 1 + x)\(^6\) = 1 + 6x + 15x\(^2\) + 20x\(^3\) + 6x\(^5\) + x)\(^6\), find, correct to three decimal places, the value of (1.998))\(^6\)
- A. 63.616
- B. 63.167
- C. 62.628
- D. 62.629
g(x) = 2x + 3 and f(x) = 3x\(^2\) – 2x + 4
find f {g (-3)}.
- A. 37
- B. 1
- C. -3
- D. -179
Solve (\(\frac{1}{9}\))\(^{x + 2}\) = 243\(^{x – 2}\)
- A. \(\frac{7}{5}\)
- B. \(\frac{6}{7}\)
- C. \(\frac{-7}{6}\)
- D. \(\frac{-6}{7}\)
Simplify \(\frac{1}{3}\) log8 + \(\frac{1}{3}\) log 64 – 2 log6
- A. log \(\frac{2}{7}\)
- B. log 2
- C. log \(\frac{2}{9}\)
- D. log 9
Given that M = \(\begin{pmatrix} 3 & 2 \\ -1 & 4 \end{pmatrix}\) and N = \(\begin{pmatrix} 5 & 6 \\ -2 & -3 \end{pmatrix}\), calculate (3M – 2N)
- A. \(\begin{pmatrix} 1 & 6 \\ 1 & 18 \end{pmatrix}\)
- B. \(\begin{pmatrix} -1 & -6 \\ 1 & 18 \end{pmatrix}\)
- C. \(\begin{pmatrix} 1 & 6 \\ -1 & -18 \end{pmatrix}\)
- D. \(\begin{pmatrix} -1 & -6 \\ -1 & -18 \end{pmatrix}\)
For what range of values of x is x\(^2\) – 2x – 3 ≤ 0
- A. {x: -1 ≤ x ≤ 3}
- B. { x: -3 ≤ x ≤ 1}
- C. { x: -3 ≤ x ≤ -1}
- D. { x: 1 ≤ x ≤ 3}
Simplify ( \(\frac{1}{2 – √3}\) + \(\frac{2}{2 + √3}\) )\(^{-1}\)
- A. \(\frac{-1}{33}\)(6 + √3)
- B. \(\frac{-1}{33}\)(6 - √3)
- C. \(\frac{1}{33}\)(6 + √3)
- D. \(\frac{1}{33}\)(6 - √3)
Consider the statements:
x: Birds fly
y: The sky is blue
Which of the following statements can be represented as x \(\to\) y?
- A. When birds fly, the sky is blue
- B. Birds fly if and only if the sky is blue?
- C. Either the bird is flying or the sky is blue.
- D. When the sky is blue, the bird flies.
If log 5(\(\frac{125x^3}{\sqrt[ 3 ] {y}}\) is expressed in the values of p, q and k respectively.
- A. 3, \(\frac{-1}{3}\), 5
- B. \(\frac{-1}{3}\), 3, 5
- C. 3, \(\frac{-1}{3}\), 3
- D. 3, \(\frac{-1}{3}\), 3
If the sum of the roots of 2x\(^2\) + 5mx + n = 0 is 5, find the value of m.
- A. - 2.5
- B. - 2.0
- C. 2.0
- D. 2.5
Find the unit vector in the direction opposite to the resultant of forces. F\(_1\) = (-2i – 3j) and F\(_2\) = (5i – j)
- A. \(\frac{1}{5}\)(-3i - 4j)
- B. \(\frac{1}{5}\)(-3i + 4j)
- C. \(\frac{1}{5}\)(3i - 4j)
- D. \(\frac{1}{5}\)(3i + 4j)
P(3,4) and Q(-3, -4) are two points in a plane. Find the gradient of the line that is normal to the line PQ.
- A. \(\frac{4}{3}\)
- B. \(\frac{3}{4}\)
- C. \(\frac{-3}{4}\)
- D. \(\frac{-4}{3}\)
The distance(s) in metres covered by a particle in motion at any time, t seconds, is given by S =120t – 16t\(^2\). Find in metres, the distance covered by the body before coming to rest.
- A. 220
- B. 222
- C. 223
- D. 225
A bag contains 5 red and 5 blue identical balls. Three balls are selected at random without replacement. Determine the probability of selecting balls alternating in color.
- A. \(\frac{7}{18}\)
- B. \(\frac{5}{18}\)
- C. \(\frac{5}{36}\)
- D. \(\frac{1}{36}\)
The variables x and y are such that y =2x\(^3\) – 2x\(^2\) – 5x + 5. Calculate the corresponding change in y and x changes from 2.00 to 2.05.
- A. 0.58
- B. 0.95
- C. 1.48
- D. 1.95
A three-digit odd number less than 500 is to be formed from 1,2,3,4 and 5. If repetition of digits is allowed, in how many ways can this be done?
- A. 125
- B. 75
- C. 60
- D. 36
Calculate the variance of \(\sqrt{2}\), (1 + \(\sqrt{2}\)) and (2 + \(\sqrt{2}\))
- A. 0
- B. \(\sqrt{\frac{2}{3}}\)
- C. \(\frac{2}{3}\)
- D. 2