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
A force of 230N acts in its direction 065\(^o\). Find its horizontal component.
- A. 208.5N
- B. 197.2N
- C. 118.5N
- D. 97.2
In what interval is the function f : x -> 2x – x\(^2\) increasing?
- A. x = 1
- B. x < 1
- C. x > 1
- D. 0 < x < 1
A function f defined by f : x -> x\(^2\) + px + q is such that f(3) = 6 and f(3) = 0. Find the value of q.
- A. - 9
- B. - 6
- C. 15
- D. 21
Which of the following is not an equation of a circle?
- A. 3x\(^2\) +3y\(^2\) + 5x + 7y =5
- B. x\(^2\) + y\(^2\) + 5x + 4y = 0
- C. 5x\(^2\) + 5y\(^2\) - 16 = 0
- D. x\(^2\) - y\(^2\) + 3x - 5y = 2
In how many ways can the letters of the word MEMBER be arranged?
- A. 720
- B. 360
- C. 180
- D. 90
Calculate, correct to two decimal places, the area enclosed by the line 3x – 5y + 4 = 0 and the axes.
- A. 0.50 square units
- B. 0.51 square units
- C. 0.53 square units
- D. 0.54 square units
A circle with centre (5,-4) passes through the point (5, 0). Find its equation.
- A. x\(^2\) + y\(^2\) + 10x + 8y + 25 =0
- B. x\(^2\) + y\(^2\) +10x - 8y - 25 = 0
- C. x\(^2\) + y\(^2\) - 10x + 8y + 25 =0
- D. x\(^2\) + y\(^2\) -10x - 8y - 25 = 0
Find the nth term of the linear sequence (A.P) (5y + 1), ( 2y + 1), (1- y),…
- A. (8 + 3n)y + 1
- B. 8y + 3n + 1
- C. (8 - 3n)y + 1
- D. 8y - 3n + 1
If the binomial expansion of (1 + 3x)\(^6\) is used to evaluate (0.97)\(^6\), find the value of x.
- A. 0.03
- B. 0.01
- C. - 0.01
- D. - 0.03
In which of the following series can be the formula S = \(\frac{a}{1 – r}\) where a is the first term and r is the common ratio, be used to find the sum of all the terms?
- A. 4 + 8 + 16 + 32 + ...
- B. \(\frac{1}{2}\) + 2 \(\frac{1}{2}\) + 12\(\frac{1}{2}\) + 62 \(\frac{1}{2}\) + ..
- C. \(\frac{4}{81}\) + \(\frac{2}{27}\) + \(\frac{1}{9}\) + \(\frac{1}{6}\) + ...
- D. 128 + 64 + 32 + 16 + ...
A stone was dropped from the top of a building 40m high. Find, correct to one decimal place, the time it took the stone to reach the ground. [Take g = 9.8ms\(^{-2}\)]
- A. 2.9.seconds
- B. 2.8 seconds
- C. 2.6 seconds
- D. 1.4 seconds