Consider the statements:
x: The school bus arrived late
y: The student walked down to school
Which of the following can be represented by y β x?
- A. The school bus arrived early and Kate ran to school
- B. Mary walked to school because the school bus arrived late
- C. Either the school bus arrived late or Maryam walked to school
- D. Emmanuella did not go to school because the school bus arrived late
Given that P = {x : 2 β€ x β€ 8} and Q = {x : 4 < x β€ 12} are subsets of the universal set ΞΌ = {x : x β R}, find (P β Q\(^1\)).
- A. {x : 4 < x < 8}
- B. {x : 2 < x β€ 4}
- C. {x : 2 β€ x β€ 4}
- D. {x : 4 β€ x β€ 8}
Find the fifth term in the binomial expansion of \((q + x)^7\).
- A. \(21q^2x^5\)
- B. \(21q^4x^3\)
- C. \(35q^3x^4\)
- D. \(35q^5x^2\)
A particle began to move at \(27 ms^{-1}\) along a straight line with constant retardation of \(9 ms^{-2}\). Calculate the time it took the particle to come to a stop.
- A. 3 sec
- B. 2 sec
- C. 4 sec
- D. 1 sec
Given that M is the midpoint of T (2, 4) and Q (-8, 6), find the length of MQ .
- A. \(β26 units\)
- B. \(β28 units\)
- C. \(β24 units\)
- D. \(β30 units\)
Find the radius of the circle \(2x^2 + 2y^2 – 4x + 5y + 1 = 0\)
- A. \(\frac{\sqrt33}{4}\)
- B. \(\frac{\sqrt5}{6}\)
- C. \(\frac{5}{6}\)
- D. \(\frac{33}{4}\)
The table shows the operation * on the set {x, y, z, w}.
| * | X | Y | Z | W |
| X | Y | Z | X | W |
| Y | Z | W | Y | X |
| Z | X | Y | Z | W |
| W | W | X | W | Z |
Find the identity of the element.
- A. W
- B. Y
- C. Z
- D. X
If\((\frac{1}{9})^{2x-1} = (\frac{1}{81})^{2-3x}\)find the value of x
- A. \(-\frac{5}{8}\)
- B. \(-\frac{3}{4}\)
- C. \(\frac{3}{4}\)
- D. \(-\frac{5}{8}\)
Given that \(sin x = \frac{4}{5}\) and \(cos y = \frac{12}{13}\), where x is an obtuse angle and y is an acute angle, find the value of sin (x – y).
- A. \(\frac{63}{65}\)
- B. \(\frac{48}{65}\)
- C. \(\frac{56}{65}\)
- D. \(\frac{16}{65}\)
Evaluate \(\int^1_0 x(x^2-2)^2 dx\)
- A. \(\frac{6}{7}\)
- B. \(1\frac{1}{6}\)
- C. \(\frac{1}{7}\)
- D. \(3\frac{1}{6}\)
The distance S metres moved by a body in t seconds is given by \(S = 5t^3 – \frac{19}{2} t^2 + 6t – 4\). Calculate the acceleration of the body after 2 seconds
- A. 19 \(ms ^{-2}\)
- B. 21 \(ms ^{-2}\)
- C. 41 \(ms ^{-2}\)
- D. 31 \(ms ^{-2}\)
Find the equation of the normal to the curve y = \(3x^2 + 2\) at point (1, 5).
- A. 6y - x - 29 = 0
- B. 6y + x - 31 = 0
- C. y - 6x - 1 = 0
- D. y - 6x + 1 = 0
Calculate, correct to one decimal place, the angle between 5 i + 12 j and -2 i + 3 j
- A. 56.3ΒΊ
- B. 76.3ΒΊ
- C. 66.4ΒΊ
- D. 54.8ΒΊ