Express 75° in radians, leaving your answer in terms of \(\pi\).
- A. \(\frac{5\pi}{12}\)
- B. \(\frac{3\pi}{4}\)
- C. \(\frac{5\pi}{6}\)
- D. \(\frac{7\pi}{6}\)
A binary operation * is defined on the set of real numbers R, by a* b = -1. Find the identity element under the operation *.
- A. -1
- B. 0
- C. 1
- D. 2
Simplify \(\frac{x^{3n + 1}}{x^{2n + \frac{5}{2}}(x^{2n – 3})^{\frac{1}{2}}}\)
- A. \(0\)
- B. \(-\frac{1}{2}\)
- C. \(1\)
- D. \(10\)
The diagram above is a velocity- time graph of a moving object. Calculate the distance travelled when the acceleration is zero.
- A. 300 m
- B. 90 m
- C. 150 m
- D. 210 m
From the diagram above, \(h[g(3)]\) is
- A. s
- B. \(\beta\)
- C. \({s, \beta}\)
- D. \({s, w, \beta}\)
From the diagram above, which of the following represents the vector V in component form?
- A. \(-5\sqrt{3} i + 5j\)
- B. \(3i + 3\sqrt{3}j\)
- C. \(i + 2\sqrt{3}j\)
- D. \(-2\sqrt{3}i - j\)
The angle of a sector of a circle is 0.9 radians. If the radius of the circle is 4cm, find the length of the arc of the sector.
- A. 3.6 cm
- B. 7.6 cm
- C. 8.0 cm
- D. 11.6 cm
The distance s in metres covered by a particle in t seconds is \(s = \frac{3}{2}t^{2} – 3t\). Find its acceleration.
- A. \(1 ms^{-2}\)
- B. \(2 ms^{-2}\)
- C. \(3 ms^{-2}\)
- D. \(4 ms^{-2}\)
A box contains 4 red and 3 blue identical balls. If two are picked at random, one after the other without replacement, find the probability that one is red and the other is blue.
- A. \(\frac{4}{7}\)
- B. \(\frac{2}{7}\)
- C. \(\frac{1}{7}\)
- D. \(\frac{1}{12}\)
Find the acute angle between the lines 2x + y = 4 and -3x + y + 7 = 0.
- A. 40°
- B. 44°
- C. 45°
- D. 54°
Find the number of different arrangements of the word IKOTITINA.
- A. 30240
- B. 60840
- C. 120960
- D. 362880
A straight line makes intercepts of -3 and 2 on the x- and y- axes respectively. Find the equation of the line.
- A. 2x + 3y + 6 = 0
- B. 3x - 2y - 6 = 0
- C. -3x + 2y - 6 = 0
- D. -2x + 3y - 6 =0
Find the constant term in the binomial expansion of \((2x – \frac{3}{x})^{8}\).
- A. 90720
- B. 1296
- C. 1120
- D. 672
Find the values of x at the point of intersection of the curve \(y = x^{2} + 2x – 3\) and the lines \(y + x = 1\).
- A. (1, -2)
- B. (0, 4)
- C. (2, -3)
- D. (1, -4)
If P(x – 3) + Q(x + 1) = 2x + 3, find the value of (P + Q).
- A. 0
- B. 1
- C. 2
- D. 3
A fair die is tossed twice. Find the probability of obtaining a 3 and a 5.
- A. \(\frac{5}{12}\)
- B. \(\frac{2}{3}\)
- C. \(\frac{1}{18}\)
- D. \(\frac{1}{36}\)
Which of the following is nor a measure of central tendency?
- A. Mean
- B. Variance
- C. Median
- D. Mode
Given that \(^{n}P_{r} = 90\) and \(^{n}C_{r} = 15\), find the value of r.
- A. 2
- B. 3
- C. 5
- D. 6
In computing the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers and obtained 20 as the mean. Find the correct mean
- A. 19
- B. 21
- C. 23
- D. 24
Find the unit vector in the direction of the vector \(-12i + 5j\).
- A. \(\frac{-12i}{13} - \frac{5j}{13}\)
- B. \(\frac{-1i}{13} + \frac{5j}{13}\)
- C. \(\frac{-12i}{13} + \frac{5j}{13}\)
- D. \(\frac{-5i}{13} + \frac{12j}{13}\)