Mathematics Past Questions And Answers
Given that \(\frac{\mathrm d y}{\mathrm d x} = 3x^{2} - 4\) and y = 6 when x = 3, find the equation for y.
- A. \(x^{3} - 4x - 9\)
- B. \(x^{3} - 4x + 9\)
- C. \(x^{3} + 4x - 9\)
- D. \(x^{3} + 4x + 9\)
The equation of a circle is given by \(x^{2} + y^{2} - 4x - 2y - 3\). Find the radius and the coordinates of its centre.
- A. \(3, (-1, 2)\)
- B. \(2\sqrt{2}, (2, -1)\)
- C. \(2\sqrt{2}, (2, 1)\)
- D. \(9, (2, 1)\)
A bag contains 3 white, 6 red, 5 blue identical balls. A ball is picked at random from bag. What is the probability that is either white or blue?
- A. 9/14
- B. 4/7
- C. 3/7
- D. 5/14
If \(tan x = \frac{1}{\sqrt{3}}\), find cos x - sin x such that \(0^o \leq x \leq 90^o\)
- A. \(\frac{\sqrt{3}+1}{2}\)
- B. \(\frac{2}{\sqrt{3}+1}\)
- C. \(\frac{\sqrt{3}-1}{2}\)
- D. \(\frac{2}{\sqrt{3}-1}\)
Factorise 27p2x2 - 48y2.
- A. 9(3px - 4y)2
- B. 3(3px - 4y)(3px - 4y)
- C. 9(px - 4y)(3p x + 4y)
- D. 3(3px -4y)(3px +4y)
I.S∩T∩W=S
II. S ∪ T ∪ W = W
III. T ∩ W = S
If S⊂T⊂W, which of the above statements are true?
- A. I and II
- B. I and III
- C. II and III
- D. I, II and III
If x2 + kx + \(\frac{16}{9}\) is a perfect square, find the value of k
- A. \(\frac{8}{3}\)
- B. \(\frac{7}{3}\)
- C. \(\frac{5}{3}\)
- D. \(\frac{2}{3}\)
If tan x = \(2\frac{2}{5}\), find the value of sin x; 0 \(\leq\) x \(\leq\) 90o
- A. 5/13
- B. 5/12
- C. 144/169
- D. 12/13
The radius of a sphere is increasing at a rate \(3cm s^{-1}\). Find the rate of increase in the surface area, when the radius is 2cm.
- A. \(8\pi cm^{2}s^{-1}\)
- B. \(16\pi cm^{2}s^{-1}\)
- C. \(24\pi cm^{2}s^{-1}\)
- D. \(48\pi cm^{2}s^{-1}\)
\(\begin{array}{c|c}
Age(years) & 13 & 14 & 15 & 16 & 17 \\
\hline
Frequency & 10 & 24 & 8 & 5 & 3
\end{array}\)
The table shows the ages of students in a club. How many students are in the club?
- A. 50
- B. 55
- C. 60
- D. 65