What is the length of an arc of a circle that substends 2\(\frac{1}{2}\) radians at the centre when the raduis of the circle = \(\frac{k}{k + 1}\) + \(\frac{k + 1}{k}\) then
- A. p< 0
- B. p\(\geq\) 0
- C. p \(\leq\) 0
- D. p < 1
- E. p > 0
Solve the given equation \((\log_{3} x)^{2} – 6(\log_{3} x) + 9 = 0\)
- A. 27
- B. 9
- C. \(\frac{1}{27}\)
- D. 18
- E. 81
The sum of the root of a quadratic equation is \(\frac{5}{2}\) and the product of its root is 4. The quadratic equation is
- A. x + 8x2 - 5 = 0
- B. 2x2 - 5x + 8 = 0
- C. 2x2 - 8x + 5 = 0
- D. x2 + 8x - 5 = 0
What is the size of an exterior angle of a regular pentagon?
- A. 36o
- B. 60o
- C. 72o
- D. 120o
- E. 360o
The difference between 4\(\frac{5}{7}\) and 2\(\frac{1}{4}\) is greater than sum of \(\frac{1}{14}\) and 1\(\frac{1}{2}\) by
- A. \(\frac{23}{28}\)
- B. \(\frac{24}{28}\)
- C. \(\frac{50}{56}\)
- D. \(\frac{27}{28}\)
- E. \(\frac{48}{56}\)
A baking recipe calls for 2.5kg of sugar and 4.5kg of flour. With this recipe some cakes were baked using 24.5kg of a mixture of sugar and flour. How much sugar was used?
- A. 12.25kg
- B. 6.75kg
- C. 8.75kg
- D. 15.75kg
- E. 8.25kg
Multiply x2 + x + 1 by x2 – x + 1
- A. x4 - x + x2
- B. x4 - x2 + x2
- C. x4 + x2 + 1
- D. x4 + x2
If b = a + cp and r = ab + \(\frac{1}{2}\)cp2, express b\(^2\) in terms of a, c, r.
- A. b2 = aV + 2cr
- B. b2 = ar + 2c2r
- C. b2 = a2 = \(\frac{1}{2}\) cr2
- D. b2 = \(\frac{1}{2}\)ar2 + c
- E. b2 = 2cr - a2
Simplify T = \(\frac{4R_2}{R_1^{-1} + R_2^{-1} + 4R_3^{-1}}\)
- A. \(\frac{4R_1 \times R_2 R_3}{R_2R_3 + R_1R_3 + 4R_1 R_2}\)
- B. \(\frac{R_1 R_2 R_3}{R_2R_3 + R_1R_2 + 4R_1 R_2}\)
- C. \(\frac{16R_1 R_2 R_3}{R_2R_3 + R_1R_2 + R_1 R_2}\)
- D. \(\frac{4R_1 R_2 R_3}{4R_2R_3 + R_1R_2 + 4R_1 R_2}\)
The first term of an Arithmetic progression is 3 and the fifth term is 9. Find the number of terms in the progression if the sum is 81
- A. 12
- B. 27
- C. 9
- D. 4
- E. 36
Show that \(\frac{\sin 2x}{1 + \cos x}\) + \(\frac{sin2 x}{1 – cos x}\) is
- A. sin x
- B. cos2x
- C. 2
- D. 3
The area of a circular plate is one-sixteenth the surface area of a ball of a ball, If the area of the plate is given as P cm2, then the radius of the ball is
- A. \(\frac{2P}{\pi}\)
- B. \(\frac{P}{\sqrt{\pi}}\)
- C. \(\frac{P}{\sqrt{2\pi}}\)
- D. 2\(\frac{P}{\pi}\)
The difference between the length and width of a rectangle is 6cm and the area is 135cm2. What is the length?
- A. 25cm
- B. 18cm
- C. 15cm
- D. 24cm
- E. 27cm
The positive root of t in the following equation, 4t2 + 7t – 1 = 0, correct to 4 places of decimal, is
- A. 1.0622
- B. 10.6225
- C. 0.1328
- D. 0.3218
- E. 2.0132
Evaluate \(\frac{6.3 \times 10^5}{8.1 \times 10^3}\) to 3 significant fiqures
- A. 77.80
- B. 778.0
- C. 7.870
- D. 8.770
- E. 88.70
The number 25 when converted from the tens and units base to the binary base (base two) is one of the following
- A. 10011
- B. 111011
- C. 111000
- D. 11001
- E. 110011
simplify \(\frac{6^{2n + 1} \times 9^n \times 4^{2n}}{18^n \times 2^n \times 12^{2n}}\)
- A. 32n
- B. 3 x 23n - 1
- C. 2n
- D. 6
- E. 1
Two cars X and Y start at the same point and travel towards a point P which is 150km away. If the average speed of Y is 60km per hour and x arrives at P 25 minutes earlier than Y. What is the average speed of X?
- A. 51\(\frac{3}{7}\)km per hour
- B. 72km per hour
- C. 37\(\frac{1}{2}\) km per hour
- D. 66km per hour
- E. 75km per hour
Given that 10x = 0.2 and log102 = 0.3010, find x
- A. -1.3010
- B. -0.6990
- C. 0.6990
- D. 1.3010
- E. 0.02
If \(\log_{2} y = 3 – \log_{2} x^{\frac{3}{2}}\), find y when x = 4.
- A. 8
- B. \(\sqrt{65}\)
- C. 4\(\sqrt{2}\)
- D. 3
- E. 1
In \(\bigtriangleup\)XYZ, XY = 3cm, XZ = 5cm and YZ = 7cm. If the bisector of XYZ meets XZ at W, what is the length of XW?
- A. 1.5cm
- B. 2.5cm
- C. 3cm
- D. 4cm
- E. None of the above