Write the decimal number 39 to base 2
- A. 100111 base 2
- B. 110111 base 2
- C. 111001 base 2
- D. 100101 base 2
- E. 19.5 base 2
If x varies inversely as y, and y varies directly as the square root of z, and z varies directly \(\frac{1}{w^2}\) write down in words how x varies with w
- A. x varies inversely as w2
- B. x varies directly as w2
- C. x varies directly as w
- D. x varies inversely as w
- E. x varies directly as square root of w
A cylindrical motor of height 12cm has uniform thickness of 2cm. If the diameter of its outer cross section is 10cm, Find the volume of the constituent material. (take \(\pi\) = \(\frac{22}{7}\)
- A. \(\frac{6600}{7}\)cm3
- B. 270cm3
- C. 660cm3
- D. \(\frac{4224}{7}\)cm3
- E. \(\frac{1980}{7}\)cm3
If a function is defined by f(x + 1) = 3×2 – x + 4, Find f(0).
- A. 4
- B. 6
- C. 9
- D. 8
- E. 2
The expression x\(^3\) – 4x\(^2\) + cx + d is such that x + 1 is its factor, and its value is 1 when x is -2. Find c and d.
- A. c = 4 and d = -9
- B. c = -4 and d = 9
- C. c = -20 and d = -15
- D. c = 20 and d = -15
- E. c = -20 and d = 15
Find the missing numerator \(\frac{5}{x + 1}\) – \(\frac{3}{1 – x}\) – \(\frac{7x – 1}{x^2 – 1}\) = \(\frac{?}{x + 1}\).
- A. -1
- B. x - 1
- C. \(\frac{3(1 - 5x)}{x + 1}\)
- D. 1
- E. 3(1 - 5x)
Simplify 102 + log105
- A. 500
- B. 2 log10 5
- C. 10
- D. 25
- E. log105 x 10100
Given log 2 = 0.69, log3 = 1, 10 and log7 = 1.90, all to a fixed base, find log 10.5 to the same base without using tables.
- A. 1.03
- B. 2.31
- C. 3.69
- D. 10.5
- E. 25
Solve the equation for the positive values of \(\theta\) less than 360o. 3 tan \(\theta\) + 2 = -1
- A. 135o or 315o
- B. 45o or 135o
- C. 315o or 180o
- D. 315v + 45o
- E. 360o or 315o
Find the area of the curved surface of a cone whose base radius is 6cm and whose height is 8cm. (take \(\pi\) = \(\frac{22}{7}\))
- A. 188.57cm2
- B. 1320cm2
- C. 188cm2
- D. 188.08cm2
- E. 10cm2
Simplify the given expression \(\sqrt{\frac{1 – cos x}{1 + cos x}}\)
- A. \(\frac{1 - cos x}{sin x}\)
- B. 1 - cos x
- C. sin x
- D. 1 + cos x
- E. \(\frac{1 + cos x}{sin x}\)
Solve the system of equation 2\(^{x + y}\) = 32, \(3^{3y – x}\) = 27
- A. (3, 2)
- B. (-3, 2)
- C. (3, -2)
- D. (-3, -2)
- E. (2, 2)
If it is given that \(5^{x + 1} + 5^x = 150\), then the value of x is equal to
- A. 3
- B. 4
- C. 1
- D. 2
- E. \(\frac{1}{2}\)
Find the solution of the equation x + 2\(\sqrt{x} – 8\) = 0
- A. (4, 16)
- B. (2, 4)
- C. (4, 1)
- D. (1, 16)
- E. (16, 16)
What will be the value of k so that the quadratic equation kx2 – 4x + 1 = 0 has two equal roots?
- A. 2
- B. 3
- C. 4
- D. 8
- E. \(\frac{1}{4}\)
(\(\frac{x^a}{x^b}\))a + b = (\(\frac{x^{a + b}}{x^{a – b}}\))\(\frac{a^2}{b}\)
- A. x-a2
- B. xb2
- C. xa2 - b2
- D. \(\frac{1}{x^{a2 + b2}}\)
- E. xb2 - a2
Find the product of (2\(\sqrt{y} – 3y\)) and (3y + 2\(\sqrt{y}\))
- A. 4y = y2
- B. 4y + 9y2
- C. 4y - 9y2
- D. -4y - 9y2
- E. 2y + y2
A pentagon has four of its angles equal. If the size of the fifth angle is 60o, Find the size of each of the four equal angles.
- A. 60o
- B. 108o
- C. 120o
- D. 150o
- E. None of the above
In triangle FGH, < G = 90º, < H = 60º, while in triangle XYZ, < X = 60º and < Y = 30º. Form XYZ write down the ratio equal to \(\frac{FG}{FH}\)
- A. \(\frac{YX}{ZX}\)
- B. \(\frac{YX}{YZ}\)
- C. \(\frac{ZX}{YZ}\)
- D. \(\frac{YZ}{XY}\)
A set of data contains a total of 130 items which are divided into six groups for display on a pie chart. If one group contains 26 items, then the sector representing this group on the pie chart contains an angle xo at the centre of the circle where x is
- A. 36o
- B. 60o
- C. 70o
- D. 72o
- E. 75o
In a school, there are 35 students in class 2A and 40 in class 2B. The mean score for class 2 in an English Literature examination is 60.0 and that for 2B in the same paper is 52.5. Find, to one place of decimal, the mean for the combined classes
- A. 2.5
- B. 56.0
- C. 56.2
- D. 56.3
- E. 6.5