In preparing rice cutlets, a cook used 75g of rice, 40g of margarine, 105g of meat and 20g of bread crumbs. Find the angle of the sector which represent meat in a pie chart?
- A. 30\(^o\)
- B. 60\(^o\)
- C. 112.5\(^o\)
- D. 157.5\(^o\)
Simplify \(\frac{324 – 4x^2}{2x + 18}\)
- A. 2(x - 9)
- B. 2(9 + x)
- C. 81 - x\(^2\)
- D. -2(x - 9)
If log\(_{10}\)2 = 0.3010 and log\(_{10}\)3 = 0.4771, eventually without using the logarithm tables, log\(_{10}\)4.5
- A. 0.3010
- B. 0.4771
- C. 0.6532
- D. 0.9542
In a class of 150 students, the sector in a pie chart representing the students offering physics has angle 12\(^o\). How many students are offering physics?
- A. 18
- B. 15
- C. 10
- D. 5
The goals scored by 40 football teams from three league divisions are recorded below
| No of goals | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 4 | 3 | 15 | 16 | 1 | 0 | 1 |
What is the total number of goals scored by all the teams?
- A. 21
- B. 40
- C. 91
- D. 96
A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room
- A. \(\frac{15}{17}\)
- B. \(\frac{8}{17}\)
- C. \(\frac{8}{15}\)
- D. \(\frac{12}{17}\)
What is the circumference of latitude 0\(^o\)S if R is the radius of the earth?
- A. cos \(\theta\)
- B. 2\(\pi\)R cos \(\theta\)
- C. R sin \(\theta\)
- D. 2 \(\pi\) r sin \(\theta\)
Four boys and ten girls can cut a field first in 5 hours. If the boys work at \(\frac{5}{4}\) the rate at which the girls work, how many boys will be needed to cut the field in 3 hours?
- A. 180
- B. 60
- C. 25
- D. 20
Reach each number to two significant figures and then evaluate \(\frac{0.02174 \times 1.2047}{0.023789}\)
- A. 0
- B. 0.9
- C. 1.1
- D. 1.2
Find all real number x which satisfy the inequality \(\frac{1}{3}\) (x + 1) – 1 > \(\frac{1}{5}\)(x + 4)
- A. x < 11
- B. x < -1
- C. x > 6
- D. x > 11
Find the median of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119
- A. 131
- B. 125
- C. 123
- D. 120
Factorise (4a + 3) \(^2\) – (3a – 2)\(^2\)
- A. (a + 1)(a + 5)
- B. (a - 5)(7a - 1)
- C. (a + 5)(7a + 1)
- D. a(7a + 1)
Evaluate (212)\(_3\) – (121)\(_3\) + (222)\(_3\)
- A. (313)\(_3\)
- B. (1000)\(_3\)
- C. (1020)\(_3\)
- D. (1222)\(_3\)
(a)
In the diagram. \(\over{Rs}\) and \(\over{RT}\) are tangent to the circle with centre O, < TUS = 68\(^o\), < SRT = x and < UTO = y. Find the value of x.
(b) Two tanks A and B are filled to capacity with diesel. Tank A holds 600 litres diesel more than tank B. If 100 litres of diesel was pumped cut of each tank, tank A would then contain 3 times as much as tank B. Find the capacity of each tank.
(a) Given that 110\(_x\) – 40\(_{five}\). find the value of x
(b) Simplify \(\frac{15}{\sqrt{75}} + \(\sqrt{108}\) + \(\sqrt{432}\), leaving the answer in the form a\(\sqrt{b}\), where a and b are positive integers.
(a) The curved surface areas of two cones are equal. The base radius of one is 5 cm and its slant height is 12cm. calculate the height of the second cone if its base radius is 6 cm.
(b) Given the matrices A = \(\begin{pmatrix} 2 & 5 \\ -1 & -3 \end{pmatrix}\) and B = \(\begin{pmatrix} 3 & -2 \\ 4 & 1 \end{pmatrix}\), find:
(i) BA;
(ii) the determinant of BA.
(a) Copy and complete the table of values for the relation y = 4x\(^2\) – 8x – 21, for -2.0 \(\leq\) x \(\leq\) 4.0
| x | -2.0 | -1.5 | -1.0 | 0.5 | 0.0 | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 |
| y | 11 | -9 | -21 | -24 | -21 | -9 | 0 |
(b) Using a scale of 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the graph for the relation y = 4x\(^2\) – 8x – 21
(ii) Use the graph to find the solution set of
(\(\alpha\)) 4x\(^2\) – 8x = 3;
(\(\beta\)) 4x\(^2\) – 7x – 21 = 0
A ladder 11m long leans against a vertical wall at an angle of 75\(^o\) to the ground. The ladder is the pushed 0.2 m up the wall.
(a) Illustrate the information in a diagram.
(b) Find correct to the nearest whole number, the:
(i) new angle which the ladder makes with the ground:
(ii) distance the foot of the ladder has moved from its original position.
a) A twenty – kilogram bag of rice is consumed by m number of boys in 10 days. When four more boys joined them, the same quantity of rice lasted only 8 days. If the rate of consumption is the same, find the value of m.
(b) If \(\frac{5}{6}\) of a number is 10 greater than \(\frac{1}{3}\) of it. find the number
(c) Find the equation of the line which passes through the points (2, \(\frac{1}{2}\)) and (-1, -\(\frac{1}{2}\)
A survey of 40 students showed that 23 students study Mathematics, 5 study Mathematics and Physics, 8 study Chemistry and Mathematics, 5 study Physics and Chemistry and 3 study all the three subjects. The number of students who study Physics only is twice the number who study Chemistry only.
(a) Find the number of students who study:
(i) only Physics.
(ii) only one subject
b) What is the probability that a student selected at random studies exactly 2 subjects?
The ages of a group of athletes are as follows: 18, 16. 18,20, 17, 16, 19, 17, 18, 17 and 13. (a) Find the range of the distribution.
(b) Draw a frequency distribution table for the data.
(c) What is the median age?
(d) Calculate, correct to two decimal places, the;
(i) mean age:
(ii) standard deviation.