(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.
NOT DRAWN TO SCALE
In the diagram, is a chord of a circle with centre 0. 22.42 cm and the perimeter of triangle MON is 55.6 cm. Calculate, correct to the nearest degree. < MON.
(b) T is equidistant from P and Q. The bearing of P from T is 60\(^o\) and the bearing of Q from T is 130\(^o\).
(i) Illustrate the information on a diagram.
(ii) Find the bearing of Q from P.
(a) Fred bought a car for $5,600.00 and later sold it at 90% of the cost price. He spent $1,310.00 out of the amount received and invested the rest at 6% per annum simple interest. Calculate the interest earned in 3 years.
(b) Solve the equations 2\(^x\)(4\(^{-7}\)) = 2 and 3\(^{-x}\)(9\(^{2y}\)) = 3 simultaneously.
The cost of dinner for a group of tourist is partly constant and partly varies as the number of tourists present. It costs $740.00 when 20 tourists were present and $960.00 when the number of tourists increased by 10. Find the cost of the dinner when only 15 tourists were present.
(a) Without using mathematical tables or calculator, simplify: \(\frac{log_28 + \log_216 – 4 \log_22}{\log_416}\)
(b) If 1342\(_{five}\) – 241\(_{five}\) = x\(_{ten}\), find the value of x.
(a) If logo a = 1.3010 and log\(_{10}\)b – 1.4771. find the value of ab
(b)
In the diagram. O is the centre of the circle,< ACB = 39\(^o\) and < CBE = 62\(^o\). Find: (i) the interior angle AOC;
(ii) angle BAC.
The second, fourth and sixth terms of an Arithmetic Progression (AP.) are x – 1, x + 1 and 7 respectively. Find the:
(a) common difference;
(b) first term;
(c) value of x.
(a) Solve the inequality: \(\frac{1 + 4x}{2}\) -\(\frac{5 + 2x}{7}\) < x -2
(b) If x: y = 3: 5, find the value of \(\frac{2x^2 – y^2}{y^2 – x^2}\)