(a) Solve the inequality: $\frac{1 + 4x}{2}$ -$\frac{5 + 2x}{7}$ < x -2

(b) If x: y = 3: 5, find the value of $\frac{2x^2 - y^2}{y^2 - x^2}$

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) 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.

(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.
 

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) 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.
 

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.

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.

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?
 

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, -$\frac{1}{2}$