Question 1

1. Arrange the given numbers in ascending order of magnitude: 0.6 and 20% of 13.
2. By listing the multiples of 2, 3 and 5, find the L.C.M of these numbers.

Question 2

1. Find the values of x and y that satisfy the equations:
   4 (original equation text was truncated in source — please check if any symbols missing).
2. Solve the equation 4 + 3\log_a x = \log_a 24.

Question 3

1. Evaluate the expression: 13 - 2 \times 3 + 14 + (2 + 5).
2. Given the universal set U = {15, 30, 45, 60, 75} and the subsets A = {15, 45} and B = {30, 60}, find (A \cup B)' and represent this information using a Venn diagram below.

Question 4

1. Show that the triangle whose vertices are A(4, -4), B(-6, -2) and C(2, 6) is an isosceles triangle.
2. In a class of 50 students, 35 are boys and 15 are girls. If a student is chosen at random, what is the probability that he is a boy?
3. Jonika has two shirts (blue, red) and three trousers (black, green, yellow). Using a tree diagram, find the probability that he will put on a blue shirt and black trouser. (A tree diagram is drawn below.)

Question 5

A man walks 4 km from village P to village Q and then 3 km to village R. Village Q is N60°E of village P; and village R is N30°W of village Q. Represent this information on a well labeled diagram and find the resultant displacement of the man from P to R.

Question 6

1. In the following figure, \(\angle RPQ = \angle PRQ\) and \(\angle SPQ = \angle SP R\). Find the size of the angle \(\angle RPS\). (Figure placeholder)
2. A rectangular field is 72 m long and 40 m wide. If a triangular field with a base of 60 m has an area which is equal to the area of the rectangular field, find the height of the triangular field.

Question 7

1. Anna walks 24 km every day. Compute in metres the distance she walks in 2 days.
2. A dealer sells mattresses whose buying price (BP) is directly proportional to the selling price (SP). If SP and BP of one mattress are Tshs 20,000 and 18,000 respectively, find (i) the equation relating BP and SP and (ii) the new selling price when the buying price is increased by 15%.
3. Ally and Jane shared 64,000 shillings in the ratio 3:5 respectively. Find the difference between their shares.

Question 8

Mr. Mrisho recorded the transactions of his business in February 2022 in a cash account. Using the given cash account (data in original paper), extract the trial balance as at 28th February, 2022.

Question 9

1. Write down the first four terms of a sequence whose general term is n(2n - 1). Explain whether it is an arithmetic progression or a geometric progression.
2. The sum of the first eleven terms of an arithmetic progression is 517. If its first term is 7, find the sum of the fourth and ninth terms.
3. A rectangular plot is 40 m long. If the length of its diagonal is 50 m, how wide is the plot?

Question 10

1. Given that A is an acute angle for which 13 \cos A - 5 = 0, find the value of \tan A without using mathematical tables.
2. A triangular pond ABC is such that AB = 8 m, AC = 5 m and \(\angle BAC = 60^\circ\). Determine the length of BC.

Question 11

If x = -3 and x = 2 are solutions of the equation ax^2 + bx + c = 0 where a, b and c are integers, determine the values of a, b and c. (Then) Solve the inequality 10 - x < 5( x + 10 ), where x is an integer. Hence state the first four values of x that satisfy the inequality.

Given the frequency distribution of 30 students (class intervals and frequencies), calculate median, mean (to 4 s.f.), draw a histogram and estimate mode.