### SECTION I (50 Marks)

Answer all questions in this section
1.

A form four mathematics teacher originally worked out the mean mark of her fourty students to be fourty one. After correction of the quiz. She added some marks to Timina, Chobola and Cheloti in the ration of 5:2:3 respectively. If the new mean marks for the students increased by 1.5 determine how many marks Cheloti was added than Chobola.

3 marks

2.

Simplify completely

3 marks

3.

Use logarithms to evaluate

4 marks

4.

In 100m race there are three main competitors namely Simiyu, Ondiek and Kamau. Simiyu is three times likely to win as Ondiek, while Ondiek is twice as likely to win as Kamau. Find the probability that

a) Ondiek wins the race (2mks)

b) Either Simiyu or Kamau (1mk)

3 marks

5.

PQR is an equilateral triangle of sides 3cm. S is a variable point on the same side of PQ as R and on the same plane such that <PSQ=300. Locate by construction the possible location of S (use a ruler and a pair of compasses only)

3 marks

6.

A point P divides AB in the ratio 7: -5 where A (2,-3, 4) and B (-4, 7,-2). Find the coordinates of P

2 marks

7.

Make Q the subject of the formula

3 marks

8.

The 2nd, 4th and 7th terms of an AP are the first 3 consecutive terms of a GP. If the common difference of the AP is 2 ,

find

a) The common ratio (2mks)
b) The sum of the first eight terms of the G.P. (3mks)

5 marks

9.

3 marks

10.

a) Find the expansion in ascending powers of x of

b) Hence evaluate (0.99)7 to four significant figures. (2mks)

4 marks

11.

. A field is 10m longer than its width. The area is 7200m2. What is the width? (4mks)

4 marks

12.

The matrix is a singular matrix, find the values of x

3 marks

13.

Water flows from a tap of diameter 7cm at a speed of 5m/s into a rectangular tank of length 5.5m by 3m and height 4.2m. If the tank was initially half full at 6.00pm.Find at what time the tank was full if no water was running out of the tank.

3 marks

14.

Solve the equation for

3 marks

15.

The overall grade (A) attained by a student is directly proportional to the teacher’s effort (t), square of students effort (s) and the general discipline level (d) of the school. A student doubled his effort; teacher went further by 5% but the school discipline dropped by 40%. Find the percentage change in the overall grade

3 marks

16.

2 marks

### SECTION II (50 Marks)

Answer ONLY five questions in this section
17.

. The table below shows income Tax rates

Faith earns a monthly basic salary of Ksh 45,000 and she is also given taxable allowances amounting to Ksh 20480 per month.

a) Calculate Faiths’ gross income tax per month. (4mks)

b) Faith is entitled to a personal tax relief of Ksh 1162. Determine her net income per month. (2mks)

c) Faith received 50% increase in her total income; calculate the corresponding percentage increase on the net income tax. (4mks)

10 marks

18.

The figure below shows points on the earth’s surface

a) State the positions of A, B, C and D in coordinate form. (2mks)

b) An aircraft flies from A to B along latitude 400N, B to C. along longitude 300E, C to D along latitude 400S. Calculate to 4 S.f the total distance it covered .(Take radius of the earth =6371km) (5mks)

c) If the aircraft leaves A at 8.00am at a speed of 720km/h to B. At what local time is it expected at B? (3mks)

10 marks

19.

. The table below shows the marks scored by eighty Form 4 students in a mathematics test

a) Calculate

i) Mean mark. (3mks)

ii) Lower quartile (2mks)

b) On the grid provided draw the cumulative frequency curve to represent the above distribution. (3mks)

c) From the graph estimate the i) 4th decile (1mk)

ii) Range of marks of the middle 70% of the students. (1mk)

10 marks

20.

. a) Complete the table below giving your values correct to 2 decimal places.

b) Plot on the same axes the graph of y=Sin x and y= 2 sin (3x- 30) 2cm rep 150 on x-axis and 2cm to rep 0.5 unit y-axis.

c) Describe the transformation that maps y=Sin x onto y=2Sin (3x-30) (2mks)

d) Use the graph of y= 2Sin (3x-30) to solve the equation 2 sin (3x-30)= -0.5 (1mk)

10 marks

21.

The figure below shows a solid of pyramid with a square top of side 4cm and a square base of side 6cm. The slant edge of the frustrum is 4.5cm

a) Calculate the volume of the frustrum. (6mks)

b) Calculate the angle between i) Line AF and the base FGHE (2mks)

ii) Plane BCHG and base EFGH. (2mks)

10 marks

22.

In a Chemistry form 4 classof the class are girls and the rest are boys,of the boys and

of the girls are right handed while the rest are left handed. The probability that a right –handed student breaks a conical flask in any practical session is and the correspondingprobability for a left handed student isThe probabilities are independent of the
students’ sex.

a) Represent the above information on a tree diagram . (2mks)

b) Determine the probability that a student chosen at random from the class is left handed and does not break a conical flask in simplest form. ( 2mks )

c) Determine the probability that the flask is broken in any Chemistry practical session in simplest form. (3mks)

d) Determine the probability that a conical flask is not broken by a right handed student in simplest form. (3mks)

10 marks

23.

In the diagram TCS is a tangent and DA is a diameter ,AB=BC and <DAC=380

Find

a) <TCD (1mk)

b) < ACS (2mks)

c) <BCA (2mks)

d) <BCS (1mk)

The radius of the circle is 10cm e) Find CA (2mks)

f) Find BC (2mks)

10 marks

24.

Kibabii university has two types of buses a big bus type X with a capacity of 52 passengers and a minibus type Y with a capacity of 28 passengers. Bungoma high school wishes to take 364 students for a tour. They have to use at most 10 buses. The high school should use at least each type of buses.

a) Form all the possible inequalities which will represent the above information. (3mks)

b) On the grid provided draw the inequalities and shade the unwanted region. (3mks)

c) The charges for hiring the vehicles are

Type x Ksh25, 000

Type y Ksh 20,000

Use your graph to determine the number of buses of each type that should be hired to maximize the income of kibabii university. (2mks)

Determine the maximum income. (2mks)

10 marks

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