**MATHEMATICS PAPER 1 K.C.S.E 1995 QUESTIONS**

**SECTION 1 (52 MARKS)**

*Answer all the questions in this section*

**MATHEMATICS PAPER 1 K.C.S.E 1995 QUESTIONS**

**SECTION 1 (52 MARKS)**

*Answer all the questions in this section*

1. Without
using logarithms tables evaluate (
3 marks)

384.16 x 0.0625

96.04

2. Simplify ( 3 marks)

2x – 2 ÷ x – 1

6x^{2}
– x – 12 2x – 3

3. Every week the number of absentees in a school was recorded. This was done for 39 weeks these observations were tabulated as shown below

Number of absentees | 0.3 | 4 -7 | 8 -11 | 12 – 15 | 16 – 19 | 20 – 23 |

(Number of weeks) | 6 | 9 | 8 | 11 | 3 | 2 |

Estimate the median absentee rate per week in the school ( 2 marks)

4. Manyatta village is 74 km North West of Nyangata village. Chamwe village is 42 km west of Nyangate. By using an appropriate scale drawing, find the bearing of Chamwe from Manyatta ( 2 marks)

5. A perpendicular to the line -4x + 3 = 0 passes through the point ( 8, 5) Determine its equation ( 2 marks)

6. The volume Vcm^{3} of an object
is given by

V = 2 π r^{3} 1 – 2

3 sc^{2}

Express in term of π r, s and V ( 3 marks)

8. Two baskets A and B each contains a mixture of oranges and lemons. Basket A contains 26 oranges and 13 lemons. Basket B contains 18 oranges and 15 lemons. A child selected basket at random and picked at random a fruit from it.

Determine the probability that the fruit picked was an orange.

9. A solid cone of height 12cm and radius 9 cm is recast into a solid sphere. Calculate the surface area of the sphere. ( 4 marks)

10. The first, the third and the seventh terms of an increasing arithmetic progression are three consecutive terms of a geometric progression. In the first term of the arithmetic progression is 10 find the common difference of the arithmetic progression. ( 4 marks)

- Akinyi bought and beans from a wholesaler. She then mixed the maize and beans the ratio 4:3 she brought the maize as Kshs. 12 per kg and the beans 4 per kg. If she was to make a profit of 30% what should be the selling price of 1 kg of the mixture? ( 4 marks)

- A clothes dealer sold 3 shirts and 2 trousers for Kshs. 840 and 4 shirts and 5 trousers for Kshs 1680.

Form a matrix equation to represent the above information. Hence find the cost of 1 shirt and the cost of 1 trouser. ( 4 marks)

- Water flows from a tap. At the rate 27cm
^{3}per second, into a rectangular container of length 60cm, breath 30 cm and height 40 cm. If at 6.00 p.m. the container was half full, what will be the height of water at 6.04 pm? ( 3 marks)

In the diagram below < CAD, = 20^{0}, < AFE = 120^{0} and BCDF is a cyclic

- In the diagram below < CAD, = 20
^{0}, < AFE = 120^{0}and BCDF is a cyclic quadrilateral. Find < FED. ( 3 marks)

- The cash prize of a television is Kshs 25000. A customer paid a deposits of Kshs 3750. He repaid the amount owing in 24 equal monthly installments.

If hw was charged simple interest at the rate of 40% p.a, how much was each installment? ( 4 marks)

- A bus takes 195 minutes to travel a distance of ( 2x + 30) km at an average speed of ( x – 20) km/h

Calculate the actual distance traveled. Give your answers in kilometers.

( 3 marks)

**SECTION II ( 48 MARKS)**

*Answer any six questions from
this section*

- At the beginning of every year, a man deposited Kshs 10,000 in a financial institution which paid compound interest at the rate of 20% p.a. He stopped further deposits after three years. The Money remained invested in the financial institution for a further eight years.

(a) How much money did he have at the end of the first three years ( 4 marks)

(b) How much interest did the money generate in the entire period ( 4 marks)

- The figure below is a right pyramid with a rectangular base ABCD and VO as the height. The vectors AD= a, AB = b and DV = v

- Express

(i) AV in terms of a and c ( 1 mark)

(ii) BV in terms of a, b and c ( 2 marks)

(b) M is point on OV such that OM: MV = 3:4, Express BM in terms of a, b and

c.

Simplify your answer as far as possible ( 5 marks)

- (a) In the figure below O is the centre of a circle whose radius is 5 cm AB = 8 cm and < AOB is obtuse.

Calculate the area of the major segment ( 6 marks)

(b) A wheel rotates at 300 revolutions per minute. Calculate the angle in radians through which a point on the wheel turns in one second.

- The table shows the height metres of an object thrown vertically upwards varies with the time t seconds

The relationship between s and t is
represented by the equations s = at^{2} + bt + 10 where b are
constants.

t | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

s | 45.1 |

- (i) Using the information in the table, determine the values of a and b

( 2 marks)

(ii) Complete the table ( 1 mark)

(b) (i) Draw a graph to represent the relationship between s and t ( 3 marks)

(ii) Using the graph determine the velocity of the object when t = 5 seconds

(2 marks)

- (a) Construct a table of values for the function y = x
^{2}– 6 for -3 < x <4 ( 2 marks)

- By drawing a suitable line on the same grid estimate the roots of the equation

X2 + 2x – 2 =0 ( 3 marks)

- The figure below represents a plot of land ABCD, where
BC = CD = 60 metres, < BCD = 120
^{0}< ABC = 75^{0}and < ADC = 85^{0}

(a) Calculate the distance from B to through D ( 5 marks)

(b) The plot is to be fenced using poles that are 3 metres apart except at corner A, where the two poles next to the corner pole are each less than 3 metres from A. Calculate the distance from the pole at corner at corner A to each of the poles next to it.

- On the grid provided on the opposite page ABCE is a trapezium

(a) ABCD is mapped onto A’B’C’D’ by a positive quarter turn. Draw the image A’B’C’D’ on the grid. ( 1 mark)

(b) A transformation maps -2 -1 A’B’C’D onto A” B” C” D”

1 -1

(i) Obtain the coordinates of A” B” C” D” on the grid ( 2 marks)

(ii) Plot the image A” B” C” D” on the grid (1mark)

(c) Determine a single matrix that maps A” B” C” D” ( 4 marks)

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