# K.C.S.E 1996 MATHEMATICS PAPER 1 QUESTIONS & ANSWERS

K.C.S.E 1996 MATHEMATICS PAPER 1 QUESTIONS & ANSWERS

MATHEMATICS PAPER 1 K.C.S.E 1996 QUESTIONS

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SECTION 1 ( 52 Marks)

#### MARKING SCHEME K.C.S.E 1996 MATHEMATICS PAPER 1

1. Use logarithms to evaluate ( 3 marks)
1. Factorize completely 3x2 – 2xy – y2 ( 2 marks)
2. The cost of 5 skirts and 3 blouses is Kshs 1750. Mueni bought three of the skirts and one of the blouses for Kshs 850.   ind the cost of each item                                                                  ( 3 marks)
3. A man walks directly from point A towards the foot of a tall building 240m away. After covering 180m, he observes that the angle of the top of the building is 45. Determine the angle of elevation of the top of the building from A. ( 3 marks)

5.         In the figure below, ABCD is a cyclic quadrilateral and BD is a diagonal. EADF is a straight line. <CDF = 680, < BDC = 450 and < BAE = 980.

#### MARKING SCHEME K.C.S.E 1996 MATHEMATICS PAPER 1

Calculate the size of

(a)        < ABD                                                                       ( 2 marks)

(b)        < CBD                                                                         ( 2 marks)

1. An employee started on a salary of £ 6,000 per annum and received a constant annual increment. If he earned a total of  £ 32,400 by the end of five years, calculate his annual increment.                                                            ( 3 marks)
1. Mr. Ngeny borrowed Kshs. 560,000 from a bank to buy a piece of land. He was required to repay the loan with simple interest for a period of 48 months. The repayment amounted to Kshs 21000 per month.

Calculate

(a) The interest paid to the bank                                                         ( 2 marks)

(b) The rate per annum of the simple interest                         ( 4 marks)

1. A rectangular tank of base 2.4 m by 2.8 m and a height of 3 m contains 3,600 liters of water initially. Water flows into the tank at the rate of 0.5 litres per second

Calculate the time in hours and minutes, required to fill the tank      ( 4 marks)

1. A car dealer charges 5% commission for selling a car. He received a commission of Kshs 17,500 for selling a car. How much money did the owner receive from the sale of his car?                         ( 2 marks)
2. Five pupils A, B, C, D and E obtained the marks 53, 41, 60, 80 and 56 respectively. The table below shows part of the work to find the standard deviation.

(a) Complete the table                                                                         ( 1 mark)

(b) Find the standard deviation                                                          ( 3 marks)

#### MARKING SCHEME K.C.S.E 1996 MATHEMATICS PAPER 1

1. Solve the equation                                                 (2 maks)

1. A fruiterer bought 144 pineapples at Kshs 100 for every six pineapples. She sold some of them at Kshs. 72 for every three and the rest at Kshs 60 for every two.

If she made a 65% profit, calculate the number of pineapples sold at Kshs 72 for every three                                                                                             ( 3 marks)

1. Make V the subject of the formula

T = 1/2 m (u2 – v2)                          ( 3 marks)

1. The figure below represents a hollow cylinder. The internal and external radii are estimated to be 6 cm and 8 cm respectively, to the nearest whole number. The height of the cylinder is exactly 14 cm.

#### MARKING SCHEME K.C.S.E 1996 MATHEMATICS PAPER 1

(a)        Determine the exact values for internal and external radii which will give maximum volume of the material used.                          ( 1 mark)

(b)        Calculate the maximum possible volume of the material used

Take the value of to be 22/7                                                   ( 2 marks)

1. Two lorries A and B ferry goods between tow towns which are 3120 km apart. Lorry A traveled at km/h faster than lorry B and B takes 4 hours more than lorry A to cover the distance.

Calculate the speed of lorry B                                                            ( 5 marks)

#### MARKING SCHEME K.C.S.E 1996 MATHEMATICS PAPER 1

SECTION II (48 MARKS)

Answer any six questions from this section

1. The data given below represents the average monthly expenditure, E in K £, on food in a certain village. The expenditure varies with number of dependants, D in the family.

a)Using the grid provided, plot E against D and draw the line of the best fit        ( 2 marks)

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b)Find the gradient and the  E- intercept of the graph                         ( 3 marks)

c)Write down an equation connecting  E and D                                  ( 1 mark)

d)Estimate the cost of feeding a family with 9 dependants                 ( 2 marks)

1. The table below shows the income tax rates

#### MARKING SCHEME K.C.S.E 1996 MATHEMATICS PAPER 1

Mr. Otiende earned a basic salary of Kshs 13,120 and a house allowance of Kshs 3,000 per month. He claimed a tax relief for a married person of Kshs 455 per month

(a) Calculate

(i) The tax payable without the relief

(ii) The tax paid after the relief

(b)        Apart from the income  tax, the following monthly deductions are made. A service charge of Kshs 100, a health insurance fund  of Kshs 280 and 2% of his basic salary as widow and children pension scheme.            Calculate

(i) The total monthly deductions made from Mr. Otiende’s income                     ( 2 marks)

(ii) Mr. Otiende’s net income from his employment               ( 2 marks)

1. The equation of a curve us y = 3x2 – 4 x + 1

(a) Find the gradient function of the curve  and its value when x = 2 ( 2 marks)

(b) Determine

(i) The equation of the tangent to the curve at the  point (2, 5)          ( 2 marks)

(ii) The angle which the tangent to the curves at the  point ( 2, 5) makes with the horizontal                                                                                               ( 1 mark)

(iii) The equation of the line through the point ( 2, 5) which is perpendicular to the tangent in (b) (i)

#### MARKING SCHEME K.C.S.E 1996 MATHEMATICS PAPER 1

1. The position of two A and B on the earth’s surface are ( 360 N, 490E) and ( 3600N, 1310 W) respectively.

(a) Find the difference in longitude between  town A and town B   ( 2 marks)

(b) Given that the radius of the earth is 6370, calculate the distance  between town A and town B.

(c) Another town, C  is 840 east of town B and  on the same  latitude as towns A   and B. Find the longitude of town C.

#### MARKING SCHEME K.C.S.E 1996 MATHEMATICS PAPER 1

1. The table below shows some values of the function y = x2 + 2x – 3

1. a) Complete the table
2. b) Using the completed table and the mid- ordinate rule with six ordinates, estimate the area of the region bounded by the y =x2 +2x –3 and the line y= 0,x =-6 and x = -3                         ( 3 marks)

(i) By integration find the actual area of the region in (b) above       2 marks)

(ii) Calculate the percentage error arising from the estimate in (b)     (2 marks)

1. In the diagram below OABC is a parallelogram, OA = a and AB = b. N is a point on OA such that ON: NA = 1: 2

• Find
• AC in terms of a and b
• BN in terms of a and b
• The lines AC and BN intersect at X, AX = hAC and BX = kBN
• By expressing OX in two ways, find the values of h and k
• Express OX in terms of a and b ( 1 mark)
1. Use ruler and compasses only in this question

The diagram below shows three  points A, B and D

(a) Construct the angle bisector of acute angle  BAD                  ( 1 mark)

(b) A point P, on the  same side of AB and D, moves in such a way that < APB = 22 ½0 construct the locus of P                                      ( 6 marks)

(c) The locus of P meets the angle bisector of < BAD  at C measure < ABC                                                                                                       ( 1 mark)

Hence find area of the image A” B” C”                           ( 2 marks)

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