Category: Kcse-1995

K.C.S.E Mathematics Q & A-MODEL 1995PP2QN24

12/5/2020

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A manufacture of jam has 720 kg of strawberry syrup and 800 kg of mango syrup for making two types of jam, grade A and B. Each types is made by mixing strawberry and mango syrups as follows:

Grade A: 60% strawberry and 40% mango
Grade B: 30% strawberry and 70% mango

The jam is sold in 400 gram jars. The selling prices are as follows:

Grade A: Kshs. 48 per jar
Grade B: Kshs 30 per jar.

(a)
- Form inequalities to represent the given information ( 3 marks)
(b)
- (i) On the grid provided draw the inequalities ( 3 marks)
- (ii) From your, graph, determine the number of jars of each grade the manufacturer should produce to maximize his profit ( 1 mark)
- (iii) Calculate the total amount of money realized if all the jars are sold ( 1 mark)

MARKING SCHEME

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K.C.S.E Mathematics Q & A-MODEL 1995PP2QN23

12/5/2020

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(a) Complete the table for the function y = 2 sin x (2 marks)

(b)
(i) Using the values in the completed table, draw the graph of y = 2 sin 3x for 0⁰≤ x ≤ 120⁰ on the grid provided
(ii) Hence solve the equation 2 sin 3x = -1.5 ( 3 marks)

MARKING SCHEME

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K.C.S.E Mathematics Q & A-MODEL 1995PP2QN22

12/5/2020

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Using ruler and compasses only, construct a parallelogram ABCD such that AB = 10cm, BC = 7cm and ∠ABC = 105⁰. Also construct the loci of P and Q within the parallel such that AP ≤ 4 cm, and BC ≤ 6 cm. Calculate the area within the parallelogram and outside the regions bounded by the loci.

MARKING SCHEME

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K.C.S.E Mathematics Q & A-MODEL 1995PP2QN21

12/5/2020

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A part B is on a bearing of 080⁰ from a port A and at a distance of 95 km. A submarine is stationed at a port D, which is on a bearing of 200⁰ from AM and a distance of 124 km from B. A ship leaves B and moves directly southwards to an island P, which is on a bearing of 140 from A. The submarine at D on realizing that the ship was heading fro the island P, decides to head straight for the island to intercept the ship.

Using a scale of 1 cm to represent 10 km, make a scale drawing showing the relative positions of A, B, D, P. ( 2 marks)
Hence find

(i) The distance from A to D ( 2 marks)
(ii) The bearing of the submarine from the ship was setting off from B (1 mark)
(iii) The bearing of the island P from D ( 1 mark)
(iv) The distance the submarine had to cover to reach the island P ( 2 marks)

MARKING SCHEME

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K.C.S.E Mathematics Q & A-MODEL 1995PP2QN20

12/5/2020

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A hillside is in the form of a plane inclined at an angle of 30⁰ to the horizontal. A straight section of road 800 metres long lies along the line of greatest slope from a point A to a point B further up the hillside.

(a) If a vehicle moves from A and B, what vertical height does it rise?
(b) D is another point on the hillside and is on the same height as B. Another height straight road joins and D and makes an angle of 600 with AB. C is a point on AD such that AC = ¾ AD.
Calculate
- (i) The length of the road from A to C
- (ii) The distance of CB
- (iii) The angle elevation of B and C

MARKING SCHEME

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K.C.S.E Mathematics Q & A-MODEL 1995PP2QN19

12/5/2020

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The probabilities that a husband and wife will be alive 25 years from now are 0.7 and 0.9 respectively.

Find the probability that in 25 years time,

(a) Both will be alive
(b) Neither will be alive
(c) One will be alive
(d) At least one will be alive

MARKING SCHEME

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K.C.S.E Mathematics Q & A-MODEL 1995PP2QN18

12/5/2020

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The table below shows high altitude wind speeds recorded at a weather station in a period of 100 days.

(a) On the grid provided draw a cumulative frequency graph for the data ( 4 marks)
(b) Use the graph to estimate
(i) The interquartile range ( 3 marks)
(ii) The number of days when the wind speed exceeded 125 knots ( 1 mark)

MARKING SCHEME

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K.C.S.E Mathematics Q & A-MODEL 1995PP2QN17

12/5/2020

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A circular path of width 14 metres surrounds a field of diameter 70 metres. The path is to be carpeted and the field is to have a concrete slab with an exception of four rectangular holes each measuring 4 metres by 3 metres. A contractor estimated the cost of carpeting the path at Kshs. 300 per square metre and the cost of putting the concrete slab at Kshs 400 per square metre. He then made a quotation which was 15% more than the total estimate. After completing the job, he realized that 20% of the quotation was not spent.
(a) How much money was not spent?
(b) What was the actual cost of the contract?

MARKING SCHEME

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K.C.S.E Mathematics Q & A-MODEL 1995PP2QN16

12/5/2020

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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~Topically Analyzed

A manufacture of jam has 720 kg of strawberry syrup and 800 kg of mango syrup for making two types of jam, grade A and B. Each types is made by mixing strawberry and mango syrups as follows:

​(a) Complete the table for the function y = 2 sin x (2 marks)

(b) (i) Using the values in the completed table, draw the graph of y = 2 sin 3x for 00≤ x ≤ 1200 on the grid provided (ii) Hence solve the equation 2 sin 3x = -1.5 ( 3 marks)

Using ruler and compasses only, construct a parallelogram ABCD such that AB = 10cm, BC = 7cm and ∠ABC = 1050. Also construct the loci of P and Q within the parallel such that AP ≤ 4 cm, and BC ≤ 6 cm. Calculate the area within the parallelogram and outside the regions bounded by the loci.

A hillside is in the form of a plane inclined at an angle of 300 to the horizontal. A straight section of road 800 metres long lies along the line of greatest slope from a point A to a point B further up the hillside.

The probabilities that a husband and wife will be alive 25 years from now are 0.7 and 0.9 respectively.

The table below shows high altitude wind speeds recorded at a weather station in a period of 100 days.

(a) Complete the table for the function y = 2 sin x (2 marks)

(b)
(i) Using the values in the completed table, draw the graph of y = 2 sin 3x for 0⁰≤ x ≤ 120⁰ on the grid provided
(ii) Hence solve the equation 2 sin 3x = -1.5 ( 3 marks)

Using ruler and compasses only, construct a parallelogram ABCD such that AB = 10cm, BC = 7cm and ∠ABC = 105⁰. Also construct the loci of P and Q within the parallel such that AP ≤ 4 cm, and BC ≤ 6 cm. Calculate the area within the parallelogram and outside the regions bounded by the loci.

A hillside is in the form of a plane inclined at an angle of 30⁰ to the horizontal. A straight section of road 800 metres long lies along the line of greatest slope from a point A to a point B further up the hillside.