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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN12

30/5/2020

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN12

Find the values of a and b where b are rational numbers

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN11

30/5/2020

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN11

ABC is a triangle and P is on AB such that P divides AB internally in the ratio 4:3. Q is a point on AC such that PQ is parallel to BC. If AC = 14 cm

(i)State the ratio AQ:QC
(ii)Calculate the length of QC

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN10

30/5/2020

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN10

On the surface of a cuboid ABCDEFGH a continuous path BFDHB is drawn as shown by the arrows below

(a)Draw and label a net of cuboid
(b)On the net show the path

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN09

27/5/2020

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN09

Expand and simplify ( 1 – 3x)⁵, up to the term in x³
Hence use your expansion to estimate (0.97)⁵ correct to 4 decimal places

KNEC MARKING SCHEME

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN08

27/5/2020

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN08

Use the trapezoidal rule with intervals of 1 cm to estimate the area of the shaded region below.

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN07

27/5/2020

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN07

Find the value of m in the following equation

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN06

26/5/2020

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A pyramid of height 10 cm stands on a square base ABCD of side 6 cm

(a)Draw a sketch of the pyramid
(b)Calculate the perpendicular distance from the vertex to the side AB

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN05

26/5/2020

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The figure below represents a circle a diameter 28 cm with a sector subtending an angle of 75⁰ at the centre.

Find the area of the shaded segment to 4 significant figures

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN04

26/5/2020

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On the figure below construct

(i) The perpendicular bisector of BC
(ii) The locus of a point P which moves such a way that
∠APB = ∠AVB and P is on the same side of AB on the same side of AB as C

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN03

24/5/2020

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN01

A commercial bank buys and sells Japanese yen in Kenya shillings at the rates shown below.

A Japanese tourist at the end of his tour of Kenya was left with Kshs. 30,000 which he converted to Japanese yen through the commercial bank. How many Japanese yen did he get?

KNEC ANSWERS

K.C.S.E Mathematics Q & A - MODEL 1997PP2QN03

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN02

24/5/2020

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Mary has 21 coins whose total value is Kshs 72. There are twice as many five shillings coins as there are ten shillings coins. The rest are one shillings coin. Find the number of ten shillings coins that Mary has.

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN01

24/5/2020

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Evaluate without using mathematical tables;

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K.C.S.E Mathematics Q & A - MODEL 1997PP1QN24

23/5/2020

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The coordinates of the points P and Q are ( 1, -2) and ( 4, 10) respectively.
A point T divides the line PQ in the ratio 2: 1

(a) Determine the coordinates of T
(b)
- (i) Find the gradient of a line perpendicular to PQ
- (i) Hence determine the equation of the line perpendicular PQ and passing through T
- (ii) If the line meets the y- axis at R, calculate the distance TR, to three significant figures

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K.C.S.E Mathematics Q & A - MODEL 1997PP1QN23

23/5/2020

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The figure on the grid shows a triangular shaped object ABC and it’s image A’B’ C’

(a)

(i) Describe fully the transformation that maps ABC and A’B’C’
(ii) Find a 2 x 2 matrix that transforms triangle ABC onto triangle A’ B’ C’

(i)Find the coordinates of A” B” C”

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K.C.S.E Mathematics Q & A - MODEL 1997PP1QN22

23/5/2020

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In the figure below OA = a, OB = b, AB = BC and OB: BD = 3:1

(a) Determine

(i)AB
(ii)CD, in terms of a and b

(b) If CD : DE = 1:k and OA : AE = 1 : m determine

(i)DE in terms of a, b and k

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K.C.S.E Mathematics Q & A - MODEL 1997PP1QN21

22/5/2020

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The water supply in a town depends entirely on two water pumps, A and B.
The probability of pump A filling is 0.1 and the probability of pump B failing is 0.2. Calculate the probability that
(a) Both pumps are working
(b) There is no water in the town
(c) Only one pump is working
(d) There is some water in the town

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K.C.S.E Mathematics Q & A-MODEL 1997PP1QN20

20/5/2020

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(a) Draw the graph of y = 6 + x - x², taking integral value of x in -4 ≤ x ≤ 5. (The grid is provided. Using the same axes draw the graph of y = 2 – 2x

(b) From your graphs, find the values of X which satisfy the simultaneous equations y = 6 + x - x²; y = 2 – 2x

(c) Write down and simplify a quadratic equation which is satisfied by the values of x where the two graphs intersect.

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K.C.S.E Mathematics Q & A-MODEL 1997PP1QN19

20/5/2020

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Using ruler and compasses only construct triangle ABC such that AB = 4 cm, BC = 5 cm and ∠ABC = 120⁰. Measure AC.

On the diagram, construct a circle which passes through the vertical of the triangle ABC.
Measure the radius of the circle
Measure the shortest distance from the centre of the circle to line BC.

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K.C.S.E Mathematics Q & A-MODEL 1997PP1QN18

20/5/2020

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A ship leaves an island ( 5⁰N, 45⁰E) and sails due east for 120 hours to another island. The average speed of the ship is 27 knots.

(a) Calculate the distance between the two islands
- (i) in nautical miles
- (ii) in kilometres
(b) Calculate the speed of the ship in kilometres per hour
(c) Find the position of the second island

(take 1 nautical mile to be 1.853 Km and the radius of the earth to be 6370 Km)

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K.C.S.E Mathematics Q & A-MODEL 1997PP1QN17

20/5/2020

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The figure below shows a portable kennel

(a) Calculate
- (i) The total surface area of the walls and the roof ( include the door as part of the wall)
- (ii) The total area of the roof
(b) The cost of roofing is Kshs 300 per square metre and that of making walls and floor Kshs 350 per square metre. Find the cost of making the kennel
(c) Find the cost of roofing another kennel whose dimensions are 50% more than those of given kennel.

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K.C.S.E Mathematics Q & A-MODEL 1997PP1QN16

20/5/2020

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(b) Work out the exact value of R

\[\frac{1}{0.003146 - 0.003130}\]

(b) An approximate value of R may be obtained by first correcting each of the decimal in the denominator to 5 decimal places
- (i) The approximate value
- (ii) The error introduced by the approximation

K.N.E.C Marking Scheme

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K.C.S.E Mathematics Q & A-MODEL 1997PP1QN15

20/5/2020

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Akinyi bough three cups and four Spoons for Kshs. 324. Wanjiku bought five cups and Fatuma bought two spoons of the same type as those bought by Akinyi. Wanjiku paid Kshs 228 more than Fatuma. Find the price of each cup and spoon.

K.N.E.C Marking Scheme

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K.C.S.E Mathematics Q & A-MODEL 1997PP1QN14

20/5/2020

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Two towns P and Q are 400 km apart. A bus left P for Q. It stopped at Q for one hour and then started the return journey to P. One hour after the departure of the bus from P, a trailer also heading for Q left P. The trailer met the returning bus ¾ of the way from P to Q. They met t hours after the departure of the bus from P.

(a) Express the average speed of the trailer in terms of t
(b) Find the ration of the speed of the bus so that of the trailer.

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K.C.S.E Mathematics Q & A-MODEL 1997PP1QN13

20/5/2020

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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

Topically Analysed

​Find the values of a and b where b are rational numbers

​ABC is a triangle and P is on AB such that P divides AB internally in the ratio 4:3. Q is a point on AC such that PQ is parallel to BC. If AC = 14 cm

​On the surface of a cuboid ABCDEFGH a continuous path BFDHB is drawn as shown by the arrows below

Expand and simplify ( 1 – 3x)5, up to the term in x3 Hence use your expansion to estimate (0.97)5 correct to 4 decimal places

​Use the trapezoidal rule with intervals of 1 cm to estimate the area of the shaded region below.

Find the value of m in the following equation

The figure below represents a circle a diameter 28 cm with a sector subtending an angle of 750 at the centre.​

On the figure below construct

A commercial bank buys and sells Japanese yen in Kenya shillings at the rates shown below.

A Japanese tourist at the end of his tour of Kenya was left with Kshs. 30,000 which he converted to Japanese yen through the commercial bank. How many Japanese yen did he get?

Mary has 21 coins whose total value is Kshs 72. There are twice as many five shillings coins as there are ten shillings coins. The rest are one shillings coin. Find the number of ten shillings coins that Mary has.

Evaluate without using mathematical tables;

The coordinates of the points P and Q are ( 1, -2) and ( 4, 10) respectively.A point T divides the line PQ in the ratio 2: 1

The figure on the grid shows a triangular shaped object ABC and it’s image A’B’ C’

​In the figure below OA = a, OB = b, AB = BC and OB: BD = 3:1

Using ruler and compasses only construct triangle ABC such that AB = 4 cm, BC = 5 cm and ∠ABC = 1200. Measure AC.

​On the diagram, construct a circle which passes through the vertical of the triangle ABC. Measure the radius of the circle Measure the shortest distance from the centre of the circle to line BC.

A ship leaves an island ( 50N, 450E) and sails due east for 120 hours to another island. The average speed of the ship is 27 knots.

​The figure below shows a portable kennel

(b) Work out the exact value of R

Akinyi bough three cups and four Spoons for Kshs. 324. Wanjiku bought five cups and Fatuma bought two spoons of the same type as those bought by Akinyi. Wanjiku paid Kshs 228 more than Fatuma. Find the price of each cup and spoon.

Find the values of a and b where b are rational numbers

ABC is a triangle and P is on AB such that P divides AB internally in the ratio 4:3. Q is a point on AC such that PQ is parallel to BC. If AC = 14 cm

On the surface of a cuboid ABCDEFGH a continuous path BFDHB is drawn as shown by the arrows below

Expand and simplify ( 1 – 3x)⁵, up to the term in x³
Hence use your expansion to estimate (0.97)⁵ correct to 4 decimal places

Use the trapezoidal rule with intervals of 1 cm to estimate the area of the shaded region below.

The figure below represents a circle a diameter 28 cm with a sector subtending an angle of 75⁰ at the centre.

The coordinates of the points P and Q are ( 1, -2) and ( 4, 10) respectively.
A point T divides the line PQ in the ratio 2: 1

In the figure below OA = a, OB = b, AB = BC and OB: BD = 3:1

Using ruler and compasses only construct triangle ABC such that AB = 4 cm, BC = 5 cm and ∠ABC = 120⁰. Measure AC.

On the diagram, construct a circle which passes through the vertical of the triangle ABC.
Measure the radius of the circle
Measure the shortest distance from the centre of the circle to line BC.

A ship leaves an island ( 5⁰N, 45⁰E) and sails due east for 120 hours to another island. The average speed of the ship is 27 knots.

The figure below shows a portable kennel