Category: Kcse-1997

K.C.S.E Mathematics Q & A - MODEL 1997PP2QN20

3/6/2020

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In the figure below PQR is the tangent to circle at Q. TS is a diameter and TSR and QUV are straight lines. QS is parallel to TV. Angles SQR = 40⁰ and angle TQV = 55⁰

K.C.S.E Mathematics Q & A - MODEL 1997PP2QN20

Find the following angles, giving reasons for each answer

(a)QST
(b)QRS
(c)QVT
(d)UTV

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN19

3/6/2020

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN19

An institute offers two types of courses technical and business courses. The institute has a capacity of 500 students. There must be more business students than technical students but at least 200 students must take technical courses. Let x represent the number of technical students and y the number of business students.

(a) Write down three inequalities that describe the given conditions
(b) On the grid provided, draw the three inequalities
(c) If the institute makes a profit of Kshs 2, 500 to train one technical students and Kshs 1,000 to train one business student, determine
- (i) the number of students that must be enrolled in each course to maximize the profit
- (ii) The maximum profit.

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN18

3/6/2020

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Complete the table below by filling in the blank spaces

ANSWER

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN17

3/6/2020

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN17

A company is to construct a parking bay whose area is 135m². It is to be covered with concrete slab of uniform thickness of 0.15. To make the slab cement. Ballast and sand are to be mixed so that their masses are in the ratio 1: 4: 4. The mass of m³ of dry slab is 2, 500kg.
Calculate

(a)
- (i) The volume of the slab
- (ii) The mass of the dry slab
- (iii) The mass of cement to be used
(b) If one bag of the cement is 50 kg, find the number of bags to be purchased
(c) If a lorry carries 7 tonnes of sand, calculate the number of lorries of sand to be purchased

ANSWER

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN16

3/6/2020

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A metal bar is a hexagonal prism whose length is 30 cm. The cross – section is a regular hexagon with each side of the length 6 cm.
Find

(i) the area of the hexagonal face
(ii) the volume of the metal bar

ANSWER

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN15

3/6/2020

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The athletes in an 800 metres race take 104 seconds and 108 seconds respectively to complete the race. Assuming each athlete is running at a constant speed. Calculate the distance between them when the faster athlete is at the finishing line.

ANSWER

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN14

3/6/2020

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Form 3 Mathematics

K.C.S.E Mathematics Q & A - MODEL 1997PP2QN14

Mogaka and Onduso working together can do a piece of work in 6 days, Mogaka, working alone takes 5 days longer than Onduso. How many days does it take Onduso to do the work alone?

ANSWER

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN13

3/6/2020

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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN13

The table below represents the mean scores in six consecutive assessment tests given a form four class.

Calculate the three moving averages of order 4

COMPREHENSIVE ANSWER

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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

ANSWER

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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

ANSWER

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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

ANSWERS

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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.

KNEC MARKING SCHEME

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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

KNEC MARKING SCHEME

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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

K.N.E.C Marking Scheme

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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

K.N.E.C Marking Scheme

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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

K.N.E.C Marking Scheme

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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.

KNEC ANSWER

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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;

KNEC ANSWERS

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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

KNEC MARKING SCHEME

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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”

KNEC MARKING SCHEME

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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

KNEC MARKING SCHEME

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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

KNEC MARKING SCHEME

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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.

KNEC MARKING SCHEME

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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

Topically Analysed

In the figure below PQR is the tangent to circle at Q. TS is a diameter and TSR and QUV are straight lines. QS is parallel to TV. Angles SQR = 400 and angle TQV = 550

Complete the table below by filling in the blank spaces

A company is to construct a parking bay whose area is 135m2. It is to be covered with concrete slab of uniform thickness of 0.15. To make the slab cement. Ballast and sand are to be mixed so that their masses are in the ratio 1: 4: 4. The mass of m3 of dry slab is 2, 500kg. Calculate

A metal bar is a hexagonal prism whose length is 30 cm. The cross – section is a regular hexagon with each side of the length 6 cm. Find

(i) the area of the hexagonal face

(ii) the volume of the metal bar

​The athletes in an 800 metres race take 104 seconds and 108 seconds respectively to complete the race. Assuming each athlete is running at a constant speed. Calculate the distance between them when the faster athlete is at the finishing line.

Form 3 Mathematics

The table below represents the mean scores in six consecutive assessment tests given a form four class.

​Calculate the three moving averages of order 4

​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

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In the figure below PQR is the tangent to circle at Q. TS is a diameter and TSR and QUV are straight lines. QS is parallel to TV. Angles SQR = 40⁰ and angle TQV = 55⁰

A company is to construct a parking bay whose area is 135m². It is to be covered with concrete slab of uniform thickness of 0.15. To make the slab cement. Ballast and sand are to be mixed so that their masses are in the ratio 1: 4: 4. The mass of m³ of dry slab is 2, 500kg.
Calculate

A metal bar is a hexagonal prism whose length is 30 cm. The cross – section is a regular hexagon with each side of the length 6 cm.
Find

The athletes in an 800 metres race take 104 seconds and 108 seconds respectively to complete the race. Assuming each athlete is running at a constant speed. Calculate the distance between them when the faster athlete is at the finishing line.

Calculate the three moving averages of order 4

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