Category: Scale Drawing

The scale of a map is 1: 200.Calculate the actual area of a triangular coffee field whose sides are 6cm, 8cm and 10cm on the map. (3 marks)

27/12/2022

The scale of a map is 1: 200.Calculate the actual area of a triangular coffee field whose sides are 6cm, 8cm and 10cm on the map. (3 marks)

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A map has a scale of 1 : 2500 and on it is square plot of land which has an area of 4cm-square. Calculate the actual area in hectares of the land.

26/11/2021

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A map has a scale of 1 : 2500 and on it is square plot of land which has an area of 4cm². Calculate the actual area in hectares of the land. (3mks)

Worked Answer:

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A small field was surveyed and the measurements recorded in a surveyor’s field book as in the table below.

23/11/2021

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(a) A small field was surveyed and the measurements recorded in a surveyor’s field book as in the table below.

(i) Using a scale of 1cm to 10m make an accurate drawing of the map of the field. (4mks)

(ii) Find the area of the field. (3mks)

(iii) Assuming that the baseline in (a) runs in a northern direction give the position of D relative to A using bearing and distance. (3mks)

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Four points B, C, Q and D lie on the same plane. Point B is 42km due southwest point Q. Point C is 50 km on a bearing of S60degreesE from Q. Point D is equidistant from B, Q and C.

23/11/2021

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Four points B, C, Q and D lie on the same plane. Point B is 42km due southwest point Q. Point C is 50 km on a bearing of S60^oE from Q. Point D is equidistant from B, Q and C.

(a) Using the scale: 1cm represents 10km, construct a diagram showing the positions of B, C, Q and D. (5mks)

(b) Determine the
(i) Distance between B and C (1mk)

(ii) Bearing of D from B (2mks)

(c) Find the distance and bearing of D from C. (2mks)

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From a point 20m away on a level ground the angle of elevation to the lower window line is 25° and the angle of elevation to the top line of the window is 34°. Calculate the height of the window.

19/11/2021

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From a point 20m away on a level ground the angle of elevation to the lower window line is 25° and the angle of elevation to the top line of the window is 34°. Calculate the height of the window. [3 marks]

Worked solution

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From a point 20m away on a level ground the angle of elevation to the lower window line is 27degrees and the angle of elevation to the top of the window is 32degrees. calculate the height of the window.

24/10/2021

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From a point 20m away on a level ground the angle of elevation to the lower window line is 27⁰ and the angle of elevation to the top of the window is 32⁰. calculate the height of the window (3mks)

Worked Answer:

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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.22

23/9/2020

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Form 1 Mathematics

A boat at point x is 200 m to the south of point Y. The boat sails X to another point Z. Point Z is 200m on a bearing of 310⁰ from X, Y and Z are on the same horizontal plane.

(a) Calculate the bearing and the distance of Z from Y ( 3 marks)

(b) W is the point on the path of the boat nearest to Y. Calculate the distance WY ( 2 marks)

(c) A vertical tower stands at point Y. The angle of point X from the top of the tower is 6⁰ calculate the angle of elevation of the top of the tower from W (3 marks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2018PP1QN07

18/9/2020

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Form 1 Mathematics

(a) Using a ruler and a pair of compasses only, construct a quadrilateral PQRS in which PQ = 5 cm, PS = 3 cm, QR = 4 cm, PQR = 135° and SPQ is a right angle.
(b) The quadrilateral PQRS represents a plot of land drawn to a scale of l:4000. Determine the actual length of RS in metres.

answer

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K.C.S.E Mathematics Q & A - MODEL 2005.PP1.QN.23

18/9/2020

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Form 2 Mathematics

A boat which travels at 5 km/h in still water is set to cross a river which flows from the north at 6km/h. The boat is set on a course of x⁰ with the north.

(a) Given that cos x⁰ = ³/₅ , calculate

(i) The resultant speed of the boat ( 2 marks)

(ii) The angle which the track makes with the north ( 2 marks)

(b) If the boat is to sail on a bearing of 135⁰, calculate the bearing of possible course on which it can be set ( 4 marks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.19

16/9/2020

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Form 1 Mathematics

For electricity posts, A,B,C, and D stand on a level ground such that B is 21 m on a bearing of 060^₀ from A, C, is 15 m to the south of B and D is 12 m on a bearing of 140^₀ from A.

(a)
- (i) Using scale of 1 cm of I cm to represents 3 metres, draw a diagram to show the relative positions of the posts
- (ii) Find the distances and the bearing of C from D
(b) The height of the post at A IS 8.4m. On a separate scale drawing, mark and determine the angle of depression of the foot of the post at C from the top of the top of the post at A.

Answer

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K.C.S.E Mathematics Q & A - MODEL 2015PP1QN07

10/9/2020

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Form 1 Mathematics

Below is part of a sketch of a solid cuboid ABCDEFGH. Complete the sketch

answer

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K.C.S.E Mathematics Q & A - MODEL 2004.PP1.QN.6

9/9/2020

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Form 1 Mathematics

Point C divide line AB given below externally in the ratio 5:2

By construction, determine the position of point c

Answer

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K.C.S.E Mathematics Q & A - MODEL 2014PP1QN23

7/9/2020

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Form 1 Mathematics

The figure below represents a piece of land in the shape of a quadrilateral in which AB =240M, BC = 70m CD = 200m ˂BCD = 150⁰ ˂ABC = 90⁰

Calculate
(a) The size of ˂BAC correct to 2decimal places
(b) The length AD correct to one decimal place
(c) The area of the piece of land, in hectares, correct to 2 decimal places

answers

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K.C.S.E Mathematics Q & A - MODEL 2003PP1QN015

3/9/2020

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Form 2 Mathematics

Three points O, A and B are on the same horizontal ground. Point A is 80 metres to the north of O. Point B is located 70 metres on a bearing of 060⁰ from A. A vertical mast stands at point B. The angle of elevation of the top of the mast from o is 20⁰.

Calculate:

a) The distance of B from O. (2mks)

b) The height of the mast in metres (2mks)

aNSWERS

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K.C.S.E Mathematics Q & A - MODEL 2002PP2QN022

30/8/2020

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Form 1 Mathematics

Four points B,C,Q and D lie on the same plane. Point B is 42km due South – West of point Q. Point C is 50km on a bearing of S 60⁰ E from Q.
Point D is equidistant B, Q and C.

a) Using the scale: 1cm represents 10km, construct a diagram showing the positions of B, C, Q and D.

Determines the:

i) Distance between B and C
ii) Bearing of D from B.

aNSWER

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K.C.S.E Mathematics Q & A - MODEL 2008PP1QN05

16/8/2020

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Form 1 Mathematics

The figure below shows a net of a solid

Below is a part of the sketch of the solid whose net is shown above.
Complete the sketch of the solid, showing the hidden edges with broken lines.

answer

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K.C.S.E Mathematics Q & A - MODEL 2007PP1QN18

12/8/2020

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Form 2 Mathematics

In the diagram below PA represents an electricity post of height 9.6 m. BB and RC represents two storey buildings of heights 15.4 m and 33.4 m respectively.
The angle of depression of A from B is 5.5⁰ While the angle of elevation of C from B is 30.5⁰ and BC = 35m.

(a) Calculate, to the nearest metre, the distance AB
(b) By scale drawing find,
(i) The distance AC in metres
(ii) Angle BCA and hence determine the angle of depression of A from C

answers

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K.C.S.E Mathematics Q & A - MODEL 2006PP2QN13

10/8/2020

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Form 1 Mathematics

The figure below is drawn to scale. It represents a field in the shape of an equilateral triangle of side 80m

The owner wants to plant some flowers in the field. The flowers must be at most, 60m from A and nearer to B than to C. If no flower is to be more than 40m from BC, show by shading, the exact region where the flowers may be planted

answer

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K.C.S.E Mathematics Q & A - MODEL 2001PP2QN017

10/8/2020

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Form 1 Mathematics

A helicopter is stationed at an airport H on a bearing 060^o and 800km from another airport P.A third airport is J is on bearing of 140⁰ and 1,200km from H.

Determine:

i) Value of P
ii)The bearing of P from J

Answer

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K.C.S.E Mathematics Q & A - MODEL 2000PP2QN18

14/7/2020

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Form 1 Mathematics

A rally car traveled from point R to point S. S is 128 km on a bearing 060⁰ from R. The car then set off S at 9.30 am towards T at an average of 150 km/h. It was expected at T at 11.30 am. After traveling for I hour and 20 minutes it broke down at point P. The bearing of T and P from S is 300⁰.

Calculate the:

(a)
- (i) Distance from R to P
- (ii) Bearing of P and R
(b) The repair took 10 minutes and the car set off to complete its journey to T. Find the speed at which car must now move to reach T on time.

Answer

K.C.S.E Mathematics Q & A - MODEL 2000PP2QN18

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K.C.S.E Mathematics Q & A - MODEL 2000PP1QN08

8/7/2020

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Form 1 Mathematics | Topical Questions and Answers

Shopping centers X, Y and Z are such that Y is 12 km south of X and Z is 15 km from X.Z is on a bearing of 330⁰ from Y.

ANSWER

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K.C.S.E Mathematics Q & A - MODEL 2000PP1QN06

8/7/2020

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Form 1 Mathematics | Topical Questions and Answers

The enclosed region shown in the figure below represent a ranch drawn to scale. The actual area of the ranch is 1075 hectares.

(a) Estimate the area of the enclosed region in square centimetres
(b) Calculate the linear scale used

K.C.S.E Mathematics Q & A - MODEL 2000PP1QN06

ANSWER

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN21

30/6/2020

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Form 1 Mathematics

The diagram below shows a garden drawn to scale of 1: 400. In the garden there are already tow trees marked A and B. The gardener wises to plant more trees. There are a number of rules he wishes to apply.

Rule 1: Each new tree must be an equal distance from both trees A and B.
Rule 2: Each new tree must be at least 4 m from the edges of the garden.
Rule 3: Each new tree is at least 14 m from tree B.

(a) Draw the locus given by each of these rules on the diagram
(b) If the new trees are to be planted 4m apart, show on your diagram the possible planting points for the new trees.

Answer

K.C.S.E Mathematics Q & A - MODEL 1999PP2QN21

K.C.S.E Mathematics Q & A - MODEL 1999PP2QN18

30/6/2020

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Form 1 Mathematics

A tower is on a bearing of 030⁰ from a point P and a distance of elevation of the top is 15⁰ and the angle of depression of the foot of the tower is 1⁰.

a) Find the height of the tower
b) A point Q is on the same horizon plane as point P. The tower is on a bearing 330⁰ from Q and at a distance of 70 m.

Answer

K.C.S.E Mathematics Q & A - MODEL 1999PP2QN18

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K.C.S.E Mathematics Q & A - MODEL 1999PP1QN05

25/6/2020

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Free 1999 K.C.S.E Mathematics Topical Question & Answers Paper 1

The figure below is a map of a forest drawn on a grid of 1 cm squares

a map of a forest drawn on a grid of 1 cm squares

(a) Estimate the area of the map in square centimeters
(b) If the scale of the map is 1: 50,000 estimate the area of the forest in hectares

ANSWER

K.C.S.E Mathematics Q & A - MODEL 1999PP1QN05

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Atika School HAS A VARIETY OF MATHEMATICS QUESTIONS AND ANSWERS SORTED ACCORDING TO LEVELS, PAPERS AND TOPICS

KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

Topically Analysed

​A map has a scale of 1 : 2500 and on it is square plot of land which has an area of 4cm². Calculate the actual area in hectares of the land. (3mks)

​​​Worked Answer:

(a) A small field was surveyed and the measurements recorded in a surveyor’s field book as in the table below. ​

​(i) Using a scale of 1cm to 10m make an accurate drawing of the map of the field. (4mks)

​(ii) Find the area of the field. (3mks)

(iii) Assuming that the baseline in (a) runs in a northern direction give the position of D relative to A using bearing and distance. (3mks)

Four points B, C, Q and D lie on the same plane. Point B is 42km due southwest point Q. Point C is 50 km on a bearing of S60oE from Q. Point D is equidistant from B, Q and C.

(a) Using the scale: 1cm represents 10km, construct a diagram showing the positions of B, C, Q and D. (5mks)

(b) Determine the (i) Distance between B and C (1mk)

(ii) Bearing of D from B (2mks)

(c) Find the distance and bearing of D from C. (2mks)

From a point 20m away on a level ground the angle of elevation to the lower window line is 25° and the angle of elevation to the top line of the window is 34°. Calculate the height of the window. [3 marks]

Worked solution

From a point 20m away on a level ground the angle of elevation to the lower window line is 270 and the angle of elevation to the top of the window is 320. calculate the height of the window (3mks)

Worked Answer:

Form 1 Mathematics

N.22

Form 1 Mathematics

7

Form 2 Mathematics

N.23

Form 1 Mathematics

N.19

Form 1 Mathematics

7

Form 1 Mathematics

N.6

Form 1 Mathematics

23

Form 2 Mathematics

15

Form 1 Mathematics

22

Form 1 Mathematics

5

Form 2 Mathematics

18

Form 1 Mathematics

13

Form 1 Mathematics

17

Form 1 Mathematics

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Form 1 Mathematics | Topical Questions and Answers

8

Form 1 Mathematics | Topical Questions and Answers

6

Form 1 Mathematics

21

Related Questions on Scale Drawing

Form 1 Mathematics

18

Free 1999 K.C.S.E Mathematics Topical Question & Answers Paper 1

5

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A map has a scale of 1 : 2500 and on it is square plot of land which has an area of 4cm². Calculate the actual area in hectares of the land. (3mks)

Worked Answer:

(a) A small field was surveyed and the measurements recorded in a surveyor’s field book as in the table below.

(i) Using a scale of 1cm to 10m make an accurate drawing of the map of the field. (4mks)

(ii) Find the area of the field. (3mks)

Four points B, C, Q and D lie on the same plane. Point B is 42km due southwest point Q. Point C is 50 km on a bearing of S60^oE from Q. Point D is equidistant from B, Q and C.

(b) Determine the
(i) Distance between B and C (1mk)

From a point 20m away on a level ground the angle of elevation to the lower window line is 27⁰ and the angle of elevation to the top of the window is 32⁰. calculate the height of the window (3mks)