Category: Scale Drawing

A forest is enclosed by four straight boundaries AB, BC, CD and DA. Point B is 25 km on a bearing of 315° from A, C is directly south of B on a bearing of 260° from A and D is 30 km on a bearing of 210° from C.

22/5/2023

Comments

A forest is enclosed by four straight boundaries AB, BC, CD and DA. Point B is 25 km on a bearing of 315° from A, C is directly south of B on a bearing of 260° from A and D is 30 km on a bearing of 210° from C.

KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 20

Comments

A vertical electric pole was erected 6.4 m from the foot of a vertical fencing pole on the same horizontal level. The fencing pole is 2 m high. The angle of elevation of the top of the electric pole from the top of the fencing pole is 30°. Determine the

22/5/2023

Comments

A vertical electric pole was erected 6.4 m from the foot of a vertical fencing pole on the same horizontal level. The fencing pole is 2 m high. The angle of elevation of the top of the electric pole from the top of the fencing pole is 30°. Determine the height of the electric pole correct to 1 decimal place. (2 marks)

KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 14

Comments

Three Jets MN and P are coming to airport A which is on the bearing 3400 from an adjacent airport B. N is East of airport A and 600km from airport B, on the bearing of 0400. M is on a bearing 0450 from A . P and M are due north of B. P is on the bearing

11/5/2023

Comments

Three Jets MN and P are coming to airport A which is on the bearing 3400 from an adjacent airport B. N is East of airport A and 600km from airport B, on the bearing of 0400. M is on a bearing 0450 from A . P and M are due north of B. P is on the bearing of 2500 from N

Comments

Transfer the measurement of the reap below to a field book (2mks)

11/5/2023

Comments

Transfer the measurement of the reap below to a field book (2mks)

Comments

Four towns PQR and S are located such that town Q is 70km on a bearing of 050° from P. Town R is 50km on a bearing of 145° from Q and town S is 55km on a bearing of S35°W of R.

29/4/2023

Comments

Four towns PQR and S are located such that town Q is 70km on a bearing of 050° from P.
Town R is 50km on a bearing of 145° from Q and town S is 55km on a bearing of S35°W of R.
(a)By scale drawing, show the relative position of the four towns.
(Use a scale of 1cm to represent 10km). (3mks)
(b) Use your diagram to determine
(i)        the distance and bearing of P from S. (3mks)
(ii)       how far R is from P. (2mks)
(c)       Determine by the diagram or otherwise how far north town P is from town S. (2mks)

ANSWER

Comments

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

Comments

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)

Comments

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

Comments

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:

Comments

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

23/11/2021

Comments

(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)

Comments

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

Comments

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)

Comments

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

Comments

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

Comments

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

Comments

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:

Comments

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

23/9/2020

Comments

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

Comments

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

18/9/2020

Comments

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

Comments

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

18/9/2020

Comments

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

Comments

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

16/9/2020

Comments

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

Comments

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

10/9/2020

Comments

Form 1 Mathematics

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

answer

Comments

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

9/9/2020

Comments

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

Comments

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

7/9/2020

Comments

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

Comments

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

3/9/2020

Comments

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

Comments

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

30/8/2020

Comments

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

Comments

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

16/8/2020

Comments

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

Comments

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

12/8/2020

Comments

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

Comments

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

10/8/2020

Comments

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

Comments

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

10/8/2020

Comments

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

Comments

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

14/7/2020

Comments

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

Comments

<<Previous

KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

Topically Analysed

A forest is enclosed by four straight boundaries AB, BC, CD and DA. Point B is 25 km on a bearing of 315° from A, C is directly south of B on a bearing of 260° from A and D is 30 km on a bearing of 210° from C.

​Transfer the measurement of the reap below to a field book (2mks)

​ANSWER

​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

18

Categories

Archives

HIGH SCHOOL EXAMINATIONS

COLLEGE RESOURCES

FREE NOVELS

PRIMARY SCHOOL RESOURCES 8-4-4

PRIMARY SCHOOL RESOURCES CBC

Transfer the measurement of the reap below to a field book (2mks)

ANSWER

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)