Category: Geometric Constructions

Using a ruler and a pair of compasses only, construct a parallelogram ABCD in which AB=6cm, BC=5cm and angle ADC=150 degrees

22/5/2023

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Using a ruler and a pair of compasses only, construct a parallelogram ABCD in which AB=6cm, BC=5cm and angle ADC=150 degrees

KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 11

Answer

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Using a ruler and pair of compasses only construct triangle ABC in which AB = 6.5cm, BC= 5.0cm and angle ABC = 600. Measure AC

13/5/2023

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a) Using a ruler and pair of compasses only construct triangle ABC in which AB = 6.5cm, BC= 5.0cm and angle ABC = 600. Measure AC (3mks)
b) On same side of AB as C (3mks)
i) Determine the locus of a point P such that angle APB = 600 (3mks)
ii) Construct the locus of R such that AR = 3cm. (1mk)
iii) Identify the region T such that AR  3 and APB  600 by shading the unwanted part. (3mks)

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Using a ruler and a pair of compasses only construct triangle ABC such that AB= 4.5cm, BC = 8.1cm and angle CBA = 60^0. Measure angle CAB. (3mks)

11/5/2023

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Using a ruler and a pair of compasses only construct triangle ABC such that AB= 4.5cm, BC = 8.1cm and angle CBA = 60^0. Measure angle CAB. (3mks)

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K.C.S.E Mathematics Q & A - MODEL 2019PP1QN12

22/9/2020

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Form 1 Mathematics

Using a ruler and a pair of compass only, construct a rhombus PQRS such that PQ = 6cm and SPQ = 75°.
Measure the length of PR.

answer

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K.C.S.E Mathematics Q & A - MODEL 2018PP2QN20

21/9/2020

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Form 1 Mathematics

(a) Using a ruler and a pair of compasses only, construct:
(i) a parallelogram ABCD, with line AB below as part of it, such that AD = 7 cm and angle BAD = 60°;

(ii) the locus of points equidistant from AB and AD;
(iii) the perpendicular bisector of BC.
(b) (i) Mark the point P that lies on DC and is equidistant from AB and AD.
(ii) Measure BP.
(c) Describe the locus that the perpendicular bisector of BC represents.
(d) Calculate the area of trapezium ABCP.

answers

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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 2017PP2QN08

17/9/2020

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Form 1 Mathematics

Using a ruler and a pair of compasses only, construct:
(a) a triangle LMN in which LM = 5 cm, LN = 5.6 cm and MLN = 45°
(b) the circle that touches all the sides of the triangle.

answer

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K.C.S.E Mathematics Q & A - MODEL 2016PP1QN22

14/9/2020

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Form 1 Mathematics

Using a pair of compasses and ruler only, construct
a)i)Triangle ABC in which AB= 5 cm, <BAC=30 and <ABC = 105.
ii)A circle that passes through he vertices of the triangle ABC. Measure the radius
iii)the height of triangle ABC with AB as the base. Measure the height
b) Determine the area of circle that lies outside the triangle correct to 2 decimal places

answers

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K.C.S.E Mathematics Q & A - MODEL 2004.PP1.QN.15

11/9/2020

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Form 1 Mathematics

The figure below is a triangle XYZ. Using a pair of compasses and a ruler only, construct an inscribed circle such that the centre of the circle and the point x are the opposite sides of line Yz.

Answer

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K.C.S.E Mathematics Q & A - MODEL 2015PP1QN19

10/9/2020

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Form 1 Mathematics

Line AB drawn below is a side of a triangle ABC.
(a) Using a pair of compasses and ruler only construct:
(i) triangle ABC in which BC = 10cm and angle CAB = 90°;
(ii) a rhombus BCDE such that angle CBE = 120°;
(iii) a perpendicular from F, the point of intersection of the diagonals of the rhombus, to meet BE at G. Measure FG;
(iv) a circle to touch all the sides of the rhombus.
b) Determine the area of the region in the rhombus that lies outside the circle

ANSWERS

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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 2014PP1QN22

7/9/2020

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Form 1 Mathematics

Using a pair of compasses and a ruler only, construct
(a) (i) Triangle ABC in which AB =5cm, ˂BAC = 30⁰ and ˂ABC = 105⁰
(ii) A circle that passes through the vertices of the triangle ABC. Measure the radius
(iii) The height of triangle ABC WITH AB as the base. Measure the height
(b) Determine the area of the circle that lies outside the triangle correct to 2decimal places

answers

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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN05

3/9/2020

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Form 1 Mathematics

(a) Using a pair of compasses and ruler only, construct an escribed circle to touch side XZ of triangle XYZ drawn below

(b) Measure the radius of the circle

answer

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K.C.S.E Mathematics Q & A - MODEL 2012PP2QN21

2/9/2020

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Form 1 Mathematics

(a) on the same diagram construct:
(i) triangle ABC such that AB = 9 cm, AC= 7 cm and angle CAB = 60°;
(ii) the locus of a point P such that P is equidistant from A and B;
(iii) the locus of a point Q such that CQ ≤ 3.5cm.
(b) On the diagram in part (a):
(i) shade the region R, containing all the points enclosed by the locus of P and the locus of Q, such that AP ≥ BP;
(ii) find the area of the region shaded in part (b)(i) above.

answers

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K.C.S.E Mathematics Q & A - MODEL 2003PP1QN008

2/9/2020

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Form 1 Mathematics

Using a ruler and a pair of compasses only.

a) Construct triangle ABC in which BC = 8cm, angle ABC = 105⁰ and BAC =45⁰
b) Drop a perpendicular from A to meet CB produced at p. Hence find the area of triangle ABC.

aNSWER

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K.C.S.E Mathematics Q & A - MODEL 2012PP2QN06

1/9/2020

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Form 1 Mathematics

Construct a circle centre x and radius 2.5 cm. Construct a tangent from a point P, 6 cm from x to touch the circle at R. Measure the length PR.

answer

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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN08

31/8/2020

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Form 1 Mathematics

Using a pair of compasses and ruler only, construct a quadrilateral ABCD in which AB = 4cm, BC = 6 cm, AD = 3 cm, angle ABC = 135° and angle
DAB = 60°.
Measure the size of angle BCD.

answer

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K.C.S.E Mathematics Q & A - MODEL 2011PP2QN10

28/8/2020

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Form 1 Mathematics

(a) In the figure below, lines NA and NB represent tangents to a circle at points A and B.
Use a pair of compasses and ruler only to construct the circle.

(b) Measure the radius of the circle.

answer

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K.C.S.E Mathematics Q & A - MODEL 2011PP1QN09

26/8/2020

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Form 1 Mathematics

Using a ruler and a pair of compases only:
(a) construct a parallelogram PQRS in which PQ = 6 cm, QR = 4 cm and angle SPQ= 75°;
(b) determine the perpendicular distance between PQ and SR.

answers

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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN13

26/8/2020

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Form 1 Mathematics

(a) Using line AB given below, construct the locus of a point P such that angle APB 90.

(b) On the same diagram locate two possible positions of point C such that point C is on the locus of P and is equidistant from A and B.

answer

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K.C.S.E Mathematics Q & A - MODEL 2010PP1QN10

24/8/2020

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Form 1 Mathematics

Using a ruler and a pair of compasses only, construct a rhombus QRST in which angle TQR = 60⁰ and QS = 10 cm.

answer

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K.C.S.E Mathematics Q & A - MODEL 2009PP2QN04

20/8/2020

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Form 1 Mathematics

In the figure below, O is the centre of the circle and radius ON is perpendicular to the line TS at N.

Using a ruler and a pair o compasses only, construct a triangle ABC to inscribe the circle, given that angle ABC = 60⁰, BC = 12 cm and points B and C are on the line TS

answer

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K.C.S.E Mathematics Q & A - MODEL 2009PP1QN14

19/8/2020

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Form 1 Mathematics

The diagonals of a rhombus PQRS intersect at T. Given that p(2,2), Q(3, 6 ) and R(-1, 5):
a) Draw the rhombus PQRS on the grid provided;
b) State the coordinates of T.

answer

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K.C.S.E Mathematics Q & A - MODEL 2009PP1QN11

19/8/2020

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Form 1 Mathematics

Line AB shown below is a side of a trapezium ABCD in which angle ABC in which angle ABC= 105⁰, BC = 4 cm,CD = 5 cm and CD is parallel to AB.

Using a ruler and a pair of compasses only:
a) Complete the trapezium;
b) Locate point t on line AB such that angle ATD = 90⁰

answer

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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN03

17/8/2020

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Form 1 Mathematics

Line AB given below is one side of triangle ABC. Using a ruler and a pair of compasses only;

(i) Complete the triangle ABC such that BC=5cm and angle ABC=45
(ii) On the same diagram construct a circle touching sides AC,BA produced and BC produced.

answer

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Using a ruler and a pair of compasses only, construct a parallelogram ABCD in which AB=6cm, BC=5cm and angle ADC=150 degrees

Answer

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Using a ruler and a pair of compasses only construct triangle ABC such that AB= 4.5cm, BC = 8.1cm and angle CBA = 60^0. Measure angle CAB. (3mks)