Form 4 Mathematics
The figure KLMN below is a scale drawing of a rectangular piece of land of length KL = 80m
(a) On the figure, construct
(i) The locus of a point P which is both equidistant from points L and M It and from lines KL and LM. (ii) the locus of a point Q such that ∠KQL = 90°. (b) (i) Shade the region R bounded by the locus of Q and the Locus of points equidistant from KL and LM. (ii) Find the area of the region R in m². (Take ℼ= 3.142).
answers
Form 4 Mathematics(a) BCD is a rectangle in which AB = 7.6 cm and AD = 5.2 cm. draw the rectangle and construct the lucus of a point P within the rectangle such that P is equidistant from CB and CD ( 3 marks) (b) Q is a variable point within the rectangle ABCD drawn in (a) above such that 600 ≤ AQB≤ 900 On the same diagram, construct and show the locus of point Q, by leaving unshaded, the region in which point Q lies
Answer
Form 4 Mathematics
The figure below is a triangle ABC.
(a) On the triangle, locate the locus of points equidistant from AC and AB and 5 cm from B.
(b) Shade the region R, inside the triangle, which is less than 5 cm from B and nearer to AC than AB.
answer
Form 4 Mathematics
Below is a lien AB and a point X. Determine the locus of a point P equidistant from points A and B and 4 cm from X.
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Form 4 Mathematics
Figure ABCD below is a scale drawing representing a square plot of side 80 metres.
On the drawing, construct:
(i) the locus of a point P, such that it is equidistant from AD and BC. (ii) the locus of a point Q such that <AQB = 60°. (i) Mark on the drawing the point Q , the intersection of the locus of Q and line AD. Determine the length of BQ1 in metres. (ii) Calculate, correct to the nearest m2, the area of the region bounded by the locus of P, the locus of Q and the line BQ1
answers
Form 4 Mathematics
The line PQ below is 8cm long and L is its midpoint
Answer
Form 4 Mathematics
A point P moves inside a sector of a circle, centre O, and chord AB such that 2cm < OP ≤ 3cm and angle APB = 65 Draw the locus of P
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Form 4 Mathematics
A point P on the line AB shown below is such that AP = 2/7 AB. By construction locate P.
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Form 4 Mathematics
The figure below represents a scale drawing of a rectangular piece of land, RSTU. RS = 9 cm and ST = 7 cm.
An electric post P, is to be erected inside the piece of land. On the scale drawing, shade the possible region in which P would lie such that PU > PT and PS ≤ 7 cm
answer
Form 4 Mathematics
The figure below shows a circle centre O and a point Q which is outside the circle
Using a ruler and a pair of compasses, only locate a point on the circle such that angle OPQ = 90o
answer
Form 4 Mathematics
The diagram below represents a field PQR
Answer
Form 4 Mathematics
The line segment BC given below is one side of triangle ABC
Answer
Use a ruler and a pair of compasses only for all constructions in this question(a) On the line BC given below, construct triangle ABC such that ∠ABC = 300 and BA = 12 cm
ANSWER
On the figure below construct
K.N.E.C Marking Scheme
Use ruler and compasses only in this questionThe diagram below shows three points A, B and D
MARKING SCHEME
Using ruler and compasses only, construct a parallelogram ABCD such that AB = 10cm, BC = 7cm and ∠ABC = 1050. Also construct the loci of P and Q within the parallel such that AP ≤ 4 cm, and BC ≤ 6 cm. Calculate the area within the parallelogram and outside the regions bounded by the loci.
MARKING SCHEME
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