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SYSTEM OF EQUATION

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State your answer correct to 3 decimal places.

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PROGRESSIONS

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12 The first three terms of a geometric progression are x+10, x-2 and x-10 respectively.
Calculate :
(a) The value of x.
(b) The sum to infinity of this progression.
Answer : (a) x=26 , (b) 108

13 The sum of the first n terms of an arithmetic progression is given Sn=2n2-5n. Find :
(a) The first term
(b) The common difference
(c) The sum of the 12th term to the 20th term.
Answer : (a) -3, (b) 4, (c) 513

14 Diagram 9 shows an archway with concrete pole which built with concrete blocks.
The volume of three consecutive blocks (in m3) are given in diagram. Find the total
volume of concrete that needed to build one of the concrete pole.

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COORDINATE GEOMETRY

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Given a square, ABCD such that points A and D are located on the y-axis and x-axis

respectively. The coordinates of C is (12,8) and the equation of AB is y=2x+4. If AD

and BC are perpendicular to AB and CD respectively, find

(a) The coordinates of A and D.

(b) The equation of BC

(c) The coordinates of B

(d) The length of CD

Answer : (a) A(0,4), D(8,0)

(b) = 1 + 14 (c) B(4,12)
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(d) √80

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8 The point P(4,7) lies on the circumference of a circle with centre T(-8,2). Find the
radius of the circle.
Answer : 13

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10 Solution by scale drawing is not accepted. Diagram 8 shows three points, P, Q and R.

The equation of straight line QR is

= 2 + 7.

(a) Find the midpoint of PQ,

(b) Calculate the area of quadrilateral OPQR

(c) Find the equation of perpendicular bisector of QR

(d) Given (14 , ℎ) is an intersection point of perpendicular bisector of straight line

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PQ and QR. Find the value of h.

Answer : (a)(4,7) (b) 34 unit2

(c) = − 1 + 8 (d) h=137

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Given an isosceles triangle with vertices A(0,-1), B(3,4) and C(-2,1). When the triangle

ABC is reflected in the line AC, find the coordinates of point B’ such that B’ is image of

point B.

Answer : B’(-5,4)

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13 Solutions by scale drawing is not accepted. Diagram 1 shows a quadrilateral OPQR,
where O is the origin.

The equation of straight line PQ is
4x + 3y = 25 and QR is x -4y -11= 0.

(a) Find the value of k.
(b) Show that ∠ OPQ = 90°.
(c) Point T moves such that its distance from point P is always 5 units. Find the

equation of the locus T.
Answer : (a) k=3 (b) shown
(c) x2 +y2 -8x -6y =0

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Answer : 15 units

15 Solution by scale drawing is not accepted. Diagram 3 shows the location of town A
and town B drawn on a Cartesian plane.

PQ is a straight road such that the distance from town A and town B to any point on

the road is always equal.

(a) Find the equation of PQ.

(b) Another straight road, ST with an equation y =2x + 7 is to be built.

(i) A traffic light is to be installed at the crossroads of the two roads. Find

the coordinates of the traffic light.

(ii) Which of the two roads passes through town C ((− 4 , 1) ?
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Answer : (a) y = -3x -3 (b) (-2,3) (c) Road PQ

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VECTORS

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Answer : (a) (i)2x (ii) -15/2 y (b) (i) 6 units (ii) 15 units
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Answer : (a) (i) OY = (4 -4h) a + 15 hb (ii) OY = (6-6k)b +6ka (b) h= 2/11 , k = 6/11
(c) 3 √21
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UCAPAN SETINGGI-TINGGI
PENGHARGAAN KEPADA

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Semua Guru Muda

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