revision exercise feb 24

7/29/2019 Revision Exercise Feb 24

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Revision ExerciseAddMaths Form 5Feb. 24, 2013

1. Given the quadratic function ( )f x = 6x13x2.(a) Express the quadratic function 6x1 3x

2in the form k+ m(x + n)

2, where k, m and n

are constants.

(b) Sketch the graph of ( )f x .

(c) Find the range of values ofp such that 6x43x2

=p has no real roots.

Diagram 1

2. Diagram 1 shows a parallelogramPQRSon a Cartesian plane.(a) Find the value oft.

Hence, state the equation of a straight linePQ in the intercept form. [3 marks]

(b) Nis a moving point such that its distance is in the ratioRQ : QN= 2 : 3.

Find the equation of the locus ofN. [2 marks]

(c) Calculate the area ofPQRS. [2 marks]

3. Diagram 2 shows a sectorOACof a circle with centre O and radius 15 cm.

Diagram 2

Given that 3:1: BODAOB and pointD lies on OCsuch that 5:4: OCOD . Calculate

(a) the value ofin radians,(b) the total area of the shaded regions.

P(t, 0)

Q(0, 2)

R(4, 12)

S(4t, 10)

x

y

O

A

B

OCD


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r r+ 1 r+ 2 r+ 3

4.

Diagram 3

Diagram 3 shows three cylinders with a constant radius of 3 cm. The height of the firstcylinders is h cm. For each subsequent cylinder, its height increases by 1 cm compared to

the previous one. Determine whether the volumes of these cylinders are in an arithmetic

progression or geometric progression. Hence, state its common difference or common ratio.

Diagram 4

5. A piece of wire, 11(4 + ) cm in length, is cut to form four quadrants of a circle, as shownin Diagram 4. The radius of each quadrant increases by 1 cm, in sequence.

Find

(a) the radius of the largest quadrant,

(b) the number of quadrant that can be formed if the original length of the wire used is 120

+ 30 cm,

6. The curve 196 23 xxxy passes through the point A(2, 3) and has two turning points,P(3, 1) and Q. Find

(a) the gradient of the curve atA,(b) the equation of the normal to the curve atA,(c) the coordinates of the point Q and determine whetherQ is the maximum or minimum

point. [SPM 2010, P2]

cmh cmh 1 cmh 2


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Q

P

S

R

9 cm10 cm

14 cm

35

Diagram 5

7. Diagram 5 shows a quadrilateralPQRS. The area of the trianglePQR is 34 cm2 and PQR isacute. Calculate

(a) PQR,(b) the length ofPR,

(c) RPS,

(d) the area ofPQRS.


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1. (a) f(x) =2

3( 1) 2x

(b)

(c) p > 1

2. (a)3

4 2

yx = 1

(b) x2 +y2

4y

257 = 0

(c) 211

3unit

2

5. (a) 7 cm

(b) n = 8

(1, 2)

1 (2, 1)

revision exercise feb 24

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