8/8/2019 Module AddHance Paper2@Set2

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Module AddHance_Paper2@Set2 Prepared by: Pn. Hayati Aini Ahmad

1. A factory produces two models of school bags, Power and Sporty, usingmachine A and machine B. In a week, the factory produces units of Powerand units of Sporty. Machine A needs 70 minutes to produce one unit of Power and 40 minutes to produce one unit of Sporty. Machine B needs 20minutes to produce one unit of Power and 80 minutes to produce one unit of Sporty. The production of the factory in week is based on the followingconstraints.I. The total time machine A is used does not exceed 4200 minutesII. The total time machine B is used is at least 1600 minutesIII. The production number of Sporty is not more than two times the number

of Power.(a) Write three inequalities, other than and , which satisfy all the

above constraints [3 marks](b) Using a scale of 2 cm to 10 units on both axes, construct and shade the

region R which satisfies all the above constraints [3 marks](c) Find

(i) the maximum number of Power in a week produced if the factorywants to produce Power that is two times the number of Sporty

(ii) the maximum profit in a week if the profit of one unit of Power andone unit of Sporty is RM20 and RM10 respectively. [4 marks]

Answer:(a)

(c) (i) 46(ii) RM 1180

2. Diagram 1 shows the straight line intersecting the curveat the points A and B.

Find(a) the value of and of [3 marks](b) the area of the shaded region [4 marks](c) the volume generated, in terms of when the shaded region is revolved

through about the y-axis. [3 marks]

Answer:(a) h= 5, k=21

(b)

(c)

3. It is given that and . If and is parallel to .

Find the value of and of for and [6 marks]

Answer:h= 6 , k= 8

4. (a) Find the gradient of the tangent to the curve at the point

(1 , 1). Hence, find the equation of the tangent to the curve at that point.[4 marks]

(b) A wire of length 60 cm is bent to form a circle. When the wire is heated,the length increases at the rate of 0.2 cms -1(use )

(i) Calculate the rate of change in the radius of the circle(ii) Hence, calculate the radius of the circle after 5 seconds [4 marks]

Answer:

(a) (b) (i) 0.03183

(i) r=9.707

8/8/2019 Module AddHance Paper2@Set2

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Module AddHance_Paper2@Set2 Prepared by: Pn. Hayati Aini Ahmad

5. Diagram 2 shows a coil of wire is bent into a few semicircles, such that theradius of each subsequent semicircle increase by 1 unit.

(a) Show that the perimeter of each semicircle form an arithmetic progressionand state the common difference. [3 marks]

(b) Given that r = 5 cm [use ](i) determine which semicircle has a perimeter of 47.13 cm(ii) find the sum of the perimeter of the first 15 semicircles [4 marks]

Answer:(a) (b)(i) n = 11(ii) 565.56 cm

6. In Diagram 3, the straight line AB has an equation . AB intersect the

x-axis and the y-axis at point A and B respectively. Point P lies on AB such thatAP : AB = 2: 3

Find(a) the coordinates of P [3 marks]

(b) the equation of the perpendicular bisector of AP. [3 marks]

Answer:(a) P(1 , 6)

(b)

7. Diagram 4 shows a sector ORP of a circle, centre O and radius 4.5 cm. RSPT is acircle, centre Q. The straight line OR and OP are tangents at the point P andpoint R respectively.[use ]

Calculate(a) the length, in cm, of radius QR [2 marks](b) the length, in cm, of the arc RSP [4 marks](c) the area, in cm 2, of the shaded region [4 marks]

Answer:(a)QR=1.797(b)Arc RSP=7.0119 cm(c) 0.392 cm 2