8/9/2019 Module AddHance Paper2@Set1

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Module AddHance_Paper2@Set1 Prepared by: Hayati Aini Ahmad

1. Use graph paper to answer this question

A furniture shop produces two types of furniture, tables and chairs. The

materials used are red wood and plywood. Table 1 shows the quantity of the

materials used to make each type of furniture.

FurnitureArea(in m

2)

Red wood Plywood

Table 5 5

Chair 20 10

The furniture shop produces tables and chairs every day. The making offurniture per day is based on the following constraints:

I: The minimum area of red wood used is 400 m2

II: The maximum area of plywood used is 450 m2

III. The number of tables produced is not more than the number of chairs

produced

(a) Write three inequalities, other than and , which satisfy all theabove constraints [3 marks]

(b) Using a scale of 2 cm to 10 furniture on both axes, construct and shade the

region R which satisfies all the above constraints [3 marks]

(c) Find

(i) the minimum number of chairs produced if 15 tables are produced per

day

(ii) the maximum profit per day if the profit of each table and each chair is

RM120 and RM90 respectively. [4 marks]

Answer:

(a)

(c) i) 16

ii) RM 6300

2. Diagram 1 shows a triangle PQR. The straight line RT intersects the straight

line QS at U.

It is given that

and .

(a) Express in terms of and . (i) (ii) [4 marks]

(b) (i) Given that , state in terms of and

(ii) Given that , state in terms of and

(c) Using and from (b),find the value of and [6 marks]

Answer:

(a) i)

(ii)

(b)

i)

ii)

(c)

3. A trading company Z calculates its annual net profit for the year on each 31

December and projects the profit to be 6% higher than the previous year. On

31 December 2004, company Z s annual net profit for the year was

RM 300 000. Calculate

(a) the companys annual net profit, to the nearest RM, for the year ending 31

December 2008 [3 marks]

(b) the least value ofnsuch that this companys annual net profit in the nth

year will exceed RM 500 000. [3 marks]

(c) the total annual net profit of company Z, to the nearest RM, for the first six

years since 1 January 2004. [2 marks]

Answer:

(a) (b) (c)

R

Q

SU

TP

8/9/2019 Module AddHance Paper2@Set1

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Module AddHance_Paper2@Set1 Prepared by: Hayati Aini Ahmad

4.

Diagram 2 shows a trapezium ABCD. The line AD is perpendicular to DC which

intersects the y-axis at P. It is given that the equation of the straight line DC is

(a) Find (i) the value of(ii) the equation of the straight line AD (iii) the coordinates of D

(b) Given DP : PC = 1 : 4 , find the coordinates of C

(c ) A point Q(x,y) moves such that 2QA=QB .Find the equation of the locus

of Q.

Answer:

(a)

(i) k = 6

(ii) y=-2x-3

(iii) D(-2,1)

(b) C(8,6)(c)

5. Diagram 3 shows the curve and the normal to the curve at the point

Calculate

a) the equation of the normal to the curve at A [3 marks]

b) the area of the region enclosed by the curve, the normal and the x-axis[3 m]

c) the volume of revolution, in terms of , if the region in 5(b) is rotated

through about the x-axis [4 marks]

Answer:

a)

b)

c)

6. Diagram 4 shows a semicircle ABC, with centre O and radius 6 cm. PB is a

tangent to the semicircle at B and PAOC is a straight line. R is the region

enclosed by the tangent PB, the arc AB and the straight line PA. Given that

PB=8 cm, calculate[Use ]

(a) the angle AOB, in radians

(b (i) the length, in cm, of the arc AB,

(ii) the perimeter, in cm, of the region R

(c) the area, in cm2, of the region R

Answer:

(a) (b)i )

ii) (c)

B

P OA C

R