Pep Semester 2 MM p2 F4

8/3/2019 Pep Semester 2 MM p2 F4

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Section A

[52 marks]

Answerall questions in this section.

1. Factorise completely

[3 marks]

2. Solve the quadratic equation

[4 marks]

3. Calculate the value ofxand ythat satisfy the following simultaneous linearequations.

[4 marks]

4.

a) Diagram 1 show setsA, B andC. Define the sets which represent the

shaded region.

b) Redraw the diagram 1 and shade the region that represent the sets ( B

C) A[3 marks]


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5. In diagram 2, the graph shows that PQ, QRand RSare straight line. P is on

the y-axis. OP is parallel to QRand PQ is parallel to RS.

The equation ofPQ is 2x + y = 5

a) State the equation of the straight line QR,

b) Find the equation of the straight line RSand hence, state its y-intercept,

c) Find the coordinate of point Q. [6 marks]

6. In diagram 3, 0 is the origin. MNand KL are straight lines. Given the gradient

of straight line KL is

and MNis parallel to straight line KL.

a) the value ofh,

b) the equation of the straight line MN,

c) thex- intercept of the straight line MN. [6 marks]

7. Diagram 4 shows a right prism with horizontal baseABCD. Calculate the

angle between the plane BCFand the baseADEF.

[4 marks]

Diagram 3

Diagram 4


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8.

a) Determine whether the given sentence below is a statement or non-

statement.

i. 5 is a factor of 12

ii. y x+ 7

b) Write down two implications based on the following sentence.

Two lines are parallel if and only if the two lines have the same gradient

c) Complete the conclusion in the following argument.

Premise 1: Ifm= n then m n = 0

Premise 2: m n 0

Conclusion: .............................................................. [5 marks]

9.

a) State whether the statement below is true or false.

"3 x 6 = 18 and 3 + 6 = 10"

b) Complete the following mathematical sentence with the symbol "=" or""

to make

i. True Statement

4 6 2

ii. False Statement

a x a 2a

c) Make a general conclusion by induction based on the information given

below;

"2, 11, 26, 47 and

3 x 1 1 =23 x 4 1 =113 x 9 1 =26

3 x 16 1 = 49

= [5 marks]


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10. A bag contains 50 pens. 15 of them are blue and the rest are red and green.A pen is chosen at random from the bag and the probability of getting a green

pen is

.

a) Find the probability that a blue pen is chosen

b) Another 10 red pens are put into the bag. Find the probability of a red

pen being chosen from the bag. [6 marks]

11. In Diagram 5, MP and LQ are two vertical flag poles standing on horizontal

ground KLM.

Given that the angle of depression of P from Q is 38, MP = 5 m, LQ = h m,

LM = 10 m and KM = 10 m. Calculate:

a) the angle of elevation of P from K

b) the value of h [6 marks]

Diagram 5

Q


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Section B

[48 marks]

Answerall questions in this section.

12.

a) Data in table1 shows the first 50 blood donors during a blood donation

campaign. Copy and complete the table below on your answer sheets

based on data in table 1.

Ages Midpoint Frequency

16 20 18 0

21 25

b) Based on your table in (a)

i. State the modal class.

ii. Calculate the mean age of blood donors and give your answer correctto 2 decimal places.

c) By using a scale 2 cm to 5 marks on the x-axis and 2 cm to2 blood donors

on y-axis, draw a frequency polygon for the distribution.

[12 marks]

13. Table 2shows a cumulative frequency and the upper boundary of each class

interval of the data of a group of 96 students which measured to the nearest

cm.

Table 2


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a) Based on table2,

i. State the size of class interval.

ii. Copy and complete table below on your answer sheets,

iii. Calculate the estimate mean height of the student.

Height (cm) Frequency CumulativeFrequency

Mid-point UpperBoundary

90 94 0 0 94.5

95 99 4 4 99.5

14 104.5

40 109.5

64 114.5

81 119.5

90 124.5

94 129.5

96 134.5

b) By using a scale 2 cm to 5 students on the x-axis and 2 cm to 10 cm on

the y-axis draw an ogive base on your table in (a) (ii).

c) From the ogive, find the interquartile range. [12 marks]

14.

a) In Diagram 6, PQRSis a parallelogram. Given that P(a, b), Q(7, 0),

R(3, -4) and S(0, 0), find the

i. gradient ofRQ,

ii. coordinates ofP,

iii. equation ofPQ.

b) Given that universal set = {x:xis an integer and 1 x 50}, set P= {oddnumbers}, set Q= {multiples of 4}, set R= {factors of 27}.

i. Represent the above information in a Venn diagram.

ii. State the set that represents P Q R.

[12 marks]

Diagram 6


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15.

a) Diagram 7 shows a right prism with a horizontal square base EFGH.

TrapeziumPQFEis the uniform cross-section of the right prism.

i. Name the angle between the line FSand the base EFGH.

ii. Calculate the angle between planes EFSand PQRS.

[6 marks]

b) Diagram 8 shows a right pyramid with a square base PQRS. Ois the

centre of the base. PR= 16 cm and VP= 17 cm.

i. State the angle between line VQand base PQRS.

ii. Find the angle between line VQand base PQRS.

[6 marks]

Diagram 7

Diagram 8

END OF THEQUESTION PAPER

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Pep Semester 2 MM p2 F4