7/30/2019 Latih Tubi Mat T4 SET 4

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TUISYEN KITA | cgnashPENCETUS BIJAK MATEMATIK

1 The Venn diagram in the answer space showssetsP, Q and R such that the universal set,

RQP .

On the diagram in the answer space, shade

(a) the set QP .

(b) the set (PQ )R .

2.

(a) State whether the following statement is true

or false. 3 33 9 or 8 2

(b) Write down two implications based on the

sentence below.The inverse matrix of a 2 2 matrix exists if and

only if the determinant is 0

(c) Given the number sequence 3, 8, 15, 24,.. and

3 = 1 2 + 2(1)

8 = 2 2 + 2(2)

15 = 3 2 + 2(3)

24 = 4 2 + 2(4)

Make a general conclusion by using the induction

method for the numerical sequence above.

2. Diagram 1 shows a parallelogram OPQR.

Find

(a) the equation of the straight linePQ.(b) thex-intercept of the straight linePQ.

3. Solve the equation 2152 2

m

mm

4. Calculate the values ofx andy that satisfy the

simultaneous linear equations :

13

23

yx

yx

5. Diagram 7 shows eight labelled cards in two

boxes. A card is picked at random from each box.

By listing all of the possible outcomes, find the

probability that:

(a) both cards are labelled with a letter.(b) one card is labelled with a number and

the other card is labelled with a letter

6. The data in Diagram 13 show the number of

hours spent by a group of 40 students surfing the

internet in a month.

(a) Based on the data in Diagram 13 and by using

a class interval of 10 hours, complete Table 2 in the

answer space.

(b) State the modal class.

(c) For this part of the question, use the graph paperBy using a scale of 2 cm to 10 hours on the

horizontal axis and 2 cm to 5 students on the verticalaxis, draw an ogive for the data.

(d) From your ogive in (c),(i) find the third quartile(ii) hence, explain briefly the meaning of the thirdquartile.

(b) modal class = .

(c) Refer to graph

(d) (i) third quartile =

(ii)

7/30/2019 Latih Tubi Mat T4 SET 4

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TUISYEN KITA | cgnashPENCETUS BIJAK MATEMATIK

7. Diagram below shows a solid right cylinder of

radius 7 cm and length 10 cm with hemispheres of

radius 7 cm attached at each end.

Calculate the total surface area, in cm2, of the

combined solids. (Use =7

22)

8. (a) In Diagram 7, the shaded region represents the

part of the flat windscreen of a van which is being

wiped by the windscreen wiperAB. The wiper rotates

through an angle of 210o about the centre O. Given

that OA = 7 cm andAB = 28 cm.Using =

7

22,

calculate

(i)the length of arcBB ,

(ii) the ratio of arclengths , AA : BB

the area of the shaded region.

(b) In Diagram 8, the pointsA,B, CandD lie on a

circleABCD with centre O. ABD = 50o and DBC= 60o.

Calculate

(i) COD,

(ii) ADC,

(iii) ADO.

9. (a) Given that = {x:xis an integer and 7 x 15},

A = {x: x is a multiple of 3 },

B = {x :x is an odd number} and

C= {x: 10 x 13 }.

(i) List the elements of the set C .(ii) Find n(AB).(iii) List all the possible subsets of setA.

Find the elementx such thatx (BC) andxA.

(b) Given that n() = 50. G andHare two sets for

which n( GH) = 6, n(G) = 18 and n(H) = 14.

(i)Draw a Venn diagram to represent the relationshipbetween sets G and H and write the number of

elements in each region.

(ii) Find n(GH).

(c) On the Venn diagram in the answer space, draw

a setN such thatNL andN M= .

10. In Diagram 5,PQRSis a parallelogram. Point Q

lies on they-axis.

Find

(a) the equation of the straight line QR,

(b) they-intercept of the straight linePS.

11. Diagram 4 shows an incomplete Venn diagramthat represents the number of students from a class of

30, according to the subjects they have studied. Each

student studied at least one of the three subjects

Physics, Chemistry and Biology.

Given the universal set, =PCB,P= {students who studied Physics}

C= {students who studied Chemistry}

B = {students who studied Biology}

20 students studied

Chemistry and 12

students studied

Biology. Based on

this information,

find

(a) the numberof students who

studied Chemistry

and Biology but not

Physics.

(b) the number of students who studied Biologyonly.

(c) the number of students who studied Physics.

12. Using factorisation, solve the followingquadratic equation :

8)2(35 2 xx .13. Calculate the values ofp and q that satisfy the

following simultaneous linear equations :