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 :
