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M10Is/MATME/SP2IENG/TZ1fXX
Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported
by working and/or explanations. In particular, solutions found from a graphic display calculator should be
supported by suitable working, e.g. if graphs are used tofind a solution, you should sketch these as part of
your answer Where an answer is incorrect, some marks may be given for a correct method, provided this
is shown by written working. You are therefore advised to show all working.
SECTION A
Answj?r all the questions in the spaces provided.
1.
Working may be continued below the lines, if necessary.
[Maximum mark: 5]
=
Let A
2 -3J4
-11 .-1
[ 2 4 -3
and B
= [ -23 J .
1
(a)
Write down A-I.
[2 marks]
(b)
Solve AX = B.
[3 marks]
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-32.
Ml O/5lMATME/SP2IENG/TZ
llXX
[Maximum mark: 6J
Consider the arithmetic sequence 3, 9, 15, ... , 1353 .
(a)
Write down the common difference.
J(b)
Find the number of terms in the sequence.
[3 marksJ
(c)
Find the sum of the sequence.
[2 marksJ
[1 markJ
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MIO/5lMATME/SP2IENG/TZl/XX
-43.
[Maximum mark: 7]
Let f(x)
(a)
J
for 0::; x::; 6.
[3 marks]
Find f'(x).
.c~
..............
(b)
= xcosx,
f~{Kl~ .. .x.~(-.~I.~~)\.f.:~~~
X (1.1.
..-:
c. ().J.X ..
~ ..
.
X ~'.""'-X. . . . . . . . . . . . . . . . . . . . . . . . . .
On the grid below, sketch the graph of y
= r (x)
.
[4 marks]
.
y.
x
,,
.
,
MIO/5lMATME/SP2IENG/TZlIXX
-54.
[Maximum mark: 6}
The following frequency distribution of marks has mean 4.5.
i
Mark
~requency _ 2
J
4
6
9
x
9
4
(a)
Find the value of x.
[4 marks}
(b)
Write down the standard deviation.
[2 marks}
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-65.
M1 0/5lMATME/SP2IENG/TZ
l
1/XX
[Maximum mark: 7J
The graph of y = p cos qx + r , for -5 :::;x :::;
14 , is shown below.
y.
(4, 7)
J
x
There is a minimum point at (0, - 3) and a maximum point at (4, 7) .
(a)
Find the value of
J
(b)
(i)
p;
(ii)
q;
(iii)
r.
[6marksJ
The equation y
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.. t
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=k
has exactly two solutions. Write down the value of k.
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-76.
Ml O/5IMATME/SP2/ENG/TZ
[Maximum mark: 7]
The acceleration, am s-2 , of a particle at time t seconds is given by
j
The particle is at rest when t = 1.
!
Find the velocity of the particle when t = 5.
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MI0/5lMATME/SP2IENG/TZIIXX
-87.
[Maximum mark: 7J
Evan likes to play two games of chance, A and B.
For game A, the probability that Evan wins is 0.9. He plays game A seven times.
rea)
!
Find the probability that he wins exactly four games.
[2 marks]
For game B, the probability that Evan wins is p. He plays game B seven times.
(b)
(c)
Write down an expression, in terms of p, for the probability that he wins exactly
four games.
[2 marksJ
Hence, find the values of p such that the probability that he wins exactly four
games is 0.15.
[3 marks]
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