NnerAO
Maru 150
Test 1
1 M A R C H2 0 1 2
Torel Menxs: 35
Dunnrrox: 1 HouR
.... SuRNeltB
& Irulrlels:.."
Srunnxr NunrsBR:
Instructions
1. Non-programmable calculators are allowed.
2. Answer all questions and show all working.
3. Unless instructed otherwise, round answers off to 3 decimal places.
4. This paper consists of 7 pages, including this front sheet. Please see that you have them all.
Useful formulae
in:
n(n*r)
?'-
irr: -
2
n(n+r)(2n+r)
2"
6
(' *a * b
" '\ n : i
( " ) a n -"r b r
2\r/-
QUESTTON L
(a) For eachof the followingnumbers,state whetherthey are elementsof the natural numbersN:
i.2+ 5
[1]
ii.3+(-7)
[1]
iii. t
iv. 1+,
[1]
trc,.;
tl
i'i
,-l
't,
"1 Jil
t.
ZrS :r
-{,
3,(--t\-
tilt=
z
,rr,.(.- ir
{
l\}
e t'il
</ll;
(b) Express0.375as
i. A fractionin its simplestform.
[1]
ii. As a percentage
t1l
0 . ' 3 4 d?
r*,
ir'
i
c 3-i5=
"l
, g1 \
4L>
{rcr
(c) A dam is 70% full. After heavy rains, the darn is 76% full and has 38 million litres of water in it.
How many litres of water was in the dam when it was 70Tofi:Jl?
[2]
L. I
T\
fk
k
Tbi,
-lO%
r
jt
),
drun't
=
=
38
liSW. x
{t{rf ei:'f-1 .
^,rJ
'ltr
lr{-,-rs
to+
i,'l,.cr
7(,%
,
C-a.
!:ror
:
, l t,/..J
-^.
r
Z g X t C , (l , h - s
,.:7o
QUESTTON 2
trl
(a) simprify(*)'
r3^\t
L'l
-: lZ:-
1r
>
"7
"4
t
:
1L\ ,"
t*q
7.' .1
V x \. il r
t
17-I
(,k
21h
(b) Write the followingas a singlefraction and simplify,
2):'
-
ft+
lrl
5f;
t-l
1_- .,i ?'ij.klJ^-11::)
_
'4r>
r--1
(r-EJ [ailj
?'nz
:
-or"-3*
I,(r>,.Lrxf3
),rr- "i
tj:
=
(c) Calculate 3I2 -2,I3
q'-
3tz
I \ ! * z ^ r -3
-**^;i:r,'I
x 104 and write the result in scientificnotation.
Z l ] t s / , r [ ':
t2)
p \tL7rr.'on Z I<r't't
=
(z izr
p erz')* ,r,h
:
.*j gr?'
y toh
I
i Z
F
tr.:,k
(d) A car moves at 12 metres per second. Convert the speed of the car to kilometres per hour.
t
tzl
i
! e {o cr ' Lr r
--.-__
, sC(
J
\
ll.fl
::
._-_"._
,/
rc,6.r,.1.
:--,"*_
,
A
r.7x"!('1;1c'"+*
'r-k*"
h3
/ [,
lX{i.,:',}t:rt
(e) Give the equation of the straight line graph passingthrough points (3, -3) and (5,3).
A
l ) , "=
N
f,
^
)
--
.
f'2
_:
[2]
!.2
-
-;"\
/l ' .. '
r,"r-r,:, ,:lJ
b)
},qt-(
t
tr
lt- .,. -(
,,
l),i
"J.
=
7
/
>^
l. r*
[5',3\
l,'r]\ c,.\ ii*
3
,)r,fb
3=3f-I-)
L:-._gL
ra-
QUESTTON 3
2
\-
,
(a) .bvaluate
. ';Jl
1)'*'(2i)
L(
[2)
,L
I
z
i'=
-7
r'
L
* rr 'Jt -
i
(z,J
-ttl
.
(- i)
"
- u f i
( *
- Lt,
i )
(- i)
--2
h
"l
t-q)
(.,)
t
F
r-r)
'
i'l
i-z)
(.-,)'*t{L )
( h )
rw
rz
*q
(]
25
(b) Evaluate \ZJ
Iol
n2
tJl
'Lr
f
.,f = *?S-
A L
: (" "L t ,)7
l.1
(-zrn)]"t." A (-r)'
L
v-
z ( r L r - ^L,")
I | 'r So
L
LL? i*e$L
{----
7t
: wfi,?4,,L
F c,t'
r-
2S? )
Z s ( z s I r ) [ Z - L \+ ,, ,\ / ' ll
I
x
b,
I
QUESTTON 4
(a) Give the binomialexpansionot (za + l)4
(r*'
?)u
t3l
= ( 2 , , \ r4 h ( 2 , . ) t ( l t {) - i l ( t " , ) ' ( ' ' , , ) '
r
Q( 2 , . ) (L / .) 3 r
': l6qt,
|
( r r ,f
/t,r^=L " 6qtb'+
abi
1 , . . . 1 - c t i , ,r,t:Jat i,.
,T"il * l (r 3 e ') -( - f \
)-
t: I
":
':
(O
1o.
t_),)
- olprtTS
*'lcr
rJ
l-[*
,,,g{-.-{)rir:nF pl
/-rr 'rk1.:"r-+,r1
*t
3=
/-
d
fb
(b) What is the coefficient of the term containing r2y3 in the binomial expansion of (32 -y)5?
Ilt
t
\(,..^
[3]
QUESTTON 5
(a) Find all r € IRsuchthat (r + 1)(z - 7) < 0
.-i g ){ €
:t
(b) Supposethat f (r) : 3r - I and g(x):
i. f-t(r)
xt f
rr. I -\r)
- 1 l
f . Find:
[1]
n-r , \
L ( ) , . )-
. .
[21
.
rlr[].)
tll
L _ l
r
Zz