Download S2 3RD LEVEL Maths test

Practice End Of Year Maths Test (2nd Year) Paper 2
SOLUTIONS
1a) - 3 + 4
=4-3
=1
think of the number line, start at - 3 and go up 4
or possibly easier to re-arrange - put 4 first
then subtract
b) - 2 – 7
=-9
think of the number line, start at -2 and go down 7
c) -5 - (- 4)
= -5 + 4
=-1
note: ‘negative 1 x negative 4’ = ‘positive 4’
d) -16 + (-3)
= -16 - 3
= - 19
think of the number line, start at -16 and go down 3
e) -3 x (-8)
= 24
note: ‘negative x negative’ = ‘positive’
f) (-8)2
=-8x–8
= 64
note: ‘negative x negative’ = ‘positive’
g) -6 x -2 x -1
= -12
note: ‘negative x negative x negative = ‘negative’
h) -42 ÷ 7
=-6
note: ‘negative’ ÷ ‘positive’ = ‘negative’
i) 35 ÷ (-5)
=-7
note: ‘positive’ ÷ ‘negative’ = ‘negative’
2) Simplify the following expressions:
a) 9a – 2a
= 7a
this is like 9 apples – 2 apples = 7 apples
b) a x a x a x a
= a4
this is called indices
Practice End Of 2nd Year Paper 2
http://maths.qahs.org.uk
Mr Milton Apr 2015
c) 5a - 2b – 3a + 7b
= 5a – 3a + 7b – 2b
= 2a + 5b
d) 9x2 – 3x – 7x2 – x
= 9x2 - 7 x2 - 3x – x
= 2x2 – 4x
e) 3a x 9b
= 27ab
collect the ‘like terms’ and simplify
ie add all the ‘a’s and ‘b’s together
collect the ‘like terms’ and simplify
this is like 3 x a x 9 x b
f) (3x)2
= 9x2
square the 3 and then square the x
3) If a = 4, b = -2 and c = 3, find:
a) 5c
=5x3
= 15
substitute ‘c for 3’
b) -2b + 2a
substitute ‘b for -2’ & 'a for 3’
= (-2 x -2) + (2 x 3) note: ‘negative x negative’ = ‘positive’
= 4 + 6 = 10
c) 3a - 2b
= 3 x 3 - 2 x -2
=9+4
= 13
substitute ‘a for 3’ & 'b for - 2’
note: ‘negative x negative’ = ‘positive’
d) (2b – 2c)2 = 100
= ((2 x -2) – (2 x 3)) 2
= (- 4 – 6) 2
= (- 10) 2
= -10 x -10
= 100
substitute ‘b for - 2’ & ‘c for 3’
Practice End Of 2nd Year Paper 2
http://maths.qahs.org.uk
Mr Milton Apr 2015
e) 3b2
= 3 x (-2) 2
= 3x4
= 12
substitute ‘b for - 2’
note: ‘negative x negative’ = ‘positive’
f) 2(a + b)
substitute ‘a for 4’ & 'b for - 2’
4
= 2 x (4 – 2)
4
= 2 x (2)
4
= 4
4
= 1
4) Solve the following equations:
a) x + 2 = - 3
x=-3-2
x = -5
‘change side, change sign’ ie + goes to –
(b) 2a = -14
a = -14/2
a = -7
change side, times goes to a divide
ie times 2 goes to a divide 2
c) 4x – 2 = 10
4x
= 10 + 2
4x
= 12
x
= 12/4
x
= 3
c) 4x + 2 = x + 1
4x – x = 1 - 2
3x = - 1
x = - 1/3
change side, change sign’ ie - goes to +
change side, times goes to a divide
put x’s on LHS & numbers on RHS
change side, change sign’
change side, times goes to a divide
Practice End Of 2nd Year Paper 2
http://maths.qahs.org.uk
Mr Milton Apr 2015
d) 3(x + 1) = 27
3x + 3 = 27
3x
= 27 – 3
3x
= 24
x
= 24/3
x
=8
f) 2 – 4x = -12 – 5x
5x – 4x = -12 – 2
x
= -14
multiply out brackets first
change side, change sign
change side, times goes to a divide
change side, change sign
f)½ x + 4 = 8
½x
= 8–4
½x
= 4
x
= 4 x 2 change side, divide goes to a times
x
= 8
h) 4 = -16
x
4 = -16 x
change sides, divide goes to a times
-16 x = 4
put letters on LHS and numbers on RHS (swap sides)
(x -1) 16x = - 4 (x -1) multiply both sides by -1 to make -16, +16
x = 4/16
change side, times goes to a divide
x = 1/4
always simplify if possible
5) Multiply out the brackets and simplify:
a)
3(x + 4)
= 3x + 12
multiply 3 by x then 3 by 4
Practice End Of 2nd Year Paper 2
http://maths.qahs.org.uk
Mr Milton Apr 2015
b) 4 + 2(y – 5)
= 4 + 2y – 10
= 2y – 6
multiply 2 by x then 2 by - 5
simplify
c) 3x(x + 4) –7x
3x2 + 12x – 7x
3x2 + 5x
6) The marks, out of 10, for an S1 Maths test are listed below:
2, 2, 2, 4, 4, 1, 7, 9, 9
a) What is the mean test mark?
Mean = Average
Mean = 2+2+2+4+4+1+7+9+9
9
Mean
= 4.4
b) What is the median test mark?
First put the numbers in order, smallest to biggest, then select the
middle number
1, 2, 2, 2,
4, 4, 7, 9, 9
Median = 4
c) What is the mode?
Most occurring number = 2
d) What is the range?
Range = Biggest Number – Smallest Number
Range = 9 – 1
Range = 8
Practice End Of 2nd Year Paper 2
http://maths.qahs.org.uk
Mr Milton Apr 2015
7) a) Andy cycles from Aberdour to Aviemore. The distance is 125 miles.
USE SPEED, DISTANCE, TIME TRIANGLE TO GET THE
CORRECT FORMULA
i)
If he cycles at an average speed of 25 miles per hour, how
long will the journey take?
T=D/S
= 125/25
= 5 hours
ii)
Andy has to be in Aviemore no later than 1735. If Andy starts
his journey at 11:15, will he be on time? Give a reason for your
answer.
11:15 + 5 hours = 16:15,
Yes he will be on time since 16:15 is earlier than 17:35
b) A motorbike travels at an average speed of 60 mph for 2 hours and
45 minutes. What distance does the motorbike travel in that time?
2 hours 45 minutes = 2.75 hours
D=SxT
= 60 x 2.75
= 165 miles
8) Two companies have offers on books.
 ‘Joe’s Books’ company are selling three books for £ 24
 ‘Jim’s Books’ company are selling six books for £42
Which is the best buy? Explain your choice by comparing two numerical
values.
Find cost of 1 book then compare.
Joe’s Books = 24/3 = £8
Jim’s Books = 42/6 = £7.
Practice End Of 2nd Year Paper 2
http://maths.qahs.org.uk
Mr Milton Apr 2015
Jim’s books is the best buy since £7 is cheaper than £8
8)
a. Write down the coordinates of each letter (Hint, x- along, y – up)
b. Reflect each letter in the x-axis (Hint – use x-axis as a mirror)
A(-4,4), B(3,3), C (6,-3) , D( -8,2), E (8,6), F (3,-5)
After reflection in the x-axis, we will have;
A’ (-4,-4), B’ (3,-3), C (6,3) , D( -8,-2), E (8,-6), F (3,5)
9)
Hint – Make up a right angled triangle and use Pythagoras’
Theorem
LET SLOPING EDGE = X
X 2 = 122 + 162
= 144 + 256
= 400
Practice End Of 2nd Year Paper 2
http://maths.qahs.org.uk
Mr Milton Apr 2015
X = √400
= 20
PERIMETER = 16 + 16 + 28 + 20 = 80m
Practice End Of 2nd Year Paper 2
http://maths.qahs.org.uk
Mr Milton Apr 2015