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WOODMILL HIGH
MATHEMATICS
INTERMEDIATE 2
END OF COURSE REVISION
(Units 1 & 2)
Intermediate 2 Maths
Exam Revision (Week 1)
1.
The population of Dunfermline is increasing at 2∙5% per year. Currently it is
55420. What will it be in 3 years time?
2.
Find the volume of this shape.
7∙9 cm
Give your answer to 2 significant figures.
3.
9∙6 cm
y
Find the equation of this straight line.
(4,5)
3
x
4.
A line has equation 3x + 4y = 12. Find the gradient of this line.
5.
Expand and simplify
(a)
6.
7.
(p – 3)(p + 4) + 2p2 + 6p
Factorise
(a)
(c)
2πrh + 2πr2
y2 – 9y + 14
(b)
(x – 7)(x2 + 3x – 6)
(b)
36 – 25a2
Find the area of this triangle.
Give your answer to 3 significant figures.
170 m
42°
152 m
8.
Find the length x, giving your answer to 2 significant figures.
9.
Solve the system of equations. 3x + 2y = 13 and 4x – 3y = 6.
10.
Draw a box plot for the following data 0, 2, 5, 8, 3, 9, 14, 16, 21, 6, 12, 1, 18
11.
Calculate the mean and standard deviation of the following set of numbers
104 110 113 120 128 133
x
Intermediate 2 Maths
Exam Revision (Week 2)
1.
The population of Mathsville decreased by 3% in 2010 but with a new factory and
housing development is expected to increase by 1∙5% in each of 2011 and 2012.
If it was 22000 at the start of 2010, what might it expect to be at the end of
2012?
2.
Find the volume of this shape.
It is a half sphere sitting on a cylinder.
Give your answer to 3 significant figures.
3.
9∙6 cm
y
Find the equation of this line.
4
8
4.
A line has equation 5x  2y  8 = 0. Find the coordinates of the point where it cuts
the y  axis.
5.
Solve the following simultaneous equations
(a)
4x + 6y = 16
x + 2y = 5
(b)
3y – 8x = 24
3y + 2x = 9
(c)
3x + 4y = 19
4x – 3y = 8
6.
Two customers enter a shop to buy milk and cornflakes. Mrs Smith buys 5 pints of
milk and 2 boxes of cornflakes for £688. Mr Brown buys 4 pints of milk and 3
boxes of cornflakes and receives £206 change from a £10 note. Form a pair of
equations to work out the cost of a pint of milk and a box of cornflakes.
7.
Multiply out and simplify
( x  3)( x  4)  ( x  4) 2
x
Intermediate 2 Maths
1.
Exam Revision (Week 3)
y
y=
1
3
x+2
Part of the graph of
1
y  x2
3
is shown.
Find the coordinates of the
point B
B
2.
x
Expand and simplify
(a)
3.
(x + 7)(x2 + 3x + 5)
(b)
(2x + 3)2
The shape of material used for a lampshade is a sector of a
circle.
280°
The circle has radius 25 cm and the angle of the sector is
280°.
Find the area of material in the lampshade.
4.
5.
In question 3, the lampshade is to have a decorative trim round its rim. How much
of the trim will be needed if a 1 cm overlap is necessary?
B
Find the length of BC in the triangle.
53°
A
6.
Factorise
(a)
7.
130 m
x2  3x + 2
(b)
4p2  49q2
(c)
6x2y + 15xy2
Find the mean and standard deviation of: 235, 252, 214, 222, 248, 236
68°
C
Intermediate 2 Maths
1.
2.
Exam Revision (Week 4)
A local shopkeeper kept a record of the number of people who bought different
numbers of newspapers one Sunday.
Number of newspapers
Frequency
0
1
2
3
4
25
43
52
24
16
(a)
Make a cumulative frequency table from the above data.
(b)
Find the median, lower quartile and upper quartile for this distribution.
The boxplot shows the number of hours of TV watched in a week by a group of
students.
5
11
21
28
35
Calculate the semi-interquartile range.
3.
(a)
The average price of a house in thousands of pounds in different areas of
the UK in 2008 is shown below.
111
113
104
117
159
107
Use appropriate formulae to calculate the mean and standard deviation.
Show all your working clearly.
(b)
In 1988 the mean was £98000 and the standard deviation was £10200.
Comment on the change in house prices.
4.
Multiply out and simplify
5.
Factorise
6.
(x  3)(x2 + 3x – 6)
(a)
9x2 – 16y2
(b)
x2 – 8x + 15
(c)
p2 – 3p – 10
(d)
12a2 - 7a – 10
Solve the pair of equations:
2x + 5y = 8 and 3x  4y = 12
Intermediate 2 Maths
1.
Exam Revision (Week 5)
A strawberry jelly is in the shape of a hemisphere.
The diameter is 18 centimetres.
As the jelly sits in a warm room it begins to melt
and loses 5% of its solid volume every hour.
What would be the solid volume of the jelly left
after 3 hours?
2.
18 cm
Find the equation of this relationship connecting P and t
P
(4,8)
5
t
3.
By accident, 5 tonnes of a chemical are released into a sea loch.
If the tides remove 40% of the chemical in the loch each week, how many tonnes
of chemical will be expected to remain after 3 weeks?
Give your answer to one decimal place.
4.
The diagram shows a glass bowl with two chopsticks resting on the rim at A and B.
The lengths of the parts of the chopsticks inside the bowl are 10 cm and 12 cm
respectively and the angle between them is 120.
B
A
Find the length of AB to 2 significant figures.
(a)
2
36p  1
(b)
2
a  7a  30
120
5.
Factorise
6.
What is the probability that a student chosen at random from this list of marks
scored less than 8?
9 5 6 8 6 9 7 8 6 5
Intermediate 2 Maths
1.
2.
Exam Revision (Week 6)
(a)
Calculate the area of this triangle
(b)
Calculate the length of AB
B
62 cm
A
Calculate the length BP in the diagram.
58 cm
B
36
C
67
P
25 km
32
A
3.
Solve algebraically the system of equations
x + 3y = 10
4.
3x  y = 10
Nairn Savings Bank offers 6% compound interest per annum.
How much interest would be received after two years on a deposit of £380 in this
bank?
5.
A new car cost £12,300. The value of the car depreciated by 16% after the first
year and by 9% after the second year.
Calculate the value of the car after the second year.
6.
Multiply out and simplify:
(a)
(p  8)(p + 3)
(c)
(x + 5)2  (x  5)2
(b)
(2m  7)2
Intermediate 2 Maths
1.
Exam Revision (Week 7)
A family wants to fence off a triangular part of their garden for their pet rabbits. They have a
long straight wall available and two straight pieces of fencing 6 metres and 7 metres in length.
They erect the fencing as shown.
120
6m
7m
Find the area of garden enclosed by the wall and the two pieces of fencing.
2.
Solve the simultaneous equations
2x + 3y = 5
x – 4y = 8
3.
800
The graph on the page shows the annual
cost, £C, of running a car, plotted against
the annual mileage, M miles.
600
Annual
Cost,
£C
400
Write down a formula connecting C and M.
4.
(a)
The following data (arranged in
order) shows the number of people
visiting a public swimming pool on
Monday mornings throughout the
first half of 2011.
12
18
22
26
30
72
13
19
23
27
30
15
20
25
27
31
16
21
26
28
32
200
18
21
26
29
63
0
4000
6000
8000
2000
Annual Mileage, M miles
Draw a box plot to illustrate this data.
(b)
The box plot below represents the attendance at the swimming pool on Saturday mornings
throughout the first half of 2011.
60
62
71
77
80
Compare the box plots in parts (a) and (b) and suggest two reasons for any differences.
Intermediate 2 Maths
1.
Exam Revision (Week 8)
A ship is first spotted at position R, which is
on a bearing of 315 from a lighthouse L. The
distance between R and L is 10 kilometres.
After the ship has travelled due West to
position T, its bearing from the lighthouse is
300.
T
N
R
10 km
W
How far has the ship travelled from R to T?
2.
3.
4.
Factorise
(a)
p2 + 6p
(b)
4x2  25y2
(c)
x2  5x + 6
(d)
10x2  11x  6
Multiply out the brackets and collect like terms
(a)
(2x + 1)(x2  5x  4)
(b)
(2x  5)2
L
(
L
ig
S
h
t
h
o
u
s
e
)
Seats on flights from London to Edinburgh are sold at two prices, £30 and £50.
Let x be the number of £30 seats and y be the number of £50 seats on the
flight.
On one flight a total of 130 seats were sold
(a)
Write down an equation in x and y which satisfy this condition.
The total cost of the seats on this flight is £6000.
5.
E
(b)
Write down a second equation in x and y which satisfies this condition.
(c)
Solve the equations to find how many seats were sold at each price.
Solve algebraically the system of equations
2a + 4b =  7
3a  5b = 17
ANSWERS
(Week 1)
59681
5.
6.
(a)
3p2 + 7p  12
(a)
2πr(h + r) (b)
(c)
(y  7)(y  2)
8650 m2
7.
2.
1
x+3
2
(b)
x3  4x2 27x + 42
36  25d2
(d)
(6 + 5a)(6  5a)
8.
120 m
9.
800 cm3
1.
3.
y=
4.
m=
3
4
x = 3, y = 2
10.
0
11.
8
2∙5
mean = 118
15
21
standard deviation = 11∙1
(Week 2)
2.
1120 cm3
1.
21985
5.
6.
(a)
x = 1, y = 2
(b)
milk = 68p, cornflakes £1∙74
1
x+4
4.
2
y = 4, x = 1∙5
(c)
7.
7x  28
3.
y=
(0, 4)
x = 1, y = 4
(Week 3)
1.
3.
6.
7.
(6, 0)
2.
(a)
x3 + 10x2 + 26x + 35
(b)
2
1527 cm
4.
123 cm
5.
121 m
(a)
(x  1)(x  2)
(b)
(2p + 7q)(2p  7q)
(c)
mean = 234∙5
standard deviation = 14∙6
4x2 + 12x + 9
3xy(2x + 5y)
(Week 4)
1.
2.
4.
5.
Number of newspapers
Frequency
Cumulative Frequency
0
25
25
1
2
43
52
68
120
3
4
24
16
144
160
median = 2,
Q1 = 1, Q3 = 2∙5
8∙5 hours
3.
mean = £118500, standard deviation £20350
3
x  15x + 18
(a)
(3x + 4y)(3x  5y) (b)
(x  5)(x  3)
(c)
(p  5)(p + 2)
(d)
(3a + 2)(4a  5)
6.
x = 4, y = 0
(Week 5)
1.
1039 cm3
2.
4.
19 cm
3
5
5.
6.
3
t+5
3.
4
(a)
(6p + 1)(6p  1)
1∙1 tonnes
14∙4 km
3.
£9402(∙12)
(b)
4m2  28m + 49
x = 4, y = 2
y = 1, x = 4
C = 0∙1 M + 100
P=
(b)
(a  10)(a + 3)
(Week 6)
1.
4.
6.
1057 cm2
2.
£46∙97
5.
2
(a)
p  5p  24
(c)
20x
(Week 7)
1.
4.
18∙2 m2
(a)
12
(b)
2.
19 25∙5 19
3.
72
Much higher attendances on Saturdays, much less spread out number of
attendances on Saturdays. Much higher attendances on 2 Mondays than
other Mondays.
Reasons
More people can go on a Saturday, eg. work, school
2 busy Mondays could be bank holidays
(Week 8)
1.
2.
3.
4.
5.
5∙18 km
(a)
p(p + 6)
(c)
(x – 3)(x – 2)
(a)
2x3  9x2  13x  4
25 seats at £30 and 105 seats
a = 1∙5, b = 2∙5
(b)
(2x + 5y)(2x – 5y)
(d)
(5x + 2)(5x – 3)
(b)
4x2  20x + 25
at £50