Intermediate 1 – Unit 1
Revision Exercises
Finding a Simple Percentage of a Quantity
1.
2.
Find
(a)
10% of £13
(b)
30% of £45
(c)
50% of £22
(d)
25% of £84
(e)
33 1 % of £84
(f)
70% of 32 litres
Nicole and Ryan bought a flat at £68000 when they moved to Inverness. They sold
it some time later for 25% more than what they paid. Calculate:
(a)
3.
3
its increase in value (b)
the selling price
Catriona’s insurance premium was £257 last year but has increased by 20% this
year. What is the new premium?
Finding a Percentage of a Quantity
1.
2.
Find
(a)
3% of £18
(c)
2% of £135
(d)
9% of 14 litres
(e)
3% of 147 tonnes
(f)
12% of 4 litres
7% of £83
A village had a population 150 in 2003 but after a new development of houses, the
population increased by 14%. Calculate:
(a)
3.
(b)
the increase in population
(b)
the new population
(a)
18% of £32
(b)
27% of £453
(c)
175% of £6200
(e)
125% of 36 litres
Find
(d)
(f)
15% of £225
36% of 75 kilograms
Expressing (or writing) one quantity as a percentage of another
Example:
Express 18 out of 45 as a percentage
18
= 18  45 = 04
45
Now change the decimal to a percentage by multiplying by 100
so
1.
18
= 40%
45
Express the following as percentages
(a)
14 out of 35 (b)
68 out of 80
Rounding to 10, 100, 1000
1.
Round 68 to the nearest 10
2.
Round 543 to the nearest 100
3.
Round 769 to the nearest 10
4.
Round 450 to the nearest 100
5.
Round 17432 to the nearest 1000
6.
Round 24437 to the nearest 1000
Rounding to the nearest whole number
1.
Round 257 to the nearest whole number
2.
Round 752 to the nearest whole number
3.
Round 43431 to the nearest whole number
4.
Round 8685 to the nearest whole number
5.
Round 158 to the nearest whole number
6.
Round 213562 to the nearest whole number
Rounding to a number of decimal places
1.
Round 372 to one decimal place
2.
Round 4588 to one decimal place
3.
Round 27316 to two decimal places
4.
Round 1458531 to two decimal places
5.
Round 38945 to three decimal places
6.
Round 513562 to 3 decimal places
Simple problems on Direct Proportion
1.
12 scones can be made from 8 ounces of flour.
How many scones could be made from 24 ounces of flour?
2.
Jane earns £320 for a normal 40 hour week. One week she had some unpaid leave
and only worked 25 hours.
How much did she earn that week?
3.
A small company employing 5 staff has a total wage bill of £1900 per week. The
company expands and employs 2 more staff.
What will the total wage bill be now if all the employees are paid at the same rate?
4.
I can travel 80 miles on 10 litres of petrol.
How much petrol will I need for a journey of 200 miles?
5.
Tom ran a 12 kilometre race in one hour.
If he kept a steady pace throughout the race, how far had he gone in 25 minutes?
Areas of simple composite shapes
10 m
Find the areas of the following shapes:
2cm
Q1.
Q2.
12 m
14 m
6cm
2cm
6cm
12 m
10 cm
7 cm
Q3.
9m
4 cm
11 cm
Q4.
7m
2m
18 cm
Volume of a cuboid
Find the volumes of the following cuboids:
1.
2.
25 m
3m
3.
27 cm
2m
38 cm
14 cm
4.
32 cm
cube
12 cm
5.
How many litres of liquid would the tank in question 4 hold?
(Remember there are 1000 cm3 in a litre.)
40 cm
25 cm
Circumference of a circle
Find the circumference of each of the following circles. Give your answers to 1 decimal
place
1.
2.
38 m
3.
75 cm
4.
52 m
Remember:
the first step is
to double the
radius to get
the diameter
283 cm
5.
A circular flower bed has a diameter of 5 m.
It is planned to put a fence round it. How much fencing will be needed?
6.
Find the circumference of a circle with radius 25 cm.
Area of a circle
Find the area of each of the following circles. Give your answer to 1 decimal place
1.
74 m
3.
47 cm
2.
436 cm
Remember:
the first step is
to half the
diameter to get
the radius
4.
63 m
5.
A circular flower bed has a radius of 3 m.
It is planned to dig up the flowers and sow grass seed on it. What area is to be sown
with the grass seed?
6.
Find the area of a circle with diameter 32 cm.
Evaluating Expressions
1.
Evaluate m + n
when m = 8 and n = 7
2.
Evaluate 5p
when p = 6
3.
Evaluate a – b
when a = 144 and b = 23
4.
Evaluate 2p – 5
when p = 6
5.
Evaluate ab – cd
when a = 3, b = 2, c = 0 and d = 24
6.
Evaluate
p
q
when p = 36 an q = 4
7.
Evaluate
m
5
when m = 95
8.
Evaluate 3a – 2b
9.
Evaluate 4e +
q
r
10.
Evaluate
a
5
-
when a = 10 and b = 5
when e = 5, q = 8 and r = 4
b
10
when a = 100 and b = 50
Evaluate formulae expressed in words
1.
The cost of joining a musical society is the membership fee plus the cost of hiring
the musical score.
How much will it cost in a year that the membership fee is £20 and the hire of the
musical score costs £9?
2.
The cost of hiring a car is £38 per day plus 4p per mile.
How much does it cost to hire this car for 5 days driving a total of 800 miles?
3.
The volume of a cone is
calculated by multiplying the
area of the base by the height
and dividing the answer by 3.
15 cm
Area of Base = 32 cm2
Find the volume of this cone.
4.
To change degrees centigrade (C) to (F), subtract 32, divide the answer by 9 and
then multiply by 5.
Change 77F to C.
5.
To find what the angles in a polygon add up to, use the following formula: Take 2
away from the number of sides in the polygon, then multiply by 180.
Find the total number of degrees in an octagon (8 sided polygon).
Evaluate simple formulae expressed in symbols
1.
V = IR
2.
R=
3.
C = d
Evaluate C when d = 18
4.
a=p-q
Evaluate a when p = 35 and q = 12
5.
V = Ah
Evaluate V when A = 45 and h = 12
6.
y = ax + b
Evaluate y when a = 3, b = 2 and x = 4
7.
P = q + rt
Evaluate P when q = 4, r = 2 and t = 5
8.
a= v-u
t
Evaluate a when v = 12, u = 4 and t = 2
9.
A = 3b – 2c
Evaluate A when b = 5 and c = 3
10.
p = mn – t
Evaluate p when m = 5, n = 3 and t = 15
V
I
Evaluate V when I = 5 and R = 12
Evaluate R when V = 120 and I = 5
Money in social contexts
1.
Find the total Hire Purchase (HP) price of a car if there is a deposit of £1300 and
24 monthly payments of £379.
2.
Sofa
Buy now and pay in January
No deposit
12 instalments of £5999
Find the total cost of the sofa on HP.
3.
TV
£399 cash
or
10% Deposit
plus 12 instalments of £39
Work out how much extra it would cost to pay for the TV by HP.
4.
Catriona normally earns £780 per hour for her job in a shop. If she works overtime
she gets time and a half. One Sunday she worked 5 hours overtime. How much did
she earn for the overtime that day?
5.
The table shows Jeremy’s working hours for the week.
Basic Pay
Overtime
Overtime
Number of hours
35
4
4
Rate
£840
time and a half
Double time
Work out Jeremy’s total wage for the week.
Foreign Currency
We Sell
Euros (€)
Swiss Francs (CHF)
Australian Dollars (A$)
US Dollars ($)
1.
138
227
224
192
This table shows
how much
foreign currency
we receive for
each British
Pound
I wish to travel to New York and I want to change £600 into US dollars. How much
would I receive in US dollars?
2.
Josephine is travelling to Italy for her cousin’s wedding. She changes £350 into
euros. How many euros will she receive?
3.
Gordon and Sandra are planning a skiing holiday in Switzerland. They change £750
into Swiss francs. How much would they get?
We Buy
Euros (€)
Swiss Francs (CHF)
Australian Dollars (A$)
US Dollars ($)
159
257
249
212
This table shows
how much foreign
currency we have
to pay for each
British Pound we
get back
4.
I bring back $200 from New York. How much British money will I get back? (Give
your answer to the nearest penny)
5.
Josephine came back from Italy with €140. She decides to keep it in case she goes
back to Europe soon. How much would she have got if she had cashed it in?
6.
How much would Gordon and Sandra get back for the 80 Swiss Francs they brought
home?
Finding the Mean, Median, Mode and Range
Find the mean, median, mode and range in each of the following three lists:
1.
11, 12, 19, 14, 17, 15, 17
2.
36, 23, 81, 23, 21, 25
3.
16, 22, 13, 24, 11, 17, 25, 21, 18
4.
The weights of 6 children are shown:
42 kg, 50 kg, 63 kg, 40 kg, 47 kg, 49 kg
Find their mean weight.
Find the median weight.
5.
Jim buys 11 packets of sweets.
The number of chocolates in each packet is as follows:
8, 7, 9, 6, 8, 7, 8, 11, 4, 9, 8.
Calculate the mean number of chocolates.
Find the mode and range.
Probability
1.
A bag contains 8 red counters and 12 blue counters.
If a counter is picked at random, what is the probability that it will be red?
2.
A bag has 6 red sweets, 9 green sweets and 3 blue sweets.
If a sweet is chosen at random, what is the probability that the sweet will be:
(a) green
(b) blue
(c) yellow
3.
A bag contains 20 raffle tickets.
Four tickets will win a holiday, two tickets will win a voucher and the rest do not win
anything.
Find the probability of:
(a) winning a holiday
(b) not winning anything
(c) not winning a voucher