n4 numeracy book 2 - calderglen high school...n4 numeracy book 2 the wee maths book of big brain...
TRANSCRIPT
N4 Numeracy
Book 2
The wee
Maths Book
of Big Brain
Growth
Length, Volume and Percentages
Grow your brain
Guaranteed to make
your brain grow, just
add some effort and
hard work
Don’t be afraid if
you don’t know how
to do it, yet!
It’s not how fast you
finish, but that you
finish.
It’s always better to
try something than
to try nothing.
Don’t be worried
about getting it
wrong, getting it
wrong is just part of
the process known
better as learning.
Page | 2
D Length and Volume
D1 I am aware of the different metric units in which length is
measured and can decide which unit is most appropriate in
a given context.
Complete this exercise without the aid of a calculator
1. Change these measurements into millimetres
(a) 7cm (b) 12cm (c) 8·6cm
(d) 3cm 4mm (e) 59·1cm (f) 702cm
2. Change these measurements to centimetres
(a) 60mm (b) 400mm (c) 250mm
(d) 3mm (e) 4m (f) 0·5m
(g) 17m (h) 8m 90cm (i) 9m 8cm
(j) 3·6m (k) 0·02m (l) 1·75m
3. Convert these measurements into metres
(a) 300cm (b) 5000cm (c) 1400cm
(d) 590cm (e) 60cm (f) 71cm
4. Convert these measurements into kilometres
(a) 19300m (b) 8650m (c) 450m
(d) 900000cm (e) 20000cm (f) 1400cm
Page | 3
5. Change the units of the following measurements as indicated
(a) 2·4 cm into mm (b) 3·2 km into m
(c) 180 cm into m (d) 1060 mm into cm
(e) 760 m into km (f) 0·03 m into cm
(g) 5·6 cm into mm (h) 0·72 km into m
(i) 69·35 cm into m (j) 34256 mm into cm
(k) 501 m into km (l) 1·94 m into cm
6. Change the units of the following measurements as indicated
(a) 31·3 cm into mm (b) 0·201 km into m
(c) 0·00503 m into cm (d) 43 mm into cm
(e) 34 m into km (f) 846·81 cm into m
(g) 0·062 cm into mm (h) 1·5 km into m
(i) 0·02 cm into m (j) 342·67 mm into cm
(k) 0·089 m into km (l) 43 m into cm
7. Change the units of the following measurements as indicated
(a) 0·71 cm into mm (b) 7·8 km into m
(c) 89·4 m into cm (d) 6·67 mm into cm
(e) 231 m into km (f) 9·08 cm into m
(g) 0·802 cm into mm (h) 1·05 km into m
(i) 27 cm into m (j) 9·34 mm into cm
(k) 0·9091 m into km (l) 202 m into cm
Page | 4
8. Elle is building some raised beds for growing vegetables.
She needs pieces of wood that are 1∙45 metres long.
When Elle goes to purchase the wood, she finds all the measurements
are in millimetres.
What length of wood does Elle need to order?
9. The heights of all of the members of One Direction are listed below.
Name Height
Niall 171cm
Harry 1780mm
Louis 1∙74m
Liam 177cm
What is the mean (average) height of the band?
10. Calculate the perimeter of the rectangle below.
32cm
1∙05m
Page | 5
11. Shaun uses a trundle wheel to measure the perimeter of the school’s
fence; he finds that it is 879 metres long. How many complete laps of
the school will Shaun need to run to ensure he covers 5 kilometres?
12. The distance from the Earth to
the Moon is approximately
370000 kilometres.
The Samsung Wind turbine in Fife is
200 metres tall.
How many of these wind turbines
would fit end-to-end between the
Earth and the Moon.?
13. Baked beans come in cylindrical tins 11 centimetres high and with
diameter 7 centimetres. The tins are packed into boxes measuring
420 mm by 280 mm by 350 mm.
(a) One layer of cans is placed (upright) into the bottom of the box
above.
How many cans will fit into the bottom layer?
(b) How many tins can be packed into the box altogether?
420mm
280mm
350mm
7cm
11cm
(tin and box not to scale)
Page | 6
D2 I can solve problems which involve perimeter and can
include inconsistent units
14. The diagram shows the dimensions of a swing park.
(a) Find the perimeter of the swing park in metres.
(b) Is 22 metres of fencing enough to fence the swing park.
Justify your answer with a calculation.
15. Another swing park is
shown.
Will 42 metres of
fencing be enough to
fence this swing park?
Justify your answer
with a calculation.
9 m
525cm
3 m
250cm
12 m
150cm
450cm
5 m
Page | 7
16. The following two shapes have the same perimeter.
Find the missing length of the triangle.
17. Lucy wants to decorate her kite with new ribbon around the
perimeter.
She bought a one metre roll of ribbon.
Will this be enough ribbon to decorate around her kite?
5cm
110mm
x
150mm
30cm
70mm 10mm
20mm 5cm
4cm
Page | 8
18. The diagram shows the room dimensions of Tammy’s bedroom.
Tammy wants to put new skirting boards round her bedroom.
(a) The door entrance is 60cm wide and will not require any skirting.
Calculate the amount of skirting board required.
(b) Skirting board costs £2·50 per metre.
Tammy has £45 will this be enough to buy the new skirting
boards?
520cm
4·7m
Page | 9
D3 I can comfortably convert between litres, millilitres and
cubic centimetres
19. Write the volume of each of the following items in litres.
(a) (b) (c)
2000 cm3 1400 cm3 350 cm3
(d) (e) (f)
5 ml 568 cm3 150 ml
(g) (h) (i)
Page | 10
500 ml 750 ml 3500 cm3
(j) (k) (l)
160000 cm3 5000 cm3 330 ml
20. Write the volume of each of the following items in millilitres.
(a) 160 litres (b) 50 litres (c) 2 litres
(d) 0·333 litres (e) 4 litres (f) 0·5 litres
(g) 0·568 litres (h) 0·75 litres (i) 0·05 litres
21. For each of your answers in Q2, give an example of a container which
would normally contain that volume.
Page | 11
22. I have 1 litre of water in a jug to be used in an experiment.
On the way to my table I spill some.
I have 780ml left. How much have I lost?
23. I have 1 litre of Sprite.
I give 300ml to William, 200ml to Paul and 250ml to Mia.
How much do I have left?
24. Mr Hart has to have a fluid intake of at least 2 litres.
He has drunk two 275ml of tea, one 300ml of coffee, 200ml of orange
juice and 180ml of water.
How much more fluid does Mr Hart require?
25. Clare is having a party and has bought three 2 litre bottles of fizzy
pop.
She has 30 party cups and decides to share the fizzy pop evenly.
How many millilitres will go in a cup?
26. Sarah needs 𝟏𝟏
𝟒 litres of vegetable stock for making lentil soup.
She decides to use OXO vegetable stock cubes and on the box it says:
“For a tasty stock dissolve one cube in 190 ml of boiling water.”
How many stock cubes will Sarah need for making her stock?
Page | 12
For this experiment you will need:
15 cm3 (1 tablespoon) of baking soda (sodium bicarbonate)
15 cm3 (1 tablespoon) of laundry detergent about 180 millilitres (3/4 cup) of water about 60 millilitres (1/4 cup) of vinegar several drops of food colouring (optional) a 400-milliliter (12-ounce) drinking glass a waterproof (plastic or metal) tray a teaspoon
27. Drew is looking at the materials needed for the Fizzing and Foaming
experiment.
(a) How many millilitres does a tablespoon hold?
(b) How many tablespoons of water are required?
(c) Drew has a 1 litre bottle of vinegar, how many Fizzing and
Foaming experiments can he complete with this bottle?
28. For the Mentos Geyser Experiment it is
advised to have one Mentos sweet per
250 ml of Diet Coke.
(a) Kate has a 1.75 litre bottle of Diet
Coke, how many Mentos sweets does
she need?
(b) Craig has a 3 litre bottle of Diet
Coke, how many Mentos sweets does
he need?
Page | 13
E Percentages
E1 I can convert comfortably between (common) fractions,
decimals fractions and percentages in order to compare
quantities given in different formats.
1. Write each of the following as a fraction and as a decimal fraction
(a) 13% (b) 24% (c) 99%
(d) 56% (e) 25% (f) 83%
(g) 10% (h) 180% (i) 75%
(j) 116% (k) 5% (l) 103%
(m) 7.2% (n) 35% (o) 1%
2. Change each fraction into a percentage (calculator),
(a) 18
100 (b)
4
5 (c)
7
10
(d) 17
25 (e)
19
20 (f)
1
4
(g) 49
50 (h)
5
8 (i)
27
40
(j) 6
75 (k)
12
8 (l)
50
40
3. Write down the percentage which is equivalent to each of the
following fractions (without a calculator)
(a) 1
2 (b)
3
4 (c)
1
10
(d) 2
3 (e)
1
5 (f)
3
10
Page | 14
4. Work out the percentage which is equivalent to each of the following
fractions.
Give your answer to 2 significant figures and how your working
clearly.
(a) 9
11 (b)
7
13 (c)
11
15
(d) 1
3 (e)
13
30 (f)
87
90
(g) 5
8 (h)
37
40 (i)
1
66
5. Write down the fraction which is equivalent to each of the following
percentages (without a calculator).
(a) 25% (b) 1% (c) 20%
(d) 12½% (e) 10% (f) 30%
(g) 90% (h) 5% (i) 15%
6. Write each of the following percentages as a fraction in its simplest
form. Show your working clearly.
(a) 30% (b) 4% (c) 85%
(d) 7·5% (e) 9·4% (f) 0·3%
(g) 65·5% (h) 8·02% (i) 0·12%
(j) 5·55% (k) 0·05% (l) 0·64%
Page | 15
E2 I can find a percentage of a quantity involving at most 4
digits (Non Calculator and Calculator).
Without a calculator
7. At a comedy show 9% of the audience buy a programme.
If 1500 attend the show, how many buy a programme?
8. A travel firm offers a discount of 40% off the full price of package
holiday.
The full price of the package holiday is £760.
How much is the discount?
9. A salesperson is paid commission of 15% of her weekly sales.
How much will her commission be in a week when her sales total
£800?
10. A bottle of iodine solution contains 7% iodine by volume.
What volume of iodine is there in a 500ml bottle?
11. A metal alloy contains 60% pure gold.
How much gold is there in 270g of the alloy?
12. A hotel in Glasgow offers 30% off the full price of a weekend break.
How much is this saving if the full price of a weekend break is £700.
Page | 16
E3 I can calculate percentage increase and decrease.
13. A new luxury villa in Florida is valued at $375000. It is expected to
rise in value by 15% during its first year.
What will the value of the villa be at the end of the first year?
14. Mrs Dodds buys a new for £25000.
It depreciates in value by 12% during its first year.
How much will Mrs Dodds car be worth at the end of the first year?
15. Jorge buys a new house for £80 000. The value of the house
depreciates by 8% in the first year.
How much would his house be worth at the end of the first year?
16. Company shares worth £1,200 depreciate in value over a month by
12%.
How much were the shares worth at the end of the month?
17. The Pollards bought a bungalow for £110,000.
It appreciated in value by 8% in first year.
How much was the bungalow worth at the end of the first year?
Page | 17
E4 I can express one quantity as a percentage of another and
work out a percentage increase or decrease using the
original value and final value.
18. Alan scored 28 out of 40 in a Maths test.
What was his percentage score?
19. The Head of First Year knows there are 300 pupils in the year group.
160 of them are girls.
What percentage are boys?
20. Jamie bought a new car for
£18000 in 2009 and sold it for
£8000 three years later.
Calculate the depreciation, and express it as a percentage of the cost
when new?
Give your answer to 1 decimal place.
21. In the 2011-2012 season Lionel Messi scored 73 of the 190 goals scored
by Barcelona.
What percentage of Barcelona’s total goals Lionel Messi score?
Give your answer to 1 decimal place.
22. Last year Sally was paid £20 per hour.
This year she gets £22.50 per hour.
Calculate her percentage increase in pay.