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1

The length of each side of a plastic cube is 2a millimetres.
The cube has mass 32a^2 grams.

Find an expression for the density of the cube in its simplest form.

Volume : 2a x 2a x 2a = 8a^3

Mass = D/V
Density = mass / volume.

32 a^2 / 8 a^3

Simplest form : 4a^2\ a^3

2-3 = -1

4a -1

2

In bag C, the ratio of red counters to yellow counters is 3:4. If 3 of the counters are removed from bag C, the ratio of red counters to yellow counters is 3:5. How many yellow counters are in bag C?

Unsimplify each ratio .

Before After
3:4 3:5
6:8 6:10
9:12 9:15
12:16 12:20
15:20

20= same number of yellow counters
15:20 - if you minus 3 it simplifies to 12:20

3

A recipe for flapjacks uses oats,butter, and syrup in the ratio 3:2:1.

Pete makes 1.5 kg of flapjacks. He uses 600 g of butter. Has he followed this recipe?

Using the same recipe, 200g of syrup is needed to make 10 flapjacks. Find the mass of oats needed to make 15 flapjacks.

Turn 1.5 kg into g = 1500g

Add the parts 3+2+1 = 6 . 1500/6 = 250 g per part.

Oats : 750g, Butter: 500g, Syrup: 250g.

No he hasn’t because he’s only used 500g of butter.

Part 2.

10F = 200 g of syrup .
To find the mass of oats needed for 10 flapjacks multiply 200 by 3 = 600.

5F = 300

600+300 = 900

900G of oats is needed.

4

A box contains only red,blue,and green pens.

The ratio of red pens to blue pens is 5:9.
The ratio of blue pens to green pens is 1:4.

Calculate the % of blue pens.

R:B
5:9
B:G
1:4

9 x 4 =36

Blue : 9/ 5+9+36
9/50 x 100 = 18.

18%

5

Write 1/125 x 25^9 as a power of 5.

1/125 = 125 ^-1 .

Cube root of 125= 5

(Five cubed ^-1) x (five squared ^9).

5^-3 x 5^18

5^15

6

In the summer, the zoo increases the prices.

An adult ticket costs £18 and is increased by 20%.
A child ticket costs £14 and is increased by 15%

How much more does it cost to go in the summer than winter?
2 adults and one child attend.

Winter =£50.

20% of £18= 3.60. £18+3.60=£21.60
15% of 14= 2.10. £14+2.10= £16.10

2 adults : £21.60+£21.60
Child = £16.10. Total = £59.30

£59.30-£50= £9.30

7

A newborn baby has an approximate mass of 3.5kg.

A human Cell has an approximate mass of 2.7x10^-11 grams.

Use these values to estimate the number of human cells in a newborn baby. Give your answer in SF.

Convert 3.5kg into g——> 3500g.

3500/2.7x10^-11 = 1.296296296x10^14.

1.30x10^14

8

Parker street is 180m long.
Neil measures the map and says Parker street is 3.5cm long. High street is 11.2cm long. Therefore, I calculate that High street is 576m long in real life.

Use these figures to show that he’s correct

SF: 180/3.5 = 360/7

1cm = 360/7

High street = 11.2 x 360/7 = 576m

9

The middle number of three consecutive whole numbers is 2A. Prove that the sum of these cannot be 250.

Consecutive integers: N-1, N, N+1.

(N-1)+(N)+(N+1)

(2A-1)+(2A)+(2A+1)

6A=250 A=125/3

2A= 125/3 (2) = 250/3.

This is not an integer because 250/3 isn’t a whole number so the sum cannot be 250

10

Joan makes cups of tea and coffee.
Each cup requires 250ml of boiling water.
She has a kettle that boils up to 1.7l of water each time.

She boils 10L of water in an urn. She then uses the kettle to boil the rest of the water she needs. Find the least number of times that Joan needs to boil the kettle to make 56 cups.

Urn: 10L x 1000=10000ml
Cups made with the urn: 10000/250=40 cups.

Kettle has 1.7L (convert into ML x1000)=1700ml

Cups made with the kettle : 1700/250=6.8~6

6+6+6=18 cups

3 boils

11

A bag contains counters.

There are 300 counters in the bag. There are only red, white, and blue counters in the bag. The probability of picking a blue counter is 23/50.
The ratio of red counters to white counters is 2:1.

Calculate the number of red counters in the bag.

23/50 x 6 = 138/300

To find white and red : 300-138= 162

162/3=54. 54 x2= 108

Red counters =108

12

D drives 240 miles. His car averages 40 miles per gallon of petrol. Petrol costs £1.30 per litre.
1 gallon=4.5 litres.

How much does he spend on petrol for this journey?

240/40 = 6 gallons.

4.5(6)= 27 litres.

1.30 x 27 =£35.10

13

A raffle is organised.
Each ticket costs 50p and 400 are sold.

The probability that a ticket,chosen at random, wins a prize is 0.1.

Each winning ticket receives a prize worth £3.
Sophie says ‘I expect the raffle to make over £100 profit’.Show that she’s wrong .

0.5 x 400=200

10% of 400=40 . 40 people win.

40 x £3 = £120

200-120= £80

14

One poppy seed weighs 3x10^-4 grams.
250 pumpkin seeds weigh 21 grams.
One sesame seed weights 3.64x 10^-6 kg.

Write the three types of seed in order. The lightest seed first.

Poppy seed =0.0003

Pumpkin seed: divide 21 by 250
= 0.084

Sesame seed = 0.00364

Poppy seed, Sesame seed, Pumpkin seed.

15

Peter makes pink paint by mixing red and white paint in the ratio 2:3.

Red paint costs £80 per 10L.
White paint costs £5 per 10L.

He sells his pink paint in 10L tins for £60 per tin. Calculate the profit he makes for each tin that he sells.

2+3 = 5 parts.
10/5=2

80/10L =£8 per litre.
5/10L=50p per litre.

R:W. R:W
2:3 X2. 4:6
He needs 4L of red paint and 6L of white paint.
Red = £8 per litre,
4x8+6x0.5 =35

Total cost = £35
Profit = 60-35=£25

16

R hires a car.
It costs £150, plus 85p for each mile he travels.
When he hires the car, its mileage is 27612 miles.
When he returns the car, its mileage is 28361 miles.

How much did R pay to hire the car?

85p =0.85

Subtract the mileage : 28361-27612= 749 miles

He drive 749 miles.
Mileage cost : 0.85(749) = 636.65

Total cost ; 150+636.65= 786.65

17

Luke invests £1500. At the end of the first year 2% interest is added. At the end of the second year, after interest has been added, the investment is worth £1606.50.

Show that 5% interest has been added at the end of the second tear.

Find 2% of 1500= 0.02 x 1500= 30.
1500+30=1530.

Find 5% of 1530= 0.05x 1530= 76.5
76.5+1530= 1606.5

18

Ali has 1 litre of squash. He mixes 0.05 litres of squash with 200ml of water to make a glass of drink.

Find the total volume of the drink that he can make. Give your answer in litres.

ML-L (divide by1000)
200ML into litres = 0.2 litres of water.

1/0.05= 20 bottles of squash.

0.2 x 20= 4l of water

4+1=5 litres