Paper 3 Flashcards
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
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
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.
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%
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
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
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
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
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
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
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
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.
- 5(6)= 27 litres.
- 30 x 27 =£35.10
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
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.
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
