Paper 1 Flashcards
The price of a computer was £750. In a sale it gets reduced by 20%.
On the final day of the sale it gets reduced by a further 12%.
How much is saved in total buying the computer on the day of the sale?
Find 20% of 750 = 600
0.2 x 750= 150
750-150=600
Then find 12% of 600 = 528
0.12 x 600 = 72
600-72= 528
Final sale price : 750-528 = £222
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
Mia puts £6400 in each account
NSB: 2.5% per year compound interest.
CAB: 2.7% per year simple interest.
Calculate the difference in value between the two accounts after 8 years (correct to the nearest penny).
NSB:
6400 x 1.025 ^8 = 7797. 778544
CAB: Simple interest
Find 2.7% of 6400 - 0.027(6400)= 172.8
Multiply 172.8 by 8 = 1382.4 .
Add 1382.4 to 6400 = 7782.4
7797.778544- 7782.4= 15.38
Martin buys 7 rulers and 15 crayons for £7.
A ruler costs 12p more than a crayon.
Find the cost of one crayon.
7R+15C = £7.
R= 0.12+C
7R+15C(0.12) multiply 7R by 0.12; =0.84
22C= 7-0.84= 6.16 C= 0.28
Students deliver catalogues and leaflets to houses.
One day they have to deliver 360 catalogues and 1440 leaflets. Each student can either deliver 15 catalogues or 80 leaflets in 1 hour.
Each student can only work for 8 hours. Work out the minimum number of students needed.
360/15 = 24. 1440/80= 18.
24+18= 42. 42/8= 5.25. Can’t have ‘5.25 students’ so round up ~ 6
Leo, Kush, and Mali share money in the ratio 3:5:8. Kush receives £750 more than Leo.
Calculate the amount of money that the shared.
Leo: 3. Kush : 5. 5-3=2
Divide 750 by 2 to find one part = £375
375(3) = 1125. 375(5)=1875. 375(8)= 3000
3000+1125+1875= 6000
Derek has £10000 that he wants to invest.
Account A: 3% per year compound interest.
Account B: 4% for the first year .
3% for the second year.
2% for the third year.
Calculate the account which would give him the most money and calculate the difference to the nearest penny after 3 years
Account A: 10000 x 1.03^3 = 10927.27
Account B: 0.04% of 10000 = 10400
- 03% of 10400= 10712.
- 02% of 10712= 10926.24
10927.27-10926.24= 103
Ali is y years old.
Bhavara is twice as old as Ali.
Ceri is 3 years younger than Ali.
The total of their ages is 125 years. Find the age of each person
Ali = y Bhavara = 2y Ceris = y-3
4Y-3 = 125
+3
4Y = 128. Y= 32
Ali = 32, Bhavara = 64, Ceris = 29
Additi, Becky, and Calli collect coins. Additi has 6 more coins than Becky. Calli has one less than Aditi. Altogether they have 71 coins. How many coins do they each have?
B = X A = X+6 C= X+6 - 1 = X+5 C= X+5
3X + 11 = 71
3X = 60 X = 20
B= 20, A = 26, C = 25
Mr and Mrs Thomas buy tickets for themselves and their four children. The cost of an adult ticket is £7 more than the cost of a child ticket. The total cost of the six tickets is £86.
Work out the cost of an adult ticket.
Child = X Adult = X+7
4X 2X + 14
6X + 14 = £86
-14
6X = 72 X = 12 12+7 = 19
Adult £19
Mr and Mrs W have five children who are all different ages.
The mean age is 6.4
The range is 9
The median is 6
The oldest child is 12.
Work out the ages of the children from youngest to eldest.
3rd number = 6
To find the youngest age : 12-9 = 3 years old
First three numbers : 3,6, 12.
3+6+12 / 5
21/5 = 6.4. 6.4(5)= 32.
32-21 = 11.
Trial and error: missing numbers = 4 and 7
Jack and Alex take rubbish to be recycled.
Jack takes 520 kg, 87% of which can be recycled.
Alex takes 750 kg, 61% of which can be recycled.
Calculate the greatest amount of rubbish that can be recycled and by how much.
- 87 (520) = 452.4
- 61 (750) = 457.5
457.5-452.4= 5.1kg
Alex by 5.1 kg
Anna and Paddy take part in the same fun run.
Anna completed the fun run in 2 hours.
Her average speed was 6 KM per hour.
Paddy completed the fun run in 90 minutes.
Work out his average speed in kilometres per hour.
Speed x Time
6 x 2 = 12
90 mins = 1 hr 30 = 1.5
12/1.5 = 8
8 KM / H
Anne, Barry, and Colin share a prize in the ratio 3:4:5.
Colin gives 1/3 of his share to charity.
What fraction of the whole prize does Colin give to charity?
3+4+5 = 12
Coin = 5/12 x 1/3 = 5/36
Claudia invests £25000 at a rate of 2% per year compound interest.
Calculate the total amount of interest she will have earned after 5 years. Give your answer correct to the nearest penny.
25,000 x 1.02^5 = £27602.02
£25602.02-£25000 = £2,602.02
James and Elizabeth buy clothes.
James buys 5 shirts and 4 jumpers he pays £163.
Elizabeth buys 3 shirts and 2 jumpers she pays £89.
Work out the cost of one shirt and one jumper
Simultaneous equations
- 5S+4J=£163
- 3S+2J=£89
15S+12J=£489
15S+10J=£445
2J=44 J=22
5S+4J=163
5S+4(22)=163
5S+88=163
5S=75. S=15.
Shirt £15. Jumper £22
A bus following route T leaves for the train station every 20 minutes.
A bus following route A leaves the airport every 18 minutes.
A bus following route T and a bus following route A both leave at 8:37am.
What is the next time one of each bus is timetabled to leave at the same time?
HCF of 18 and 20 =180
180 mins = 3 hours
8:37am+3hrs =11:37
11:37am
Delia, Edwin, and Freya share money in the ratio 5:7:8.
Freya’s share is £1600. How much money did they share?
1600/8 = 200. 200 per part
200(5)= 1000
200(7)=1400
1400+1000+1600 =4000
Mike drinks 2/5 of a litre of juice everyday.
Juice costs £4.40 for a 2 litre carton and £2.60 for a 1 litre carton.
He buys enough juice to last 7 days.
What’s the lowest price that he can pay for this juice?
2/5 = 0.4
0.4 (7)= 2.8. 2.8~3
He needs a 3 litre carton
£2.60+4.40
£7.00
The perimeter of a pentagon is equal to the perimeter of a square and has the sides : 5X+3, 7X+4, 9X-10, 2X+3, 5X+8.
Give the answers in terms of X in its simplest form
Collect like terms
28X+8
Divide by 4
7X+2
A rectangle has the length :
5X-Y-8 and 3X+5Y-4.
&width : 3X+Y-4 and 2X-6Y-3
Work out the length and width of the rectangle
Opposite sides are equal.
5X-Y-8= 3X+5Y+4
2X-6Y=12
3X+Y-4=2X-6Y-3
X-5Y=1
Simplify ‘2X-6Y=12’ = X-3Y=6
X-7Y=1
X-3Y=6
10Y = -5
Y=-0.5
sub ‘Y=-0.5’ into X-3Y=6
X-3(-0.5)=6. X=4.5
To find the length sub ‘4.5’ and ‘-0.5’into ‘3X+5Y+4’. 3(4.5)+ 5(-0.5)+4= 15.
Width: sub ‘4.5 and 0.5’ into 3X+Y-4
3(4.5)+(-0.5)-4=9
Kieran, Chris , and Jermaine play football. Kieran has scored 8 more goals than Chris. Jermaine has scored 5 more than Kieran. Altogether they’ve scored 72 goals. How many goals did they each score?
Chris = X Kieran= X+8 Jermaine= X+13
3X+21=72
3X= 51. X=17.
Chris= 17, Kieran= 25, Jermaine= 30
Some children arrive at the nursery by car.
40% of the children at the nursery are boys.
70% of the boys at the nursery arrive by car.
60% of the girls at the nursery arrive by car.
What’s the probability that a child chosen at random from the nursery arrives by car?
Frequency trees.
- Boy 0.6. Girl 0.4.
- Car 0.7. No car 0.3
- Car 0.6. No car 0.4
Probability of arriving by car = P(B) + P(G)
0.4x 0.7+0.6+0.6
=0.64
Kim is paid £9.40 per hour for the first 35 hours she works each week. After 35 hours she is paid 1 1/4 times the hourly rate.
One week Kim works 42 hours.
Calculate how much she’s paid for that week.
£9.40 x 35= £329.
42-35= 7 extra hours.
1/4 x £9.40= £11.75 per hour.
£11.75 x 7= £82.25
Total pay: £329+82.25= £411.25
James works from 2pm until 8:30pm on Thursday and Friday. He’s paid £12 per hour and on Saturday he’s paid 1/2 times this hourly pay.
He works 5H on Saturday.
Calculate how much he earns in total for these three days.
2–> 8:30= 6 hours 30 mins = 6.5 hours .
One day pay : £12 x 6.5= £78
Thursday and Friday pay= £156
Saturday: 1/2 x £12= £18
£18 per hour.
5x£18= £90. Total pay= £156+90
£246
Hector can run 400 metres in 66 seconds. Use this information to show that he could run 5KM in less than 14 minutes.
Turn 5KM into M (x1000)= 5000M
5000M/400M= 12.5.
12.5 x 66= 825
400M:66 seconds
5000M: 825 seconds
825 s into minutes (divide by 60)
=13.75
The volume of a piece of wood is 620cm. Its density is 0.85 cm.
Work out it’s mass
Mass = DxV
620x 0.85= 527
P chooses four numbers.
The mode is 8, the range is 7, and the mean is 11. Find the four numbers.
Mode: 8,8,
Range: 8+7 = 15.
Finding the mean : the sum of all numbers/ amount of numbers.
8+8+15/4 = 11
31+ X / 4 = 11. ( multiply by 4).
31+ X = 44. Minus 31
X= 13
8,8, 13, 15
Donald swims 3 lengths of a swimming pool in 93 seconds. Use this information to show that he could swim 100 lengths in under 55 minutes.
Divide the lengths - 100/3 = 33.3
- 3 x 93= 3069.9 seconds
- 9/60= 51.6 minutes
Maria mixes white and red paint in the ratio 2:3. She mixes a total of 15L of paint.
How much more red paint does she need to add to the mixture so that the ratio of white paint to red paint becomes 1:5?
3+2= 5 parts
15/5 = 3 per part. W:R 2:3 White :2(3)= 6L. Red: 3(3)=9L. W:R is = to 1:5 White : 6, Red = 5(6)=30.
30-9= 21.
There’s 20L of red paint.
Trish and Marc both cycled the same distance. Trish completed the distance in 2 hours.
Her average speed was 16 miles per hour. Marc completed the distance in 4 hours.
Find Marc’s average speed for the journey.
16(2)= 32
32/4= 8
8 mph
The scale on a map is 1:25000.
How many kilometres on the ground is represented by 6 cm on the map?
1cm = 25000m
6cm : 25000(6)= 150000m
150000/100= 1500.
1500m (km divide by 1000)
1.5 km
