Flashcards in Paper 1 Deck (32)

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1

##
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

2

##
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?

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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

3

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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).

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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

4

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Martin buys 7 rulers and 15 crayons for £7.

A ruler costs 12p more than a crayon.

Find the cost of one crayon.

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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

5

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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.

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360/15 = 24. 1440/80= 18.

24+18= 42. 42/8= 5.25. Can’t have ‘5.25 students’ so round up ~ 6

6

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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.

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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

7

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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

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Account A: 10000 x 1.03^3 = 10927.27

Account B: 0.04% of 10000 = 10400

0.03% of 10400= 10712.

0.02% of 10712= 10926.24

10927.27-10926.24= 103

8

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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

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Ali = y

Bhavara = 2y

Ceris = y-3

4Y-3 = 125

+3

4Y = 128. Y= 32

Ali = 32, Bhavara = 64, Ceris = 29

9

## 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

10

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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.

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Child = X Adult = X+7

4X 2X + 14

6X + 14 = £86

-14

6X = 72 X = 12

12+7 = 19

Adult £19

11

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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.

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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

12

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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.

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0.87 (520) = 452.4

0.61 (750) = 457.5

457.5-452.4= 5.1kg

Alex by 5.1 kg

13

##
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

14

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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

15

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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

16

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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

1. 5S+4J=£163

2.3S+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

17

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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

18

##
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

19

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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?

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2/5 = 0.4

0.4 (7)= 2.8. 2.8~3

He needs a 3 litre carton

£2.60+4.40

£7.00

20

##
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

21

##
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

22

## 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

23

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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?

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Frequency trees.

1. Boy 0.6. Girl 0.4.

2.Car 0.7. No car 0.3

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

24

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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

25

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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.

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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

26

## 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

27

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The volume of a piece of wood is 620cm. Its density is 0.85 cm.

Work out it’s mass

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Mass = DxV

620x 0.85= 527

28

##
P chooses four numbers.

The mode is 8, the range is 7, and the mean is 11. Find the four numbers.

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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

29

## 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.

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Divide the lengths - 100/3 = 33.3

33.3 x 93= 3069.9 seconds

3069.9/60= 51.6 minutes

30