The GCSE Maths Tutor Flashcards

1
Q

The mobile phone is reduced by 20% in a sale.
The sale price is £500.
Work out the original price of the mobile.

A

The mobile phone is reduced by 20% in a sale.
The sale price is £500.
Work out the original price of the mobile.

80% of 500
500 ÷ 80 = 6.25 which is 1%
£6.25 x 100 = £625

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2
Q

A house rises in value by 3%.
The value of the house increases by £7500.
Work out the value before the increase.

A

A house rises in value by 3%.
The value of the house increases by £7500.
Work out the value before the increase.

Need to find 100% + 3%

£7500 ÷ 3 = £2500 which is 1%
£2500 x 100% = 250 000

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3
Q

Emily invests £150 000 in a savings account offering a compound interest of 2.4% per annum for 4 years.
Work out the amount of interest she earns over 4 years.

A

Emily invests £150 000 in a savings account offering a compound interest of 2.4% per annum for 4 years.
Work out the amount of interest she earns over 4 years.

150 000 x 1.024^4
=164 926.74 - 150 000
=£14 926.74

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4
Q

Mary buys a car for £4000.
Each year it depreciates by 20%.
Work out the value of the car in 3 years.

A

Mary buys a car for £4000.
Each year it depreciates by 20%.
Work out the value of the car in 3 years.

Year 1 is £4000
20% = £800
4000 - 800 = £3200

Year 2 is £3200
10% = 320
20% = £640
3200 - 640 = £2560

Year 3 is £2560
10% = 256
20% = £512
2560 - 512 = £2048

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5
Q

In a bike store there are 8 different bikes and 10 different paint choices.
How many cominations are there?

A

In a bike store there are 8 different bikes and 10 different paint choices.
How many cominations are there?

8 x 10 = 80 combinations

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6
Q

A three digit padlock uses the numbers from 0 - 9.
How many of the possible three digit number combinations use three different digits?

A

A three digit padlock uses the numbers from 0 - 9.
How many of the possible three digit number combinations use three different digits?

10 x 9 x 8 = 720

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7
Q

6.4 has been truncated to one decimal place.
Write the error interval.

A

6.4 has been truncated (cut off) to one decimal place.
Write the error interval.

(Can’t write symbols so I’ve written the answer in words)
6.4 is lesser or equal to x which is lesser than 6.5

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8
Q

3 calculators and 4 books cost £23.
2 calculators and 3 books cost £16.

Work out the price of a single calculator and a single book.

A

3c + 4b = 23 x3 9c + 12b = 69
2c + 3b = 16 x4 8c + 12b = 64
c = 5

2(5) + 3b = 16
10 + 3b = 16
-10 -10
3b = 6
÷3 ÷3
b = 2

so c = 5 and b = 2

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9
Q

Find an expression in terms of n for the sequence 3, 5, 11, 15, 19
Hence the 50th term.

A

4n - 1
=4(50) - 1
=199

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10
Q

Find an expression in terms of n for the sequence 6, 11, 16, 21,26
Will 84 be in the sequence? Explain answer.

A

No, because the numbers all end in 6 or 1.

or

5n+1 = 84
-1 -1
5n = 83
÷5 ÷5
n = 16.6
So, no as it’s not a whole number.

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11
Q

Here are the equations of three straight lines.
Line 1: 2y = 6x +5
Line 2: y + 3x = 5
Line 3: 3x - y = 5

Two of these lines are parallel. Explain which two.

A

Need to turn each equation into the form y = mx + c

Line 1: 2y = 6x +5 is y = 3x + 2.5
Line 2: y + 3x = 5 is y = -3 + 5
Line 3: 3x - y = 5 is y = 3x + 5
(for line 3, to get rid of the -y, have to add y to both sides)

So, lines 1 and 3 both have a gradient of 3 so they are parallel.

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12
Q

Emily and James share some money in the ration 4:7.
James receives £21 more than Emily.
How much do they share between them?

A

E : J
4 : 7
There are 3 parts between them so 3 parts is £21.
21 ÷ 3 = £7
7 x 4 = 28
7 x 7 = 49

E : J
28 : 49 28 + 49 = £77
They share £77 between them.

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13
Q

A car has to travel 30 miles along a motorway in 24 minutes. Will the car have to travel faster than 70 mph to get there in 24 minutes?

A

70 miles = 60 minutes
÷ 10 ÷10
7 miles = 6 minutes
x4 x4
28 miles = 24 minutes

No.

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14
Q

6 taps take 3 hours to fill a tank with water. How long will it take 9 taps to fill the same tank?
State any assumptions you have made.

A

1 tap = 3x6 = 18 hours
18 ÷ 9 = 2 hours

*assuming all the taps are running at the same rate.

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