Year 8 Number Revision

Dr J Frost (jfrost@tiffin.kingston.sch.uk)

Last modified: 1st February 2013

RECAP: Negative Numbers

4 × -3 = -12-2 × -3 = 6-10 ÷ 2 = -5(-5)2 = 25

-3 + 7 = 4-3 – 8 = -114 – -7 = 11-5 + -3 = -8-5 – -4 = -1

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a = -2, b = 3, c = -4

Help Gary find the crumpet by finding the values of the following expressions.

a2 + c = 0

b – 2c = 11

2b – a2 = 2

3a + 3c = -18

ac – bc = 20

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Being careful with BIDMAS

BI

DMAS

Let a = -3 and b = 2. What is the value of:

-a2 = -9(-a)2 = 9ab2 = -12(ab)2 = 36a2b = 18

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ExercisesGiven that q = 5, r = -3 and s = -1, find the value of:

a) qr + s = -16b) rs – q = -2c) r2 + s2 = 10d) 2q – 3s = 13

Given that a = -10, b = 5 and c = -2, find the value of:

a) a – c = -8b) b – c2 = 1c) 3b + 2a = -5d) b – ac = -15

Given a = 1, b = -2, c = 3 and d = -4, find the value of:

0.5cd2 + b(a + d) = 30

Given that m = -4, n = 3 and p = -2, find the value of:

a) 2m/p = 4b) = -1/50c) pn2 = -18d) (pn)2 = 36e) -m2 = -16f) (-m)2 = 16

Given that s = -4, t = 7, r = -9, find the value of:

g) = -2h) 6 – (r – t) = 22i) -r2 = -81j) 1 – ts2 = -111

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RECAP: Fractions

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Adding/Subtracting Fractions

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Multiplying/Dividing FractionsCalculate the following, leaving any fractions/fractional parts in their simplest form.Give answers as improper fractions where appropriate.

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Fraction Puzzles

A farmer has some sheep. After one day, a quarter of his sheep wandered off. After a second day, a third of the sheep that were left wandered off. After a third day, a fifth of the remaining sheep wandered off. What fraction of the original number of sheep are left?

Two fifths.

Answer: D

Answer: D

PUZZLE 1(JMC)

PUZZLE 2(IMC)

PUZZLE 3(IMC)

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PercentagesA shirt costing £24 is reduced by 26% in a sale. What is the new cost?

Non-Calculator Method Calculator Method

10% £2.4020% £4.805% £1.201% £0.2426% £6.24

£24 - £6.24 = £17.76

Find the decimal multiplier which represents a 26% reduction:

£24 x 0.74 = £17.76 ? ?

The Key to Percentages

It’s all about identifying a decimal multiplier!

original value multiplier new value

What would you multiply by in order to:

Find 20% of the value.

Increase value by 37%.

Decrease value by 10%.

Increase value by 101%.

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Decrease value by 25%, then by 25% again. ?

Questions (use multipliers and a calculator)

The cost of a t-shirt bought in for £14 and sold for a 28% profit.

The value of a car after one year, if it was bought for £15000 and lost 17% of its value.

Homer Simpson’s sperm count, if it starts at 25,000,000, and he loses 46% due to radiation exposure from the Nuclear Plant.

The value of your Apple shares, which were initially worth $35,000, and increased by 3%.

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Exercise 1

Find the value of my shares if they were worth £25,000 yesterday and increased in value by 3%.

Find the cost of a car in a sale with 27% off, if its full price is £9000.

The polar bear population was 2500 last year. This year it dwindled by 53%. How many polar bears are there now?

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1b

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For Q1, work out the following with a calculator, showing what multiplication you used to get the answer.

For Q2, work out the following without a calculator (you must show working).

Find 35% of £12.802a

2b Find 56% of £14

Find 17.5% of £302c

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1d A population of fish in a tank starts at 1500, before 20% die. The day after some guppies give birth and the population increases by 30%. How many fish are there now?

My bank account earns 110% interest p.a. I put £35,000 into it. How much do I have a year later?

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Find 23% of 940

Find 22.5% of 50

Find 79% of 240

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Finding the percentage change

h𝑐 𝑎𝑛𝑔𝑒𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒×100

£64 as a percentage of £80:An increase from £80 to £100:A decrease from £100 to £80:An increase from £50 to £68:A decrease from £68 to £50:An increase from £78 to £100:

Formula:

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Exercise 2Find the percentage change:

A t-shirt that was £16 now costs £13.6015% decrease

The population of 8IW this year is 26 when it was previously 28.7.1% decrease

The value of my house is £325,000 this year when it was £286,000 last year. 12% increase

The population of Kenneytown increased from 1420 to 1950.37.3% increase

A muffin increases from £15,400 in value to £46400.201.3%

The polar population decreases by 10% each year. To the nearest year, how many years will it be before the population reduces to 40% of what it was originally?

9 years (more precisely: 8.696718…)

[IMC] On my jog home from school, I run 25% faster than I did the previous day. What is the percentage reduction in time?

20%

The value of my muffin decreases by 10%, before increasing by 10%. What is the percentage change from its original value? 1% decrease

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RECAP: Expanding Brackets

𝑥𝑦 (2−𝑥 )=2𝑥𝑦−𝑥2 𝑦?

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