Year 8 Number Revision Dr J Frost jfrosttiffin

Year 8 Number Revision Dr J Frost (jfrost@tiffin. kingston. sch. uk) Last modified: 1 st February 2013

RECAP: Negative Numbers ? 4 × -3 = -12 -2 × -3 = 6? -10 ÷ 2 = -5? ? (-5)2 = 25 -3 + 7 = 4? ? -3 – 8 = -11 ? 4 – -7 = 11 -5 + -3 = -8? -5 – -4 = -1? Help Gary find the crumpet by finding the values of the following expressions. a 2 + c = 0 ? a = -2, b = 3, c = -4 b – 2 c = 11? 2 b – a 2 = 2? 3 a + 3 c = -18 ? Nom ac – bc = 20?

Being careful with BIDMAS Let a = -3 and b = 2. What is the value of: -a 2 (-a)2 ab 2 (ab)2 a 2 b = -9? = -12 ? = 36? = 18? B I DM AS

Exercises 1 Given that q = 5, r = -3 and s = -1, find the value of: a) b) c) d) qr + s rs – q r 2 + s 2 2 q – 3 s a–c b – c 2 3 b + 2 a b – ac ? ? ? = -16 ? = -2? = 10? = 13? 2 Given that a = -10, b = 5 and c = -2, find the value of: a) b) c) d) 4 = -8? =1? = -5? = -15 ? 3 Given a = 1, b = -2, c = 3 and d = -4, find the value of: 0. 5 cd 2 + b(a + d) = 30? 5 ? ?

RECAP: Fractions ? ? ?

Adding/Subtracting Fractions ? 1 ? 2 ? 3 4 ? ? 5 6 ? 7 ? 8 ?

Multiplying/Dividing Fractions Calculate the following, leaving any fractions/fractional parts in their simplest form. Give answers as improper fractions where appropriate. 1 ? 8 ? 16 2 ? 9 ? 17 ? 18 ? 3 4 ? ? ? 6 ? ? ? 11 ? ? 12 5 7 10 13 ? 14 ? 15 ? ?

Fraction Puzzles PUZZLE 1 (JMC) Answer: ? D PUZZLE 2 (IMC) Answer: ? D PUZZLE 3 (IMC) 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.

Percentages A shirt costing £ 24 is reduced by 26% in a sale. What is the new cost? Non-Calculator Method 10% 20% 5% 1% 26% £ 2. 40 £ 4. 80 £ 1. 20 £ 0. 24 ? £ 6. 24 £ 24 - £ 6. 24 = £ 17. 76 Calculator Method 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! What would you multiply by in order to: ? ? ?

Questions (use multipliers and a calculator) ? ? ? ?

Exercise 1 For Q 1, work out the following with a calculator, showing what multiplication you used to get the answer. 1 d 1 a ? 1 b ? ? 1 e 1 c ? ? For Q 2, work out the following without a calculator (you must show working). 2 a 2 b 2 c ? ? ? 2 d 2 e 2 f ? ? ?

Finding the percentage change Formula: 1 2 3 4 5 6 ? ? ?

Exercise 2 1 Find the percentage change: a A t-shirt that was £ 16 now costs £ 13. 60 15% decrease ? b The population of 8 IW this year is 26 when it was previously 28. 7. 1% decrease ? c The value of my house is £ 325, 000 this year when it was £ 286, 000 last year. 12% increase ? d The population of Kenneytown increased from 1420 to 1950. 37. 3% increase ? e A muffin increases from £ 15, 400 in value to £ 46400. 201. 3% ? 2 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…) 3 [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% ? 4 The value of my muffin decreases by 10%, before increasing by 10%. What is the percentage change from its original value? 1% decrease ?

RECAP: Expanding Brackets ? ? ?