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Year 8 Number Revision

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.

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Year 8 Number Revision

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

  2. 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. ? ? ? a2 + c = 0 ? a = -2, b = 3, c = -4 ? b – 2c = 11 ? ? 2b – a2 = 2 ? ? ? 3a + 3c = -18 ? Nom ? ac – bc = 20 ? ?

  3. Being careful with BIDMAS B I DM AS Let a = -3 and b = 2. What is the value of: -a2 = -9 (-a)2 = 9 ab2 = -12 (ab)2 = 36 a2b = 18 ? ? ? ? ?

  4. Exercises Given that q = 5, r = -3 and s = -1, find the value of: qr + s = -16 rs – q = -2 r2 + s2 = 10 2q – 3s = 13 Given that m = -4, n = 3 and p = -2, find the value of: 2m/p = 4 = -1/50 pn2= -18 (pn)2= 36 -m2= -16 (-m)2= 16 Given that s = -4, t = 7, r = -9, find the value of: = -2 6 – (r – t) = 22 -r2= -81 1 – ts2= -111 1 4 ? ? ? ? ? ? ? ? ? Given that a = -10, b = 5 and c = -2, find the value of: a – c = -8 b – c2 = 1 3b + 2a = -5 b – ac = -15 Given a = 1, b = -2, c = 3 and d = -4, find the value of: 0.5cd2 + b(a + d) = 30 ? 2 5 ? ? ? ? ? ? ? 3 ? ?

  5. RECAP: Fractions ? ? ?

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

  7. 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 ? ? ? 17 2 9 ? ? 18 ? 10 3 ? 11 ? 4 ? 12 ? 5 ? 13 ? 6 ? 14 ? ? 7 15

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

  9. Percentages A shirt costing £24 is reduced by 26% in a sale. What is the new cost? Non-Calculator Method Calculator Method ? ? Find the decimal multiplier which represents a 26% reduction: £24 x 0.74 = £17.76 10% £2.40 20% £4.80 5% £1.20 1% £0.24 26% £6.24 £24 - £6.24 = £17.76

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

  11. 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. ? ? The value of your Apple shares, which were initially worth $35,000, and increased by 3%. Homer Simpson’s sperm count, if it starts at 25,000,000, and he loses 46% due to radiation exposure from the Nuclear Plant. ? ?

  12. Exercise 1 For Q1, work out the following with a calculator, showing what multiplication you used to get the answer. 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? 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? 1a ? ? 1b ? 1e 1c ? ? For Q2, work out the following without a calculator (you must show working). Find 23% of 940 Find 22.5% of 50 Find 79% of 240 Find 35% of £12.80 2d 2a ? ? 2b Find 56% of £14 2e ? ? Find 17.5% of £30 2c 2f ? ?

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

  14. Exercise 2 1 Find the percentage change: a A t-shirt that was £16 now costs £13.60 15% 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 Kenneytownincreased from 1420 to 1950. 37.3% increase A muffin increases from £15,400 in value to £46400. 201.3% ? b ? c ? d ? e ? 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…) [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 ? 3 ? 4 ?

  15. RECAP: Expanding Brackets ? ? ? ? ?

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