S3 (3.1) Percentages.notebook November 24, 2015
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1 Daily Practice Q1. State the equation of the line joining (0, -4) and (2, -3) Q2. Multiply out and simplify 2(3x - 4) + 4(x - 8) - 3 Q3. How much is a TV priced at % VAT? Today we will be learning about percentage multipliers. Homework Online due Q4. Rearrange y = at 2 - b so that t is the subject Q5. Solve the equation Writing percentages as decimals A percentage is a fraction over 100. Writing percentages as decimals Write the following percentages as decimals: (a) 29% (e) 4.5% (i) 103.2% So to write a percentage as a decimal, just divide the numerator by the denominator (In this case the denominator is 100) (b) 100% (f) 0.23% (j) 4.05% For example: (c) 5% (g) 88.1% (k) % 35% = (d) 2.3% (h) 103% (l) 25.5% Percentages are converted to decimals to allow calculations using a calculator. Of means to multiply So find 64% of 700 means 64% x 700 or in other words 0.64 x 700 Convert the percentages to decimals and use your calculator to work out the answers (Give answers to 1 d.p. where rounding is needed): (a) 51% of 84 (c) 2.5% of 47 (e) 10.5% of 184 (b) 92% of 638 (d) 3.08% of 112 (f) 2.99% of 3021
2 Daily Practice Q1. Find 19% of 3000 Q Q x 0.6 Today we will be continuing to learn about percentage multipliers. Q4. Factorise 45gh - 18h 2 Q x 46 Other % calculations can be made easier using decimals too. Adding on or taking off a percentage. Examples: 1. Find the value of a TV that costs % VAT 2. Find the value of a car that was worth and depreciated in value by 4% Work out the following: 1. A house that increased in value from by 7.5% Work out the following: 1. A house that increased in value from by 7.5% 2. A dress that cost 60 and was reduced in the sale by 15% 2. A dress that cost 60 and was reduced in the sale by 15% 3. A loan for 5000 that has an APR of 4.25% at the beginning of the next year 4. A person's salary that was p.a. and they got a payrise of 2% 3. A loan for 5000 that has an APR of 4.25% at the beginning of the next year 4. A person's salary that was p.a. and they got a payrise of 2% 5. A carton of milk cost 1.21 and increased in line with inflation by 1.3%. How much does it cost now? %
3 Q1. Daily Practice Q2. Evaulate 3a 2 b - 2b when a = 4 and b = -3 Q3. Two bottles are similar in size, the diameter of the smaller bottle is 6cm and its volume is 250ml. If the diameter of the larger bottle is 8cm, what is its volume? Q4. Find 54.5% of 281 (Give answer to 2 s.f.) Percentage multipliers can then be used to work out long term values provided that the percentage increase/decrease stays the same. Today we will be learning to use percentage multipliers to work out long term effects. Examples: 1. John has in his ISA, it has an interest rate of 2.5% p.a. provided he does not withdraw any money for 3 years. How much is there in John's ISA at the end of 3 years? 2. There are 300 lice on Dan's head, when he rinses his hair out with Bye Bye Lice, the lice die at a rate of 15% per minute, how many lice are left after 4 minutes? Source: Investopdia.com
4 Credit_Worksheets/AppreciationAndDepreciation.pdf Daily Practice Q1. Calculate the current value of a car that was worth 4000 and depreciated by 3% p.a. for 3 years Q Q3. Factorise fully 3x 2 a + 15xb + 12x Q4. Q5. Solve 7x 3 = 4x + 27 Today we will be learning about percentages working backwards. Homework due Percentages working backwards Given the new amount with a percentage increase/decrease, this means finding the original amount. Percentages working backwards Examples: 1. Find the original size of a box of cereal that is marked 20% extra free and now contains 600grams Always let the original amount = 100% (or 1 in decimal form) 2. Calculate the original cost of a painting that is priced in the sale with 15% marked off
5 Percentages working backwards Task: Make up a question on percentages working backwards. Write down the solution. Every time someone sits beside you, show them the question and work out theirs. Then check solutions and move on. Daily Practice Q1. Calculate the area of a quarter circle with a radius of 7cm Q2. Multiply out and simplify 7(2x - 1) - 3x + 4 Q3. Factorise 3x 2-15x Q4. Calculate the value of a car thatw as worth 6000 and depreciated by 6% per annum for 3 years Q5. Today we will be completing a check-up on percentages and marking the homework.
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