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Maths Foundation Exam Prep 2014

Maths Foundation Exam Prep 2014. Data Handling. YOU MUST SHOW YOUR WORKING:. A 2 MARK QUESTION SHOULD HAVE A MINIMUM OF 1 LINE OF WORKING OUT The difference between a D & a C grade is only 1 mark! Don’t lose marks because you didn’t write it down!. Bar Charts (G-F). Used for discrete

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Maths Foundation Exam Prep 2014

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  1. Maths Foundation Exam Prep 2014

  2. Data Handling

  3. YOU MUST SHOW YOUR WORKING: A 2 MARK QUESTION SHOULD HAVE A MINIMUM OF 1 LINE OF WORKING OUT The difference between a D & a C grade is only 1 mark! Don’t lose marks because you didn’t write it down!

  4. Bar Charts (G-F) • Used for discrete data • Gaps between the bars

  5. Charts – PICTOGRAMS (G)

  6. Histograms & Frequency Polygons (C) Histograms have bars touching

  7. Pie Charts (F/E)

  8. Stem & Leaf (D) YOU MUST PUT IN A KEY OR YOU WILL LOSE A MARK!!

  9. Averages & Range Mode – Most Common (G) Median – Put in order & find the middle one (G) Mean – add the up & divide by how many there are (F) Range = Largest – smallest (F)

  10. Averages from tables Modal (or mode) Number of hamsters is 1 For the median, list the numbers to find the middle, so its 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2

  11. To do the MEAN (C): Total = 40 Total = 126

  12. Scatter Graphs Draw a line of best fit onto your graph If using your graph to show information, (eg the birth rate for 60% Literacy) PUT IN DOTTED LINES!!

  13. Correlation Positive Correlation Negative Correlation No Correlation

  14. Probability Probability ‘ ‘ Probabilities will add up to 1 (D) Sample Space Diagrams List All the possible Outcomes As adds up to 1 in total

  15. Question: A Fair dice is rolled • What is the probability it lands on a ‘5’? (F) b) What is the probability it lands on a ‘5’ or ‘6’? (C)

  16. Question: The probability a biased coin lands ‘heads’ is 0.7 Estimate the number of heads if the coin is tossed 200 times (C) P(Head) = 0.7 Estimated number = Prob x Total no of times = 0.7 x 200 = 140

  17. Number & Algebra

  18. READ THE QUESTION TO SEE HOW TO ROUND YOUR ANSWERS!! Never round mid calculation You WILL lose marks if you don’t round your answer how the question wants (decimal places or Sig Figs) USE BRACKETS!!!

  19. Order of Operations BBrackets IIndices (powers) DDivision MMultiplication AAddition SSubtraction 15 – 3 x 4 = 15 – 12 = 3

  20. Negative Numbers -3 + -5 = -3 – 5 = -8 7 - - 8 = 7 + 8 = 15 -8 x -2 = +16 or just 16 -10 ÷ 2 = -5

  21. SQUARE NUMBER 1x1 = 1 2x2 = 4 3x3 = 9…….. Number that divides exactly into…… Factors of 20 are 1,2,4,5,10,20 FACTOR Numbers in that ‘times table’ Multiples of 14 are 14, 28,42, 56,….. MULTIPLE HCF HIGHEST COMMON FACTOR LCM LOWEST COMMON MULTIPLE

  22. Rounding to Decimal Places 2.654098 1dp = 2.7 2dp = 2.65 3dp = 2.654 4dp = 2.6541 5dp = 2.65410

  23. 508.305920 1sf = 500 2sf = 510 3sf = 508 4sf = 508.3 5sf = 508.31 Rounding to Significant Figures WHEN ESTIMATING, ALWAYS ROUND EACH NUMBER TO 1 SIG FIG FIRST

  24. FRACTIONS to DECIMALS TOP ÷ BOTTOM FRACTIONS to PERCENTAGE

  25. DECIMALS to FRACTIONS Note ⅓ = 0.3333333333….. NOT 0.3

  26. PERCENTAGES To compare fractions, decimals & percentages, change into percentages first Example: Write these numbers in order smallest first 0.23 25% ⅕ 0.23 x 100 = 23% THIS IS A VERY USEFUL METHOD Answer: ⅕, 0.23, 25%

  27. FRACTIONS What happens if I have Mixed numbers like 3⅕ + 2⅙?

  28. Multiplying Fractions Top x Top Bottom x Bottom

  29. Dividing Fractions Keep it Kiss it Flip it

  30. Question

  31. Question

  32. Finding a Percentage of an Amount Calculate the VAT at 17½% on a TV costing £480 100%= £480 10% = 48 5% = 24 2 ½% = 12 17 ½% = 48+24+12 = £84 Find 40% of £360 100% = £360 10% = 36 20% = 72 40% = £144 TOP TIP: Only add on your increase if the question ASKS you to (similarly for decreases)

  33. Finding a Percentage of an Amount (Calc method) Calculate the VAT at 17½% on a TV costing £480 17½% = 17½÷100 = 0.175 0.175 x £480 = £84 Find 40% of £360 40%=40÷100 = 0.40 0.40x360=£144 TOP TIP: Only add on your increase if the question ASKS you to (similarly for decreases)

  34. Increase/decrease as a Percentage A house cost £300 000 in 2008 & sold for £360 000 in 2011. What was the percentage increase?

  35. Question: Adam scored 24 out of 50 on a test. Write this as a percentage

  36. Reverse Percentages A tshirt was in a 20% off sale reduced to £16. How much did it originally cost? Remember the ORIGINAL AMOUNT is 100% 20% off is 100% - 20% = 80% that you pay for 80% =£16 1% = 0.2 100% = £200

  37. Reverse Percentages (Calc paper) A bar of chocolate had 25% extra free and now weighed 450g. How much did it originally weigh? Original +25% = 100% + 25% = 125% 125% = 450g 1% = 3.6 100% = 360g

  38. RATIO Mr Yates has 12 sweets to every 3 sweets that Mr Sanders gets. Write this as a ratio in its simplest terms? Mr Yates : Mr Sanders 12 : 3 4 : 1 Divide both by 3 Miss Williams decides to share 1kg of sweets between herself, Mr Yates & Mr Sanders in the ratio 1: 4 : 5. How much sweets does each person get? 1+4+5 =10 parts in total = 1kg (or 1000g) 1 part = 100g 4 parts = 400g 5 parts = 500g 100g:400g:500g

  39. Proportion Mr Set is making a cake for 6 people His recipe below is to make a cake for 4 people. How much of each ingredient does he need? Recipe for 4 people: 200g sugar 300g flour 4 eggs 100g butter For 2 people: 100g sugar 150g flour 2 eggs 50g butter Mr Set need ingredients for 6 people: 300g sugar 450g flour 6 eggs 150g butter ÷2 x3

  40. ALGEBRA RULES a + a + a = 3a 4a + b + b - a = 3a + 2b a x a = a2 a x b = ab 5(2a + 3) = 10a + 15 a x a x b x b x b = a2b3 Question: Simplify a2 + 2a + b + 3a2 – a + 5b = 4a2 + a + 6b REMEMBER A SQUARE APPLE IS DIFFERENT TO A ROUND ONE!!

  41. Factorise means ‘put into brackets’

  42. Indices & Powers

  43. Graphs Make sure you put in your working lines when reading from your graphs

  44. Quadratic Graphs Draw the graph y = x2 -2x +5

  45. Quadratic Graphs When plotting a quadratic graph correctly it will have this shape If you are asked to solve the equation from the graph, look at where it crosses the axis X=-1.8 & x=0.2

  46. FORMULAE A WORD FORMULA uses words to describe a rule Egpay = rate of pay x hours worked An ALGEBRAIC FORMULA uses letters to describe a rule Egp = r x h To Change the Subject of a Formula rearrange it as if it was an equation: Eg Make r the subject of the formula

  47. SOLVING EQUATIONS A little trickier...... Square Root √ is the opposite of squaring 2

  48. Equations with Brackets Expand the brackets first -3 from BOTH sides ÷ 3 on BOTH sides Can leave answer as a fraction if its simplified

  49. Questions

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