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GCSE Linear Starters Higher
- 1. GCSE Linear Questions (H) β’ Question set 1 β’ Question set 2 β’ Question set 3 β’ Question set 4 β’ Question set 5 β’ Question set 6 β’ Question set 7 β’ Question set 8 β’ Question set 9 β’ Question set 10 β’ Question set 11 β’ Question set 12 β’ Question set 13 β’ Question set 14 β’ Question set 15 β’ Question set 16 β’ Question set 17 β’ Question set 18 β’ Question set 19 β’ Question set 20 Odd numbers β Non calculator Even numbers - Calculator
- 2. Number Algebra Shape, Space, Measure Handling Data Solve the following simultaneous equations Arrange these in ascending order 25 , 64 1 2, 2β1 , 80 , 16 1 4 5π₯ + 2π¦ = 16 3π₯ β π¦ = 14 8 9 14 ? The mean of the numbers of these 4 cards is 9. What is the number on the fourth card? 4 + 3x x + 6 The perimeter is equal to 32cm. What is the value of x?
- 3. Number Arrange these in ascending order 25, 64 1 2, 2β1, 80, 16 1 4 25 = 2 x 2 x 2 x 2 x 2 = 32 64 1 2 = 64 = 8 2β1 = 1 21 = 1 2 80 = 1 16 1 4 = 4 16 = 2 2β1 , 80 , 16 1 4, 64 1 2, 25
- 4. Algebra Solve the following simultaneous equations 5π₯ + 2π¦ = 16 3π₯ β π¦ = 14 a b Multiply equation b by 2, 6π₯ β 2π¦ = 28 c Add equations a and c 11π₯ = 44 π = π Substitute x back into one of the original equations and solve
- 5. Shape, Space, Measure 4 + 3x x + 6 The perimeter is equal to 32cm. What is the value of x? Perimeter = 32cm Perimeter = 4 + 3π₯ + π₯ + 6 + 4 + 3π₯ + π₯ + 6 = 8π₯ + 20 Therefore 8π₯ + 20 = 32 8π₯ = 12 π₯ = 1.5
- 6. Handling Data 8 9 14 ? The mean of the numbers of these 4 cards is 9. What is the number on the fourth card? Total of the four cards is the mean multiplied by four 9 Γ 4 = 36 So find the missing card by subtraction 36 β 8 β 9 β 14 = 5
- 7. Number Algebra Shape, Space, Measure Handling Data Expand and Simplify the followingA bank account gains 6% compound interest per annum. If Tom puts Β£700 into his account, how much could he expect after 6 years? 4 π₯ β 5 β 3(2π₯ β 6) (π₯ + 2)(π₯ β 7) π‘ + 5 2 Calculate the mean number of cars per household 35Β° Work out the missing length x π₯ 15 No. of cars Frequency 0 4 1 8 2 7 3 2
- 8. Number A bank account gains 6% compound interest per annum. If Tom puts Β£700 into his account, how much could he expect after 6 years? To calculate the money after one year of interest, multiply by 1.06 ππππ πππ β 700 Γ 1.06 ππππ π‘π€π β 700 Γ 1.06 Γ 1.06 ππππ π‘βπππ β 700 Γ 1.06 Γ 1.06 Γ 1.06 ππππ π ππ₯ β 700 Γ 1.06 Γ 1.06 Γ 1.06 Γ 1.06 Γ 1.06 Γ 1.06
- 9. Algebra Expand and Simplify the following 4 π₯ β 5 β 3(2π₯ β 6) (π₯ + 2)(π₯ β 7) π‘ + 5 2 4 π₯ β 5 β 3 2π₯ β 6 = 4π₯ β 20 β 6π₯ + 18 = β2π₯ β 2 π₯ + 2 π₯ β 7 = π₯2 β 7π₯ + 2π₯ β 14 = π₯2 β 5π₯ β 14 π‘ + 5 2 = π‘ + 5 π‘ + 5 = π‘2 + 5π‘ + 5π‘ + 25 = π‘2 + 10π‘ + 25
- 10. Shape, Space, Measure 35Β° Work out the missing length x π₯ 15 35Β° π₯ 15 Label your sides (in play) h a Decide your triangle h a c Cover up what you are looking for and write down your formula β = π cos π β = 15 cos 35 β = 18.31161883 β = 18.3 (3. π . π)
- 11. Handling Data Calculate the mean number of cars per household No. of cars Frequency 0 4 1 8 2 7 3 2 No. of cars Frequency Mean 0 4 4 x 0 = 0 1 8 8 x 1 =8 2 7 7 x 2 = 14 3 2 3 x 2 = 6 Total 21 28 ππππ = 28 21 = 1. 3
- 12. Number Algebra Shape, Space, Measure Handling Data Write out the nth term for each sequence. Hence work out what the 10th and 100th term will be. Approximate the answer to 12.31 Γ 16.9 0.394 Γ 0.216 5, 8, 11, 14, β¦ 10, 4, β2, β8, β14 4, 7, 12, 19, 28, β¦ 6, 11, 18, 27, 38, β¦ Three cards are drawn from a deck and replaced each time. What is the probability of drawing 3 hearts? Iron has a density of 8g/cm3 . What will be the mass of the above cuboid? 4cm 2cm 5cm
- 13. Number Approximate the answer to 12.31 Γ 16.9 0.394 Γ 0.216 Round all numbers to 1 significant figure 10 Γ 20 0.4 Γ 0.2 Calculate this sum 200 0.8 Use equivalent fractions to help divide by a decimal 200 0.8 = 2000 8 = 250
- 14. Algebra Write out the nth term for each sequence. Hence work out what the 10th and 100th term will be. 5, 8, 11, 14, β¦ 10, 4, β2, β8, β14 4, 7, 12, 19, 28, β¦ 6, 11, 18, 27, 38, β¦ Sequence nth term 10th term 100th term 5, 8, 11, 14, β¦ 3π + 2 32 302 10, 4, β2, β8, β14, β¦ 16 β 6π -44 -584 4, 7, 12, 19, 28, β¦ π2 + 3 103 10003 6, 11, 18, 27, 38, β¦ π2 + 2π + 3 123 10203
- 15. Shape, Space, Measure Iron has a density of 8g/cm3 . What will be the mass of the above cuboid? 4cm 2cm 5cm πΆπππ π π πππ‘πππππ ππππ = 4ππ Γ 5ππ = 20ππ2 ππππ’ππ = πΆπππ π π πππ‘πππππ ππππ Γ ππππ‘β = 20 Γ 2 = 40ππ3 The density is 8π/ππ3 this means, every ππ3 weighs 8g. So the mass will be πππ π = 40 Γ 8 = 320π
- 16. Handling Data Three cards are drawn from a deck and replaced each time. What is the probability of drawing 3 hearts? ππππππππππ‘π¦ π»ππππ‘ π΄ππ· π»ππππ‘ π΄ππ· π»ππππ‘ = 1 4 Γ 1 4 Γ 1 4 π π»π»π» = 1 64
- 17. Number Algebra Shape, Space, Measure Handling Data Solve the following quadratic equation, leave your answers to 3 significant figures. πΆππππ’πππ‘π 4.2 Γ 7.3 5.2 β 9.3 Write down your full calculator display Round this number to 3 significant figures 3π₯2 β 5π₯ = 18 A school of 800 pupils want to do a survey on school dinners. They decided to take a stratified sample of 30 pupils. How many of each year group should they ask? π₯ Work out the size of angle x 18 13 Year 7 Year 8 Year 9 Year 10 Year 11 182 124 128 195 171
- 18. Number πΆππππ’πππ‘π 4.2 Γ 7.3 5.2 β 9.3 Write down your full calculator display Round this number to 3 significant figures For Casio fx-83GT plus Type 4 . 2 x 7 . 3 5 . 2 - 9 . 3 = πΊ βͺ=β«D β7.478048 β7.48
- 19. Algebra Solve the following quadratic equation, leave your answers to 3 significant figures. 3π₯2 β 5π₯ = 18 Make it look like a usual quadratic 3π₯2 β 5π₯ = 18 3π₯2 β 5π₯ β 18 = 0 Difficult to factorise ο so use the formula. πΉππ ππ₯2 + ππ₯ + π = 0, π€βπππ π β 0 π₯ = βπ Β± π2 β 4ππ 2π π = 3 π = β5 π = β18 π₯ = β β5 Β± β5 2 β 4 Γ 3 Γ β18 2 Γ 3 π₯ = 5 Β± 25 + 216 6 π₯ = 5 + 241 6 ππ π₯ = 5 β 241 6 π₯ = 3.42 ππ π₯ = β1.75
- 20. Shape, Space, Measure π₯ Work out the size of angle x 18 13 Label your sides (in play) o a Decide your triangle a o t Cover up what you are looking for and write down your formula tan π₯ = π π tan π₯ = 18 13 π₯ = tanβ1 18 13 π₯ = 54.2Β° π₯ 18 13
- 21. Handling Data A school of 800 pupils want to do a survey on school dinners. They decided to take a stratified sample of 30 pupils. How many of each year group should they ask? Year 7 Year 8 Year 9 Year 10 Year 11 182 124 128 195 171 30 pupils out of 5 year groups β must mean 6 from each year group? Wrong. We take a stratified sample β this means we take a fair representation of each year group. There should be more year 7 than year 8 in the sample. Year 7 = 182 800 Γ 30 = 6.825 = 7 ππ’ππππ Year 8 = 124 800 Γ 30 = 4.65 = 5 ππ’ππππ Year 9 = 128 800 Γ 30 = 4.8 = 5 ππ’ππππ Year 10 = 195 800 Γ 30 = 7.3125 = 7 ππ’ππππ Year 11 = 171 800 Γ 30 = 6.4125 = 6 ππ’ππππ Check the student numbers add up to your sample size. 7 + 5 + 5 + 7 + 6 = 30 Each year group gets a fair representation.
- 22. Number Algebra Shape, Space, Measure Handling Data Factorise fullySimplify the following 48 = 3 Γ 12 = 2 5 Γ 3 10 = 300 β 75 = 5π₯4 π¦3 π§2 β 15π₯6 π¦5 π§ π₯2 + 11π₯ β 12 π₯2 β 64 9π₯2 β 25π¦2 4, 6, 2, 5, 7, 9, 9, 2, 1, 4, 8 Draw a box plot for the following data Calculate the area of the rectangle 3 cm 5π₯ β 3 cm 3π₯ + 5 cm
- 23. Number Simplify the following 48 = 3 Γ 12 = 2 5 Γ 3 10 = 300 β 75 = See Surds or the think SQUARE numbers 48 = 16 Γ 3 = 16 3 = 4 3 What is the largest square number which is a factor of 48. 16 3 Γ 12 = 36 = 6 2 5 Γ 3 10 = 6 50 = 6 25 Γ 2 = 6 25 2 = 30 2 When adding fractions, the denominator needs to be the same number. Similarly, when adding Surds, the Surds need to be the same number β so simplify them 300 = 100 Γ 3 = 100 3 = 10 3 75 = 25 Γ 3 = 25 3 = 5 3 300 β 75 = 10 3 β 5 3 = 5 3
- 24. Algebra 5π₯4 π¦3 π§2 β 15π₯6 π¦5 π§ π₯2 + 11π₯ β 12 π₯2 β 64 9π₯2 β 25π¦2 Factorise fully 5π₯4 π¦3 π§2 β 15π₯6 π¦5 π§ = 5π₯4 π¦3 π§(π§ β 3π₯2 π¦2 ) π₯2 + 11π₯ β 12 = π₯ + 12 π₯ β 11 π₯2 β 64 = π₯ + 8 π₯ β 8 9π₯2 β 25π¦2 = (3π₯ + 5π¦)(3π₯ β 5π¦)
- 25. Shape, Space, Measure Calculate the area of the rectangle 3 cm 5π₯ β 3 cm 3π₯ + 5 cm Remember the features about a rectangle β two pairs of equal sides! You can set up an equation using this information to work out the length of the rectangle. 5π₯ β 3 = 3π₯ + 5 2π₯ β 3 = 5 2π₯ = 8 π₯ = 4 Therefore the length is 3 x 4 + 5 = 17cm. π΄πππ = 17 Γ 3 = 51ππ2
- 26. Handling Data 4, 6, 2, 5, 7, 9, 9, 2, 1, 4, 8 Draw a box plot for the following data When working with Quartiles, Median and Range β it is always useful to arrange your data in size order. 1, 2, 2, 4, 4, 5, 6, 7, 8, 9, 9 Need a few pieces of information for a box plot. Highest value β 9 Lowest value β 1 The Median, since there are 11 numbers, the middle number will be the 11+1 2 = 6th number. So the 6th number is 5 Lower quartile will be the 11+1 4 = 3ππ number in our list. So LQ = 2 Upper quartile will be the 3 11+1 4 = 9π‘β number in our list. UQ = 8
- 27. Number Algebra Shape, Space, Measure Handling Data Using trial and improvement to find a solution to 1 decimal place The lengths of a room have been calculated to the nearest metre. Calculate the greatest and least area that the room could be. π₯3 β 5π₯ = 50 The probability of Man Utd winning a match under David Moyes is 0.3 and losing is 0.2. Man Utd play 3 matches, what is the probability that out of these, 2 are won and one is drawn. Calculate the volume and surface area. Leave your answer to 3 significant figures. 8 ππ 5 ππ 9 4
- 28. Number The lengths of a room have been calculated to the nearest metre. Calculate the greatest and least area that the room could be. 9 4 Lower bound 3.5 8.5 π΄πππ = 3.5 Γ 8.5 = 29.75 π2 Upper bound 9.5 4.5 π΄πππ = 4.5 Γ 9.5 = 42.75 π2
- 29. Algebra Using trial and improvement to find a solution to 1 decimal place π₯3 β 5π₯ = 50 π π π β ππ Comment 4 43 β 5 Γ 4 = 44 Low 5 53 β 5 Γ 5 = 100 High 4.3 4.33 β 5 Γ 4.3 = 58.007 High 4.2 4.23 β 5 Γ 4.2 = 53.088 High 4.1 4.13 β 5 Γ 4.1 = 48.421 Low Draw a table β it helps! 4.153 β 5 Γ 4.15 = 50.723375 Since 4.15 is too high, everything about it must be too high as well. Therefore the solution to 1 decimal place is 4.1
- 30. πΆπππ π π πππ‘πππππ ππππ = π΄πππ ππ ππππππ = π Γ π2 = π Γ π2 = 16π cm2 ππππ’ππ = πΆπππ π π πππ‘πππππ ππππ Γ ππππ‘β = 16π π₯ 5 = 80π = 251.3274123 = 251 ππ3 Shape, Space, Measure Calculate the volume and surface area. Leave your answer to 3 significant figures. 8 ππ 5 ππ
- 31. Handling Data The probability of Man Utd winning a match under David Moyes is 0.3 and losing is 0.2. Man Utd play 3 matches, what is the probability that out of these, 2 are won and one is drawn. Probability of drawing a match is 1 β 0.3 β 0.2 = 0.5 List all the possible combinations Win Win Draw Win Draw Win Draw Win Win π π π΄ππ· π π΄ππ· π· = 0.3 Γ 0.3 Γ 0.5 = 0.045 π π π΄ππ· π· π΄ππ· π = 0.3 Γ 0.5 Γ 0.3 = 0.045 π π· π΄ππ· π π΄ππ· π = 0.5 Γ 0.3 Γ 0.3 = 0.045 Therefore, the probability of winning two and drawing one match is 0.045 + 0.045 + 0.045 = 0.135
- 32. Number Algebra Shape, Space, Measure Handling Data Solve the following Leave all answers as mixed numbers 1 3 + 4 5 = 3 5 7 β 1 2 3 = 4 9 Γ 3 8 = 4π₯ + 6 = π₯ β 12 7π₯ β 8 = 20 β 3π₯ 5π₯ + 4 6 = 3π₯ + 8 5 Draw a cumulative frequency graph for the following data. Construct a box plot from this information. Calculate the distance between the coordinates (-1, 4) and (11, 9) Marks Frequency 0 β 10 2 11 β 20 7 21 β 30 13 31 β 40 8
- 33. Number Leave all answers as mixed numbers 1 3 + 4 5 = 3 5 7 β 1 2 3 = 4 9 Γ 3 8 = 1 3 + 4 5 = 5 15 + 12 15 = 17 15 = π π ππ 3 5 7 β 1 2 3 = 26 5 β 5 3 = 78 15 β 25 15 = 53 15 = π π ππ 4 9 Γ 3 8 = 12 72 = π π
- 34. Algebra Solve the following 4π₯ + 6 = π₯ β 12 7π₯ β 8 = 20 β 3π₯ 5π₯ + 4 6 = 3π₯ + 8 5 4π₯ + 6 = π₯ β 12 βπ₯ 3π₯ + 6 = β12 βπ₯ β6 3π₯ = β18 β6 Γ· 3 π = βπ Γ· 3 7π₯ β 8 = 20 β 3π₯ +3π₯ 10π₯ β 8 = 20 +3π₯ +8 10π₯ = 28 +8 Γ· 10 π = π. π Γ· 10 5π₯ + 4 6 = 3π₯ + 8 5 Γ 5 25π₯ + 20 6 = 3π₯ + 8 Γ 5 Γ 6 25π₯ + 20 = 18π₯ + 48 Γ 6 β18π₯ 7π₯ + 20 = 48 β18π₯ β20 7π₯ = 28 β20 Γ· 7 π = π (Γ· 7)
- 35. Shape, Space, Measure Calculate the distance between the coordinates (-1, 4) and (11, 9) (-1,4) (11,9) 11 β β1 = 12 9 β 4 = 5 ππ π ππ¦π‘βππππππ π‘π πππππ’πππ‘π π‘βπ πππππ‘β ππ π‘βπ ππππ π2 + π2 = π2 52 + 122 = π2 25 + 144 = π2 169 = π2 ππ = π
- 36. Handling Data Draw a cumulative frequency graph for the following data. Construct a box plot from this information. Marks Frequency 0 β 10 2 11 β 20 7 21 β 30 13 31 β 40 8Marks Frequency Cumulative Frequency 0 β 10 2 2 11 β 20 7 9 21 β 30 13 22 31 β 40 8 30 Plot your graph using the end points and cumulative frequency.
- 37. Number Algebra Shape, Space, Measure Handling Data Rearrange the formula to make x the subject Tins of paint are on offer, buy 5 get 1 free. John the painter needs 27 tins of paint. If a tin of paint costs Β£3.43, how much will John have to pay? π¦ = 4π₯ β 2 jπ₯ + π‘ = ππ₯ β π Calculate an estimate for the mean Table on time of goal scored Calculate the area of the sector and the arc length. Leave all answers to 1 decimal place. 132Β° 3 ππ Time of match Frequency 0 < π₯ β€ 15 8 15 < π₯ β€ 30 4 30 < π₯ β€ 45 5 45 < π₯ β€ 60 7 60 < π₯ β€ 75 7 75 < π₯ β€ 90 10
- 38. Number Tins of paint are on offer, buy 5 get 1 free. John the painter needs 27 tins of paint. If a tin of paint costs Β£3.43, how much will John have to pay? If John buys 5 tins he gets 6. So using this, if he buys 20 tins, he will actually get 24. Therefore he only needs to purchase another 3 tins to have 27. John needs to buy 23 tins. 23 Γ 3.43 = Β£78.89
- 39. Algebra Rearrange the formula to make x the subject π¦ = 4π₯ β 2 jπ₯ + π‘ = ππ₯ β ππ¦ = 4π₯ β 2 +2 π¦ + 2 = 4π₯ +2 Γ· 4 π¦ + 2 4 = π₯ Γ· 4 ππππ π₯ π‘βπ π π’πππππ‘ ππ¦ ππ’π‘π‘πππ ππ π‘βπ ππππ‘ βπππ π πππ. π₯ = π¦ + 2 4 jπ₯ + π‘ = ππ₯ β π βππ₯ ππ₯ β ππ₯ + π‘ = βπ βππ₯ βπ‘ ππ₯ β ππ₯ = βπ‘ β π βπ‘ πΉπππ‘ππππ π π‘π πππππππ π₯ π₯ π β π = βπ‘ β π Γ· π β π π₯ = βπ‘ β π π β π Γ· π β π
- 40. Shape, Space, Measure Calculate the area of the sector and the arc length. Leave all answers to 1 decimal place. 132Β° 3 ππ 3 ππ Calculate the area and circumference of the full circle. π΄πππ = π Γ πππππ’π 2 π΄πππ = π Γ 32 π΄πππ = 9π πΆππππ’ππππππππ = π Γ ππππππ‘ππ πΆππππ’ππππππππ = π Γ 6 πΆππππ’ππππππππ = 6π π΄πππ ππ ππππ‘ππ = 9π 360 Γ 132 π΄πππ ππ ππππ‘ππ = 10.36725576 π΄πππ ππ ππππ‘ππ = 10.4 ππ2 π΄ππ πΏππππ‘β = 6π 360 Γ 132 π΄ππ πΏππππ‘β = 6.911503838 π΄ππ πΏππππ‘β = 6.9 ππ
- 41. Handling Data Calculate an estimate for the mean Table on time of goal scored Time of match Frequency Midpoint Midpoint x Frequency 0 < π₯ β€ 15 8 7.5 60 15 < π₯ β€ 30 4 22.5 90 30 < π₯ β€ 45 5 37.5 187.5 45 < π₯ β€ 60 7 52.5 367.5 60 < π₯ β€ 75 7 67.5 472.5 75 < π₯ β€ 90 10 82.5 825 Total 41 2002.5 Time of match Frequency 0 < π₯ β€ 15 8 15 < π₯ β€ 30 4 30 < π₯ β€ 45 5 45 < π₯ β€ 60 7 60 < π₯ β€ 75 7 75 < π₯ β€ 90 10 Not sure what time the goal was scored β so we use the mid point as an estimate. ππππ = 2002.5 41 ππππ = 48.8 A goal was scored on average at 48.8 minutes.
- 42. Number Algebra Shape, Space, Measure Handling Data Evaluate 80 = 64 1 2 = 7β2 = 4 81 1 2 = πΉπππ‘ππππ π π₯2 + 7π₯ + 12 πΉπππ‘ππππ π 3π₯2 + 14π₯ + 15 π»ππππ ππππππππ¦ π₯2 + 7π₯ + 12 3π₯2 + 14π₯ + 15 Draw a histogram for the following data. Work out the value of x in this regular pentagon Marks Frequency 0 < x β€ 5 3 5 < x β€ 15 14 15 < x β€ 30 18 30 < x β€ 40 85x - 12
- 43. Number Evaluate 80 = 64 1 2 = 7β2 = 4 81 1 2 = 80 = 1 64 1 2 = 64 = 8 7β2 = 1 72 = 1 49 4 81 1 2 = 4 81 = 4 81 = 2 9
- 44. Algebra πΉπππ‘ππππ π π₯2 + 7π₯ + 12 πΉπππ‘ππππ π 3π₯2 + 14π₯ + 15 π»ππππ ππππππππ¦ π₯2 + 7π₯ + 12 3π₯2 + 14π₯ + 15 π₯2 + 7π₯ + 12 = π₯ + 3 π₯ + 4 3π₯2 + 14π₯ + 15 = 3π₯ + 5 π₯ + 3 π₯2 + 7π₯ + 12 3π₯2 + 14π₯ + 15 = π₯ + 3 π₯ + 4 3π₯ + 5 π₯ + 3 = π₯ + 4 3π₯ + 5
- 45. Shape, Space, Measure Work out the value of x in this regular pentagon 5x - 12 Interior angles of a pentagon add up to 540Λ. Regular pentagon has equal angles, 540 Γ· 5 = 108Β° Therefore, 5π₯ β 12 = 108 5π₯ = 120 π₯ = 24Β°
- 46. Handling Data Draw a histogram for the following data. Marks Frequency 0 < x β€ 5 3 5 < x β€ 15 14 15 < x β€ 30 18 30 < x β€ 40 8 Marks Frequency Frequency Density 0 < x β€ 5 3 3 Γ· 5 = 0.6 5 < x β€ 15 14 14 Γ· 10 = 1.4 15 < x β€ 30 18 18 Γ· 15 = 1.2 30 < x β€ 40 8 8 Γ· 10 = 0.8 Calculate the frequency density by frequency Γ· class width. Area of the bar is the frequency
- 47. Number Algebra Shape, Space, Measure Handling Data Fill in the table of values and complete the quadratic graph, π¦ = π₯2 β 5π₯ + 6 for -4 β€ x β€ 4 1) Out of a class of 28, 19 of the pupils support Barnsley. What percentage of pupils do not support Barnsley. 2) An antique was bought for Β£210, it was later sold for Β£400. What percentage of the price it was sold for, was profit? There are 7 green balls and 3 red balls in a bag. A ball is chosen at random and not replaced. What is the probability of picking 3 balls and a) Them being all the same colour b) 2 green balls and a redCalculate the area of the Isosceles triangle x -4 -3 -2 -1 0 1 2 3 4 y 42 2 42Β° 6 ππ
- 48. Number 1) Out of a class of 28, 19 of the pupils support Barnsley. What percentage of pupils do not support Barnsley. 2) An antique was bought for Β£210, it was later sold for Β£400. What percentage of the price it was sold for, was profit? 19 pupils support Barnsley, this means 9 pupils donβt support Barnsley. 9 28 = 9 Γ· 28 = 0.32142857 = 32% Β£190 was profit. So 190 400 =190 Γ· 400 = 0.475 = 47.5%
- 49. Algebra Fill in the table of values and complete the quadratic graph, π¦ = π₯2 β 5π₯ + 6 for -4 β€ x β€ 4 x -4 -3 -2 -1 0 1 2 3 4 y 42 2 x -4 -3 -2 -1 0 1 2 3 4 y 42 30 20 12 6 2 0 0 2
- 50. Shape, Space, Measure Calculate the area of the Isosceles triangle 42Β° 6 ππ π΄πππ = πππ π Γ βπππβπ‘ 2 21Β° 3 ππ Need to calculate the height of the triangle. Use Trigonometry Label your sides (in play) o a Decide your triangle a o t Cover up what you are looking for and write down your formula π = tan π₯ Γ π π = tan 42 Γ 3 π = 2.701 π΄πππ = 6 Γ 2.701 2 π΄πππ = 8.1 ππ2 (3. π . π)
- 51. Handling Data There are 7 green balls and 3 red balls in a bag. A ball is chosen at random and not replaced. What is the probability of picking 3 balls and a) Them being all the same colour b) 2 green balls and a red a) List the combinations β All three green or all three red π π π΄ππ· π π΄ππ· π = 3 10 Γ 2 9 Γ 1 8 = 6 720 π πΊ π΄ππ· πΊ π΄ππ· πΊ = 7 10 Γ 6 9 Γ 5 8 = 210 720 π π΄ππ πππππ ππ π΄ππ πππ = 6 720 + 210 720 = πππ πππ = π ππ b) List the combinations β GGR or GRG of RGG π πΊπΊπ = 7 10 Γ 6 9 Γ 3 8 = 126 720 π πΊπ πΊ = 7 10 Γ 3 9 Γ 6 8 = 126 720 π π πΊπΊ = 3 10 Γ 7 9 Γ 6 8 = 126 720 π πΊπΊπ ππ πΊπ πΊ ππ π πΊπΊ = 126 720 + 126 720 + 126 720 = πππ πππ = ππ ππ
- 52. Number Algebra Shape, Space, Measure Handling Data Estimate 387 β 43 0.18 πΈπ₯ππππ πππ ππππππππ¦ 3 2π₯ β 5 β 7 6 β π₯ 3π₯3 π¦2 π§5 3 (3π₯ β 2π¦)(2π₯ + 5π¦) Below is a table to show how James spends his day. Draw a pie chart to represent this data Calculate the perimeter of this isosceles triangle 5x - 711 - x 4x + 6 Activity Hours Sleeping 9 hours Work 8 hours Eating/Cleaning/Cooking 3 hours Reading 2 hours Commuting 2 hours
- 53. Number Round all numbers to 1 significant figure 400 β 40 0.2 Calculate this sum 360 0.2 Use equivalent fractions to help divide by a decimal 360 0.2 = 3600 2 = 1800 Estimate 387 β 43 0.18
- 54. Algebra πΈπ₯ππππ πππ ππππππππ¦ 3 2π₯ β 5 β 7 6 β π₯ 3π₯3 π¦2 π§5 3 (3π₯ β 2π¦)(2π₯ + 5π¦) 3 2π₯ β 5 β 7 6 β π₯ 6π₯ β 15 β 42 + 7π₯ = 13π₯ β 57 3π₯3 π¦2 π§5 3 = 3π₯3 π¦2 π§5 Γ 3π₯3 π¦2 π§5 Γ 3π₯3 π¦2 π§5 = 27π₯9 π¦6 π§15 3π₯ β 2π¦ 2π₯ + 5π¦ = 6π₯2 + 15π₯π¦ β 4π₯π¦ β 10π¦2 = 6π₯2 + 11π₯π¦ β 10π¦2
- 55. Shape, Space, Measure Calculate the perimeter of this isosceles triangle 5x - 711 - x 4x + 6 Isosceles β two sides are equal. 11 β π₯ = 5π₯ β 7 +π₯ 11 = 6π₯ β 7 +π₯ +7 18 = 6π₯ +7 Γ· 6 3 = π₯ (Γ· 6) Perimeter = 11 β π₯ + 5π₯ β 7 + 4π₯ + 6 = 8π₯ + 10 Substitute π₯ = 3, π‘π πππ‘ 8 Γ 3 + 10 = ππ
- 56. Handling Data Below is a table to show how James spends his day. Draw a pie chart to represent this data Activity Hours Sleeping 9 hours Work 8 hours Eating/Cleaning/Cooking 3 hours Reading 2 hours Commuting 2 hours Activity Hours Degrees Sleeping 9 hours 135 Work 8 hours 120 Eating/Cleaning/Cooking 3 hours 45 Reading 2 hours 30 Commuting 2 hours 30 24 hours in a day. Find out what each hour is worth 360 Γ· 24 = 15Β° Each hour is worth 15Λ on our pie chart. So sleeping is 9 x 15Λ = 135Λ
- 57. Number Algebra Shape, Space, Measure Handling Data Solve the following Simultaneous Equations 5π₯ β π¦ = 9 15π₯ β 2π¦ = 24 2π₯ + 3π¦ = 58 1) A gardens perimeter is 34m (rounded to the nearest m), garden fence panels are 130cm (rounded to the nearest 10cm). a) What is the most number of panels that may be needed? b) What is the least numbers of panels that may be need? Probability of Eric passing his Maths exam is 0.7, the probability of passing his English exam is independent of this, and is 0.6. What is the probability of Eric passing at least one of his exams? What is the straight line distance between the coordinates (4, -5) and ( 10, -3)
- 58. Number 1) A gardens perimeter is 34m (rounded to the nearest m), garden fence panels are 130cm (rounded to the nearest 10cm). a) What is the most number of panels that may be needed? b) What is the least numbers of panels that may be need? Change measurements into the same units. 34m = 3400cm. a) The most number of fence panels needed are when you have a large perimeter and small fence panels. Upper bound for perimeter = 3450cm Lower bound for fence panel = 125cm How many βsmallβ fence panels will you need for a βlargeβ perimeter. ππππ Γ· πππ = ππ. π You would need 28 panels! b) The least number of fence panels needed are when you have a small perimeter and large fence panels Lower bound for perimeter = 3350cm Upper bound for fence panel = 135cm How many βlargeβ fence panels will you need for a βsmallβ perimeter. ππππ Γ· πππ = ππ. ππ π You would need 25 panels!
- 59. Algebra Solve the following Simultaneous Equations 5π₯ β π¦ = 9 15π₯ β 2π¦ = 24 5π₯ β π¦ = 9 (π) 15π₯ β 2π¦ = 24 π ππππ π‘π ππππ π ππππππππππ‘ πππ’ππ π Γ 2 10π₯ β 2π¦ = 18 π π β π 5π₯ = 6 Γ· 5 π = π. π Γ· 5 ππ’ππ π‘ππ‘π’π‘π ππππ πππ‘π π 5 1.2 β π¦ = 9 6 β π¦ = 9 β6 β π¦ = 3 β6 Γ β1 π = βπ (Γ β1) 2π₯ + 3π¦ = 58 (π) 7π₯ = 6π¦ + 5 π π ππππππππ π π‘π πππ‘ ππππππππππ‘π ππ ππππ‘ βπππ π πππ β6y 7π₯ β 6π¦ = 5 β6π¦ π Γ 2 4π₯ + 6π¦ = 116 π π + π 11π₯ = 121 Γ· 11 π = ππ Γ· 11 ππ’ππ π‘ππ‘π’π‘π ππππ πππ‘π π 2 11 + 3π¦ = 58 22 + 3π¦ = 58 β22 3π¦ = 36 β22 Γ· 3 π = ππ (Γ· 3)
- 60. Shape, Space, Measure What is the straight line distance between the coordinates (4, -5) and ( 10, -3) (4,-5) (10,-3) β3 β β5 = 2 10 β 4 = 6 ππ π ππ¦π‘βππππππ π‘π πππππ’πππ‘π π‘βπ πππππ‘β ππ π‘βπ ππππ π2 + π2 = π2 62 + 22 = π2 36 + 4 = π2 40 = π2 6.32 (3.s.f)= π
- 61. Handling Data Probability of Eric passing his Maths exam is 0.7, the probability of passing his English exam is independent of this, and is 0.6. What is the probability of Eric passing at least one of his exams? List the combinations β Pass Maths (0.7), Fail English (0.4) Pass English (0.6), Fail Maths (0.3) Pass English (0.6), Pass Maths (0.7) π πππ π π π΄ππ· πΉππππΈ = 0.7 Γ 0.4 = 0.28 π πππ π πΈ πππ πΉππππ = 0.6 Γ 0.3 = 0.18 π πππ π πΈ πππ πππ π π = 0.6 Γ 0.7 = 0.42 π πππ π ππ‘ ππππ π‘ πππ = 0.28 + 0.18 + 0.42 = π. ππ Alternative Solution. Probability of passing at least once = 1 β probability of not passing either exam π πΉππππΈ πππ πΉππππ = 0.4 Γ 0.3 = 0.12 π β π. ππ = π. ππ
- 62. Number Algebra Shape, Space, Measure Handling Data Put the following, in ascending order π0, 2β5, 81 1 2, 1 4 β2 , 3 2 2 ππππ£π 4π₯ β 1 = 2 β π₯ 10π₯ + 5 = 8π₯ β 9 π₯ β 1 2 + 4π₯ β 3 3 = 4 Construct a frequency polygon for the following The area of the rectangle is 60ππ2 calculate the perimeter π₯ β 7 Cost x (Β£) Frequency 0 β€ x < 10 8 10 β€ x < 20 11 20 β€ x < 30 5 30 β€ x < 40 14 40 β€ x < 50 6 π₯
- 63. Number Put the following, in ascending order π0, 2β5, 81 1 2, 1 4 β2 , 3 2 2π0 = 1 (anything to the power 0 is equal to 1. 2β5 = 1 25 = 1 32 81 1 2 = 81 = 9 1 4 β2 = 4 1 2 = 42 12 = 16 1 = 16 3 2 2 = 32 22 = 9 4 Therefore, πβπ, π π, π π π , ππ π π, π π βπ
- 64. Algebra ππππ£π 4π₯ β 1 = 2 β π₯ 10π₯ + 5 = 8π₯ β 9 π₯ β 1 2 + 4π₯ β 3 3 = 4 4π₯ β 1 = 2 β π₯ +π₯ 5π₯ β 1 = 2 +π₯ +1 5π₯ = 3 +1 Γ· 5 π = π π = π. π (Γ· 5) 10π₯ + 5 = 8π₯ β 9 β8π₯ 2π₯ + 5 = β9 β8π₯ β5 2π₯ = β14 β5 Γ· 2 π = βπ (Γ· 2) π₯ β 1 2 + 4π₯ β 3 3 = 4 Γ 2 π₯ β 1 + 2 4π₯ β 3 3 = 8 Γ 2 Γ 3 3 π₯ β 1 + 2 4π₯ β 3 = 24 Γ 3 3π₯ β 3 + 8π₯ β 6 = 24 11π₯ β 9 = 24 +9 11π₯ = 33 +9 Γ· 11 π = π (Γ· 11)
- 65. Shape, Space, Measure The area of the rectangle is 60ππ2 calculate the perimeter π₯ β 7 π₯ π΄πππ = 60ππ2 π΄πππ = π₯ π₯ β 7 = π₯2 β 7π₯ πβπππππππ, π₯2 β 7π₯ = 60 ππππ ππ‘ ππππ ππππ π π’π π’ππ ππ’πππππ‘ππ β60 π₯2 β 7π₯ β 60 = 0 β60 πππ€ π πππ£π. πΌπ‘ π€πππ ππππ‘ππππ π, ππ’π‘ π¦ππ’ πππ π’π π π‘βπ πππππ’ππ π₯ β 12 π₯ + 5 = 0 π₯ β 12 = 0 ππ π₯ + 5 = 0 π₯ = 12 ππ π₯ = β5 We are working with lengths, so we will ignore the -5, π₯ = 12. πβπππππππ, πππππππ‘ππ = π₯ β 7 + π₯ + π₯ β 7 + π₯ = 4π₯ β 14 ππ’ππ π‘ππ‘π’π‘π ππ π₯ = 12 = 4 12 β 14 = ππππ
- 66. Handling Data Construct a frequency polygon for the following Cost x (Β£) Frequency 0 β€ x < 10 8 10 β€ x < 20 11 20 β€ x < 30 5 30 β€ x < 40 14 40 β€ x < 50 6 See polygon β think straight lines. Is this 8 things at Β£0 or Β£9.99? We canβt be sure so use the midpoint.
- 67. Number Algebra Shape, Space, Measure Handling Data Calculate the ππ‘β term for the following sequences 3, 7, 11, 15, 19, β¦ 8, 11, 16, 23, 32, β¦ 2, 7, 14, 23, 34, β¦ Barnsley Football club is organising travel for an away game. 1300 adults and 500 juniors want to go. Each coach holds 48 people and costs Β£320 to hire. Tickets to the match are Β£18 for adults and Β£10 for juniors. The club is charging adults Β£26 and juniors Β£14 for travel and a ticket. How much profit does the club make out the trip? Calculate an estimate for the meanThese two shapes are Mathematical Similar. Calculate the missing volume and surface area 4cm 12cm Surface area = Volume = 72ππ3 Surface area = 729ππ2 Volume = Cost x (Β£) Frequency 0 β€ x < 10 8 10 β€ x < 20 11 20 β€ x < 30 5 30 β€ x < 40 14 40 β€ x < 50 6
- 68. Number Barnsley Football club is organising travel for an away game. 1300 adults and 500 juniors want to go. Each coach holds 48 people and costs Β£320 to hire. Tickets to the match are Β£18 for adults and Β£10 for juniors. The club is charging adults Β£26 and juniors Β£14 for travel and a ticket. How much profit does the club make out the trip? Cost to supporter 1300 Γ Β£26 = Β£33,800 500 Γ Β£14 = Β£7,000 πππ‘ππ = Β£40,800 Cost to the club Ticket costs 1300 Γ Β£18 = Β£23,400 500 Γ Β£10 = Β£5,000 πππ‘ππ = Β£28,400 Coach costs Coaches needed: (1300 + Profit to the club Β£40,800 β Β£40,560 = Β£240
- 69. Algebra Calculate the ππ‘β term for the following sequences 3, 7, 11, 15, 19, β¦ 8, 11, 16, 23, 32, β¦ 2, 7, 14, 23, 34, β¦ 3, 7, 11, 15, 19, β¦ πΌππππππ πππ ππ¦ 2 πππβ π‘πππ 2π + 1 8, 11, 16, 23, 32, β¦ 3 5 7 9 2 2 2 π2 1, 4, 9, 16, 25, β¦ +7 2, 7, 14, 23, 34, β¦ 5 7 9 11 2 2 2 π2 1, 4, 9, 16, 25, β¦ 1, 3, 5, 7, 9 + 2π β 1
- 70. Shape, Space, Measure These two shapes are Mathematical Similar. Calculate the missing volume and surface area 4cm 12cm Surface area = Volume = 72ππ3 Surface area = 729ππ2 Volume = Mathematical similar β they are in scale. πππππ πΉπππ‘ππ = 12 4 = 3 Shape B has been enlarged by the linear scale factor of 3. The surface area will therefore be 32 as big. 729 32 = 81ππ2 The volume will be 33 as big. 72 Γ 33 = 1944ππ3 A B ππππ π ππππππ π Top Tip: Area is measured in ππ π , so when enlarging a shape β donβt forget to square the scale factor when working out the enlarged area. Volume is measured in ππ π , so when enlarging a shape β donβt forget to cube the scale factor when working out the enlarged volume.
- 71. Calculate an estimate for the mean Time of match Frequency Midpoint Midpoint x Frequency 0 β€ x < 10 8 5 40 10 β€ x < 20 11 15 165 20 β€ x < 30 5 25 125 30 β€ x < 40 14 35 490 40 β€ x < 50 6 45 270 Total 44 1090 Not sure what time the cost is β so we use the mid point as an estimate. ππππ = 1090 44 ππππ = Β£24.78 Handling Data Cost x (Β£) Frequency 0 β€ x < 10 8 10 β€ x < 20 11 20 β€ x < 30 5 30 β€ x < 40 14 40 β€ x < 50 6
- 72. Number Algebra Shape, Space, Measure Handling Data πΉπππ‘ππππ π 4π₯2 β 18π₯ π₯2 β 12π₯ + 32 6π₯2 + 13π₯ β 5 25π₯2 β 9π¦2 Give two criticisms of the following questionnaire A rectangles width to length ratio is 2:5, if the perimeter is 84cm, what is the area? 2.1 x 0.48 = 0.021 x 4.8 = 162.9 Γ· 0.09 = Do you agree that Barnsley FC are by far the greatest team the world has ever seen? Strongly agree Agree Not sure
- 73. Number 2.1 x 0.48 = 0.021 x 4.8 = 162.9 Γ· 0.09 = Ignore the decimal places and do your calculations when multiplying decimals. ππ Γ ππ = ππππ Now add your decimal point into your answer. The question had three decimal places β so your answer needs three decimal places. 1 008. Ignore the decimal places and do your calculations when multiplying decimals. ππ Γ ππ = ππππ Now add your decimal point into your answer. The question had four decimal places β so your answer needs four decimal places. 1 008 . Use equivalent fractions when dividing with decimals. 162.9 0.09 = 16290 9 = 1810
- 74. Algebra πΉπππ‘ππππ π 4π₯2 β 18π₯ π₯2 β 12π₯ + 32 6π₯2 + 13π₯ β 5 25π₯2 β 9π¦2 4π₯2 β 18π₯ = 2π₯ 2π₯ β 9 π₯2 β 12π₯ + 32 = π₯ β 8 π₯ β 4 6π₯2 + 13π₯ β 5 = (3π₯ β 1)(2π₯ + 5) 25π₯2 β 9π¦2 = (5π₯ β 3π¦)(5π₯ + 3π¦)
- 75. Shape, Space, Measure A rectangles width to length ratio is 2:5, if the perimeter is 84cm, what is the area? 5π₯ 2π₯ πππππππ‘ππ = 84ππ πππππππ‘ππ = 5π₯ + 2π₯ + 5π₯ + 2π₯ = 14π₯ πβπππππππ, 14π₯ = 84 Γ· 14 π₯ = 6 Γ· 14 π΄πππ = 2π₯ Γ 5π₯ = 10π₯2 ππ’ππ π‘ππ‘π’π‘π π₯ = 6 π΄πππ = 10 62 = πππππ π
- 76. Handling Data Give two criticisms of the following questionnaire Do you agree that Barnsley FC are by far the greatest team the world has ever seen? Strongly agree Agree Not sure 1. A leading question, do you agree, puts pressure on the person answering the question. 2. No response boxes for if you disagree (but why would you?)
- 77. Number Algebra Shape, Space, Measure Handling Data Fill in the table of values and complete the cubic graph, π¦ = π₯3 β 2π₯ +1 for -3 β€ x β€ 3 2 3 7 β 4 1 4 = 5 8 Γ 4 15 = 4 5 Γ· 6 7 = A bag contains 3 blue balls, 5 red balls and 4 green balls. When a ball is taken out, it is not replaced. What is the probability of picking three balls that are all the same colour. Calculate the area of the following quadrilateral x -3 -2 -1 0 1 2 3 y -3 1 22
- 78. Number 2 3 7 β 4 1 4 = 5 8 Γ 4 15 = 4 5 Γ· 6 7 = For Casio fx-83GT plus Type shift 32 7 - shift 14 4 = β 51 28 5 8 4 15 =x 1 6 4 5 6 7 =Γ· 14 15
- 79. Algebra Fill in the table of values and complete the cubic graph, π¦ = π₯3 β 2π₯ +1 for -3 β€ x β€ 3 x -3 -2 -1 0 1 2 3 y -3 1 22 x -3 -2 -1 0 1 2 3 y -20 -3 2 1 0 5 22
- 80. Shape, Space, Measure Calculate the area of the following quadrilateralWill need these (found at the front of your exam) Find the area of the two triangles and add these together... 1 2 Sin B b = Sin A a πππ B 3 = Sin 83 12 πππ π΅ = 3πππ 83 12 π΅ = πππβ1 3 sin 83 12 π΅ = 14.367Β° 1 B πβπ πππ π‘ π’πππππ€π πππππ ππ π‘πππππππ 1 180 β 83 β 14.367 = 82.633Β° 2 πΉπππ ππ πππππ ππ π‘πππππππ 2 π’π πππ π‘βπ πππ πππ ππ’ππ πππ¦ πππππ ππ ππππππππππ π2 = π2 + π2 β 2ππ πΆππ π΄ 122 = 102 + 42 β 2 Γ 10 Γ 4 πΆππ π΄ 144 = 116 β 80πΆππ π΄ 28 = β80 πΆππ π΄ β 28 80 = πΆππ π΄ πΆππ β1 β 28 80 = π΄ π΄ = 110.487
- 81. Shape, Space, Measure Calculate the area of the following quadrilateralWill need these (found at the front of your exam) Find the area of the two triangles and add these together... 1 2 ππ π π΄πππ = 1 2 πππππ πΆ π΄πππ ππ ππππππππ 1 = 1 2 Γ 12 Γ 3 Γ πππ 82.633 π΄πππ ππ ππππππππ 1 = 17.851ππ2 π΄πππ ππ ππππππππ 2 = 1 2 Γ 10 Γ 4 Γ πππ 110.487 π΄πππ ππ ππππππππ 2 = 18.735ππ2 π΄πππ ππ ππ’πππππππ‘ππππ = 17.851 + 18.735 = ππ. πππ
- 82. Handling Data A bag contains 3 blue balls, 5 red balls and 4 green balls. When a ball is taken out, it is not replaced. What is the probability of picking three balls that are all the same colour. List the combinations β Blue, Blue, Blue, Red, Red, Red, Green, Green, Green π π΅ π΄ππ· π΅ π΄ππ· π΅ = 3 12 Γ 2 11 Γ 1 10 = 6 1320 π π π΄ππ· π π΄ππ· π = 5 12 Γ 4 11 Γ 3 10 π πΊ π΄ππ· πΊ π΄ππ· πΊ = 4 12 Γ 3 11 Γ 2 10 π π΅π΅π΅ ππ π π π ππ πΊπΊπΊ = 6 1320 + 60 1320 + 24 1320 = 90 1320 = 3 44
- 83. Number Algebra Shape, Space, Measure Handling Data ππππππππ¦ β0 3π2 π‘4 π§ 3 10π₯π¦2 π§4 2π₯3 π¦2 π§ π₯2 + 7π₯ + 12 π₯ + 4 The mean weight of ten footballers is 73.5kg. A new player comes along and the mean weight goes down to 72kg. How much does the new player weigh? Calculate the area of the isosceles triangle Calculate the area and perimeter of the rectangle. Leave your answer in Surd form if applicable 18 2 10cm 13cm
- 84. Number Calculate the area and perimeter of the rectangle. Leave your answer in Surd form if applicable 18 2 π΄πππ = 18 Γ 2 = 36 = π πππππ π πππππππ‘ππ = 18 + 2 + 18 + 2 = 9 Γ 2 + 2 + 9 Γ 2 + 2 = 9 2 + 2 + 9 2 + 2 = 3 2 + 2 + 3 2 + 2 = π π πππππ
- 85. Algebra ππππππππ¦ β0 3π2 π‘4 π§ 3 10π₯π¦2 π§4 2π₯3 π¦2 π§ π₯2 + 7π₯ + 12 π₯ + 4 β0 = 1 3π2 π‘4 π§ 3 = 3π2 π‘4 π§ Γ 3π2 π‘4 π§ Γ 3π2 π‘4 π§ = 27π6 π‘12 π§3 10π₯π¦2 π§4 2π₯3 π¦2 π§ = 5π₯β2 π§3 = 5π§3 π₯2 π₯2 + 7π₯ + 12 π₯ + 4 = π₯ + 3 π₯ + 4 (π₯ + 4) = π₯ + 3
- 86. Shape, Space, Measure Calculate the area of the isosceles triangle 10cm 13cm π΄πππ ππ π π‘πππππππ = πππ π Γ βπππβπ‘ 2 Need to calculate the perpendicular height of the triangle. 13cm 5cm h ππ π ππ¦π‘βππππππ π‘π πππππ’πππ‘π π‘βπ βπππβπ‘ π2 + π2 = π2 52 + π2 = 132 25 + π2 = 169 π2 = 144 π = 12 π»πππβπ‘ ππ 12ππ. πβπππππππ, π΄πππ = 12 Γ 5 2 π΄πππ = ππππ π
- 87. Handling Data The mean weight of ten footballers is 73.5kg. A new player comes along and the mean weight goes down to 72kg. How much does the new player weigh? 10 footballers in total weigh 10 Γ 73.5ππ = 735ππ. 11 footballers in total weigh 11 Γ 72 = 792ππ The eleventh footballer must have weight 792 β 735 = ππππ
- 88. Number Algebra Shape, Space, Measure Handling Data The formula to convert Celsius to Fahrenheit is 9 5 πΆ + 32 = πΉ Use your calculator to work out the value of 3.92 β 1.42 Write down the full display. Round your answer to 2 significant figures Complete a histogram for the following data Height, h (cm) Frequency 151 β€ h < 153 64 153 β€ h < 154 43 154 β€ h < 155 47 155 β€ h < 159 96 159 β€ h < 160 12 What is the temperature in Fahrenheit, when it 18Λ Celsius? What is the temperature in Celsius when it is 53.6Λ Fahrenheit? An exterior angle of a regular polygon is 30Λ. Work out the number of sides of the polygon.
- 89. Number Use your calculator to work out the value of 3.92 β 1.42 Write down the full display. Round your answer to 2 significant figures 3 For Casio fx-83GT plus Type . 9 - 1 . 4 π π = 3.640054945 3.6 π π
- 90. Algebra The formula to convert Celsius to Fahrenheit is 9 5 πΆ + 32 = πΉ What is the temperature in Fahrenheit, when it 18Λ Celsius? What is the temperature in Celsius when it is 53.6Λ Fahrenheit? 9 Γ 18 5 + 32 = β 64.4 = β ππβ = ππ. πβ 9 5 πΆ + 32 = 53.6 β32 9 5 πΆ = 21.6 β32 Γ 5 9πΆ = 108 Γ 5 Γ· 9 πΆ = 12 Γ· 9 ππβ = ππ. πβ
- 91. Shape, Space, Measure An exterior angle of a regular polygon is 30Λ. Work out the number of sides of the polygon. Exterior angles add up to 360Β°, therefore 360 Γ· 30 = 12 The polygon has 12 sides (Dodecagon) 30Β°
- 92. Handling Data Complete a histogram for the following data Height, h (cm) Frequency 151 β€ h < 153 64 153 β€ h < 154 43 154 β€ h < 155 47 155 β€ h < 159 96 159 β€ h < 160 12 Marks Frequency Frequency Density 151 β€ h < 153 64 64 Γ· 2 = 32 153 β€ h < 154 43 43 Γ· 1 = 43 154 β€ h < 155 47 47 Γ· 1 = 47 155 β€ h < 159 96 96 Γ· 4 = 24 159 β€ h < 160 12 12 Γ· 1 = 12 Calculate the frequency density by frequency Γ· class width. Area of the bar is the frequency
- 93. Number Algebra Shape, Space, Measure Handling Data πΈπ₯ππππ πππ ππππππππ¦ 3π¦ 4π¦ β 2 4 π₯ β 2 β 5 π₯ + 3 π₯ + 4 π₯ β 7 (3π + 2π)(2π β 3π) What is the probability of rolling a dice three times and getting two square numbers and a prime number. Convert 8ππ3 to ππ3 Convert 40,000ππ2 to π2 Four pumps usually empty water from a tank in 1 hour 36 minutes. One of the pumps breaks down. How long will three pumps, working at the same rate, take to empty the same tank.
- 94. Number Four pumps usually empty water from a tank in 1 hour 36 minutes. One of the pumps breaks down. How long will three pumps, working at the same rate, take to empty the same tank. 1 hour 36 minutes = 96 minutes If four pumps take 96 minutes to empty a tank, that must mean one pump would take four times as long 4 Γ 96 = 384 ππππ’π‘ππ If three pumps were to do this, they would do it in a third of the time 384 Γ· 3 = 128 ππππ’π‘ππ 128 minutes = 2 hours 8 minutes.
- 95. Algebra πΈπ₯ππππ πππ ππππππππ¦ 3π¦ 4π¦ β 2 4 π₯ β 2 β 5 π₯ + 3 π₯ + 4 π₯ β 7 (3π + 2π)(2π β 3π) 3π¦ 4π¦ β 2 = 12y2 β 6y 4 π₯ β 2 β 5 π₯ + 3 = 4π₯ β 8 β 5π₯ β 15 = βπ₯ β 23 π₯ + 4 π₯ β 7 = π₯2 β 7π₯ + 4π₯ β 28 = π₯2 β 3π₯ β 28 3π + 2π 2π β 3π = 6π2 β 9ππ + 4ππ β 6π2 = 6π2 β 5ππ β 6π2
- 96. Shape, Space, Measure Convert 8ππ3 to ππ3 Convert 40,000ππ2 to π2 1cm 1cm 1cm 10mm 10mm 10mm ππππ’ππ = 1ππ Γ 1ππ Γ 1ππ = 1ππ3 ππππ’ππ = 10ππ Γ 10ππ Γ 10ππ = 1000ππ3 π¬ππππ πππ π ππ ππππππππππ ππ ππππππ π , π»ππππππππ, πππ π = ππππππ π 1m 1m 100cm 100cm π΄πππ = 1π Γ 1π = 1π2 π΄πππ = 100ππ Γ 100ππ = 10,000ππ2 π¬ππππ ππ π ππ ππππππππππ ππ ππ, πππππ π, π»ππππππππ, ππ, πππππ π = ππ π
- 97. Handling Data What is the probability of rolling a dice three times and getting two square numbers and a prime number. List the combinations β Square, Square, Prime Square, Prime, Square Prime, Square, Square π π π΄ππ· π π΄ππ· π = 1 3 Γ 1 3 Γ 1 2 = 1 18 π π π΄ππ· π π΄ππ· π = 1 3 Γ 1 2 Γ 1 3 = 1 18 π π π΄ππ· π π΄ππ· π = 1 2 Γ 1 3 Γ 1 3 = 1 18 Square numbers 1, 4 π πππ’πππ = 1 3 Prime numbers 2, 3, 5 π πππππ = 1 2 π πππ ππ πππ ππ πππ = 1 18 + 1 18 + 1 18 = 3 18 = 1 6
- 98. Number Algebra Shape, Space, Measure Handling Data Write down all the integers n that satisfy 5 β€ π < 9 β3 < 2π β€ 1 β2 β€ 4π + 2 β€ 0 Β£1 = $1.67 A laptop costs Β£320 in the UK, and $530 in the USA. Where is the laptop cheaper, and by how much? The table shows van rentals for the company VansRCool. Calculate a 3 point moving average for the months below Hayley can run 100m in 13 seconds. What is her average speed in miles per hour?
- 99. Number Β£1 = $1.67 A laptop costs Β£320 in the UK, and $530 in the USA. Where is the laptop cheaper, and by how much? UK price Β£320 USA price $530 Γ· 1.67 = Β£317.37 USA cheaper by Β£2.63 UK price Β£320 Γ 1.67 = $534.40 USA price $530 USA cheaper by $4.40 OR
- 100. Algebra π = 5, 6, 7, ππ 8 Write down all the integers n that satisfy 5 β€ π < 9 β3 < 2π β€ 1 β2 β€ 4π + 2 β€ 0 β3 < 2π β€ 1 Γ· 2 β 1.5 < π β€ 1 Γ· 2 π = β1, 0 ππ 1 β2 β€ 4π + 2 β€ 0 β2 β 4 β€ 4π β€ β2 β2 Γ· 4 β 1 β€ π β€ β0.5 Γ· 4 π = β1, 0
- 101. Shape, Space, Measure Key Facts: 60 seconds in a minute 60 minutes in a hour 1600m in a mile. Hayley can run 100m in 13 seconds. What is her average speed in miles per hour? 100 πππ‘πππ ππ 13 π ππππππ 100 13 πππ‘πππ ππ 1 π πππππ 60 Γ 100 13 πππ‘πππ ππ 1 ππππ’π‘π 60 Γ 60 Γ 100 13 πππ‘πππ ππ 1 βππ’π 360000 13 πππ‘πππ ππ 1 βππ’π 360000 13 Γ 1600 πππππ ππ 1 βππ’π. 17.3 miles per hour
- 102. Handling Data 3 point moving average β work out the mean in groups of 3 The table shows van rentals for the company VansRCool. Calculate a 3 point moving average for the months below 9 + 22 + 37 3 = 22. 6 22 + 37 + 14 3 = 24. 3 37 + 14 + 18 3 = 23 14 + 18 + 24 3 = 18. 6 πβπ 3 πππππ‘ πππ£πππ ππ£πππππ ππ 22.6, 24.3, 23, 18.6
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