1. Assessment 2 Revision

2. Revision List Stem and Leaf Scatter Graphs Bar Charts Solving Equations Indices Pythagoras’ Theorem Trigonometry Sequences Substituting in a Formula Rearranging Formulae

3. Pictograms We must remember – your pictogram must always have a key. Example 1. How many pupils chose Tennis? 2. How many more pupils chose Netball than Hockey? 5 pupils 3 pupils

4. Bar Charts When constructing a bar chart we need to remember 1)To leave gaps between the bars 2)Label the axes 3)Give the graph a title

5. Scatter Graphs A scatter graph shows two variables plotted against each other. Two variables are correlated if they are related to each other. Positive correlation means that the variables increase and decrease together. Negative correlation means that as one variable increases, the other decreases. The diagrams below show different correlations No Correlation Positive Correlation Negative Correlation

6. Scatter Graphs Example The scatter graph shows the science mark and the maths mark for 15 students. a)What type of correlation does this scatter graph show? b)Draw a line of best fit. c)Sophie scored 42 in science. Use your line of best fit to estimate her maths mark. Draw a line of best fit which ensures the line has roughly the same number of points on each side of the line. Always draw dashed lines when estimating. It allows the examiner to see where you have derived your estimate from. 47

7. Stem & Leaf Diagrams A stem and leaf diagram is used to see the spread of data and can be used to compare two data sets. Example The data below details the ages of the employees in a company. 23, 25, 84, 26, 63, 45, 54, 62, 22, 21, 72, 19, 32, 33, 21, 34, 44, 66, 71, 18. Create an ordered stem and leaf to represent this data. The tens are the “stem” 1234567812345678 9 8 3 5 6 2 1 1 2 3 4 5 4 4 3 2 6 2 1 4 The units are “the leaf” 8 9 1 1 2 3 5 6 2 3 4 4 5 4 2 3 6 1 2 4 We need to order the diagram. To do this we sort the “leaf” part. Normally we would draw two diagrams. 1 3 = 13 years old Lastly we always need a key

8. Stem & Leaf Diagrams – Finding Averages Once we have our stem and leaf diagram, we can use it to find the median, mode and range. 1234567812345678 8 9 1 1 2 3 5 6 2 3 4 4 5 4 2 3 6 1 2 4 Let’s recap Mode = Most Common Median = Middle when in order Range = largest – smallest 1 3 = 13 years old For this stem and leaf, Mode =21 years old Median =Cross off from start and end until we get to the middle = half way between 34 and 34 = 34.5 years old

9. 1) + 7 = 10 2) 3) Solve each of the following equations: - 9 = 2 4) 4 = 11 - 7 = 3 + 9 = 11 x 4 = 44 5 = 40 ÷ 5 = 8

10. 1)x + 4 = 10 2)d – 2 = 9 3)p + 7 = 12 4)12 – f = 7 5)6r = 24 6)k = 7 3 7)10c = 30 8)5b = 12 9)g + 2 = -4 10)20 = 5 a 11)2m + 3 = 15 12) 6y + 1 = 31 13) 5k – 2 = 18 14) 7w – 3 = 20 Solving Equations

11. 1)x + 4 = 10 x = 6 2)d – 2 = 9 d = 11 3)p + 7 = 12 p = 5 4)12 – f = 7 f = 5 5)6r = 24 r = 4 6)k = 7 k = 21 3 7)10c = 30 c = 3 8)5b = 12 b = 12 / 5 9)g + 2 = -4 g = -6 10) 20 = 5 a = 4 a 11) 2m + 3 = 15 m = 6 12) 6y + 1 = 31 y = 5 13) 5k – 2 = 18 k = 4 14) 7w – 3 = 20w = 23 / 7 Solving Equations

12. Examples 1) 2x + 5= 9 2) 3x – 2= 13 2x= x= 3x= x= 4242 15 5 Subtract 5 from both sides -5 +2 Add 2 to both sides Solving Equations with Two Steps

13. 1) 2x + 1 = 9 2)3x + 4 = 10 3) 5x + 2 = 27 4) 3x – 1 = 11 5) 4x – 3 = 37 6) 10x + 4 = 54 7) 7x – 2 = 33 8) 4x + 11 = 43 9) 2x + 1 = 16 10) 10 – 2x = 6 11) 16 – 3x = 7 12) 5x= 10 2 Solving Equations with Two Steps

14. 1) 2x + 1 = 9 2)3x + 4 = 10 3) 5x + 2 = 27 4) 3x – 1 = 11 5) 4x – 3 = 37 6) 10x + 4 = 54 7) 7x – 2 = 33 8) 4x + 11 = 43 9) 2x + 1 = 16 10) 10 – 2x = 6 11) 16 – 3x = 7 12) 5x= 10 2 x = 4 x = 5 x = 2 x = 8 x = 5 x = 7.5 x = 4 x = 2 x = 10 x = 3 x = 5 x = 4 Solving Equations with Two Steps

15. Examples 1)2(x + 5) = 14 2)3(x – 2) = 9 2x + 10 = 14 2x = 4 x = 2 3x – 6 = 9 3x = 15 x = 5 Solving Equations with Brackets Expand the brackets first

16. 1) 2(x + 3) = 18 2) 3(x – 1) = 15 3) 5(x + 4) = 30 4) 10(x – 2) = 50 5) 2(x – 5) = 17 6) 10(x + 2) = 23 7) 2(3x + 1) = 20 8) 3(4x – 1) = 21 9) 5(2x + 3) = 25 10) 3(3x – 5) = 75 Solving Equations with Brackets

17. 1) 2(x + 3) = 18 2) 3(x – 1) = 15 3) 5(x + 4) = 30 4) 10(x – 2) = 50 5) 2(x – 5) = 17 6) 10(x + 2) = 23 7) 2(3x + 1) = 20 8) 3(4x – 1) = 21 9) 5(2x + 3) = 25 10) 3(3x – 5) = 75 x = 6 x = 2 x = 7 x = 13.5 x = 0.3 or x = 3 / 10 x = 3 x = 2 x = 1 x = 10 Solving Equations with Brackets

18. Examples 1) 5x + 4= 2x + 10 2) 7x – 3 = 3x + 5 3x + 4 = 10 3x = 6 x = 2 4x – 3 = 5 4x = 8 x = 2 Subtract 2x from both sides -2x Subtract 3x from both sides -3x Solving Equations with Letters on Both Sides

19. Examples 3) 2x + 1= 16 – 3x 4) 20 – 5x = x – 4 5x + 1 = 16 5x = 15 x = 3 20 = 6x – 4 24 = 6x x = 4 Add 3x to both sides +3x Add 5x to both sides +5x Solving Equations with Letters on Both Sides

20. 1) 5x + 1 = 2x + 4 2) 6x – 5 = 3x + 4 3) 8x + 3 = 3x + 28 4) 3x + 18 = 5x – 4 5) 3x + 5 = 10 – 2x 6) 2x – 3 = 11 – 5x 7) 2(3x + 1) = 3x + 11 8) 5(2x – 1) = 6x + 31 9) 2x + 2 = 2(5 – 3x) 10) 3(5x – 2) = 5(x + 4) Solving Equations with Letters on Both Sides

21. 1) 5x + 1 = 2x + 4 2) 6x – 5 = 3x + 4 3) 8x + 3 = 3x + 28 4) 3x + 18 = 5x – 4 5) 3x + 5 = 10 – 2x 6) 2x – 3 = 11 – 5x 7) 2(3x + 1) = 3x + 11 8) 5(2x – 1) = 6x + 31 9) 2x + 2 = 2(5 – 3x) 10) 3(5x – 2) = 5(x + 4) x = 1 x = 3 x = 5 x = 11 x = 1 x = 2 x = 3 x = 9 x = 1 x = 2.6

22. 5 cm 12 cm ? 1 Examples Steps Calculator Keys Square itx 2 5 2 = 25 Square itx 2 12 2 = 144 ADD it+ 25+144= 169 Square root it   169= 13 Answer = 13cm

23. 7 cm ? 3cm 2 Examples Steps Calculator Keys Square itx 2 3 2 = 9 Square itx 2 7 2 = 49 ADD it+ 9+49= 58 Square root it   58= 7.615773 Answer = 7.6cm

24. x m 9 m 11m 1 Examples Steps Calculator Keys Square itx 2 11 2 = 121 Square itx 2 9 2 = 81 SUBTRACT it– 121 – 81= 40 Square root it   40= 6.324555... Answer = 6.3m (1dp)

25. 11 cm x cm 23.8 cm 2 Examples Steps Calculator Keys Square itx 2 23.8 2 = 566.44 Square itx 2 11 2 = 121 SUBTRACT it– 566.44 – 121 = 445.44 Square root it   445.44= 21.1054... Answer = 21.1cm (1dp)

26. 1)2)3)4)5) 6) 7)8)9) 11)12)13)14) Pythagoras’ Theorem 10)

27. Pythagoras’ Theorem Answers 1)10cm 2)24cm 3)17cm 4)29cm 5)35cm 6)4m 7)13cm 8)12cm 9)15mm 10) 5km 11)13cm 12)15cm 13)61cm 14)17cm

28. Finding a Missing Side missing side is at the top of the ratio sin angle = opp hyp cos angle = adj hyp tan angle = opp adj (opp) (hyp) (adj) (angle)

29. Finding a Missing Side missing side is at the top of the ratio sin angle = opp hyp cos angle = adj hyp tan angle = opp adj (opp) (hyp) (adj) (angle)

30. Finding a Missing Side missing side is at the bottom of the ratio sin angle = opp hyp cos angle = adj hyp tan angle = opp adj (opp) (hyp) (adj) (angle)

31. Finding a Missing Side missing side is at the bottom of the ratio sin angle = opp hyp cos angle = adj hyp tan angle = opp adj (opp) (hyp) (adj) (angle)

32. Finding a Missing Side