Welcome to the Revision Conference Name: School:

Session 1 - Data Sampling & Questionnaires Stem-and-leaf Scatter Graphs Frequency Polygons

Comment on these sampling techniques You want to find out how much exercise people in your town do. You go to the local sports centre to carry out a survey You want to work out what proportion of a magazine is pictures. You count the number of pictures on the first 3 pages This data is fictional. Ask questions such as “How many people took part in the survey altogether?” “How many spent under £5/ £7 etc?” “What is the mean/ median/ modal amount spent?”

Questionnaires – Important Points Normally 2 parts to an exam question: Questionnaire involves: A question Response boxes Critique a questionnaire – say what is wrong Improve a questionnaire Questions: Must state a time period e.g. per day, per week, per month etc Response Boxes: Must NOT overlap Is there a zero or more than option? Options must mean the same thing to everyone (a lot, excellent, not much are NOT GOOD numerical options are normally better) This data is fictional. Ask questions such as “How many people took part in the survey altogether?” “How many spent under £5/ £7 etc?” “What is the mean/ median/ modal amount spent?”

Questionnaires Critique & Improve: “How much money do you spend on magazines?”   State TWO criticisms: Improve this questionnaire: This data is fictional. Ask questions such as “How many people took part in the survey altogether?” “How many spent under £5/ £7 etc?” “What is the mean/ median/ modal amount spent?”

Questionnaires Critique & Improve: “How many pizzas have you eaten?”   State TWO criticisms: Improve this questionnaire: This data is fictional. Ask questions such as “How many people took part in the survey altogether?” “How many spent under £5/ £7 etc?” “What is the mean/ median/ modal amount spent?”

Questionnaires Critique & Improve: “How many DVDs do you watch?”   State TWO criticisms: Improve this questionnaire: This data is fictional. Ask questions such as “How many people took part in the survey altogether?” “How many spent under £5/ £7 etc?” “What is the mean/ median/ modal amount spent?”

The data below represents test results for 16 students in year 11. Stem and Diagram 7 38 41 22 20 8 5 24 15 13 23 45 17 11 17 30 4 3 2 1 Leaf (units) Stem (tens) Ask questions such as “How many people took part in the survey altogether?” “How many spent under £5/ £7 etc?” “What percentage smoke more than 20 a fortnight?” as well as the averages and range. 8

Interpreting 0 5 5 7 1 1 4 8 5 3 7 4 1 2 2 2 5 7 8 3 1 4 6 7 8 2 Leaf (units) Stem (tens) Key 2 | 3 = 23 Mode Median Range

BE CAREFUL OF SCALES What can you expect…….. Plot (extra) coordinates Scatter graphs What can you expect…….. Plot (extra) coordinates Describe the correlation Draw a line of best fit Use you line of best fit to estimate values BE CAREFUL OF SCALES

Scales Plot (10, 1000) (3, 500) (8, 600) (11, 750)

Describe the Correlation 40 45 50 55 60 140 150 160 170 180 190 Height (cm) Weight (kg) 50 55 60 65 70 75 80 85 20 40 100 120 Number of cigarettes smoked in a week Life expectancy

Correlation Decide whether each of the following graphs shows, A B positive correlation negative correlation zero correlation D C E F

This graph shows the relationship between student’s results in a non-calculator and a calculator paper If a student scored 74 in the Calculator paper, what would be a good estimate for their non calculator paper? 50 55 60 65 70 75 80 85 20 40 100 Non calculator paper Calculator paper Pupils would benefit from a print out of the graph. The approximate equation of the line is y = –0.21x + 73. Note that the gradient is roughly (73 – 52) /100 not 73/100.

The table shows this information for two more Saturdays. Maximum outside temperature (C) 15 24 Number of People 260 80 Plot this information on the scatter graph. What type of correlation does this scatter graph show? Draw a line of best fit on the scatter graph. The weather forecast for next Saturday gives a maximum temperature of 17. Estimate the number of people who will visit the softball playground. On another Saturday, 350 people were recorded to have visited the playground. Estimate the maximum outside temperature on that day.

This data is fictional. However, some research does suggest links between smoking and a number of fatal diseases such as cancer. For further details, see the ASH website (www.ash.co.uk).

Frequency Polygons Plot the MID POINT with the frequency Join points with a ruler. Modal Class

You Try 60 students take a science test. The test is marked out of 50. This table shows information about the students’ marks Science Mark 0<m≤10 10<m≤20 20<m≤30 30<m≤40 40<m≤50 Frequency 4 13 17 19 7 What is the modal class? Draw a frequency polygon to represent this information

Session 2 - Algebra Simplifying Substitution Expanding Brackets Rules of Indices

Collecting together like terms Simplify these expressions by collecting together like terms. 1) a + a + a + a + a 2) 4r + 6r 3) 5a x 4b 4) 4c + 3d – 2c + d 5) 4x x 3x Whenever possible make comparisons to arithmetic by substituting actual values for the letters. If it is true using numbers then it is true using letters. For example, in 1) we could say that 7 + 7 + 7 + 7 + 7 is equivalent to 5 × 7. For example 1) and example 2), remind pupils that in algebra we don’t need to write the number 1 before a letter to multiply it by 1. 1a is just written as a and 1b is just written as b. For example 3), explain that when there are lots of terms we can write like terms next to each other so that they are easier to collect together. The numbers without any letters are added together separately. In example 4) emphasize that n² is different from n, this can be demonstrated by thinking about possible values for n, and because they are different they cannot be collected together. 4n – 3n is n and n² stays as it is. If we can’t collect together any like terms, as in example 5), we write ‘cannot be simplified’. 6) r x r x r x r

3 x 4 = -3 x -4 = -3 x 4 = 3 x -4 = 20 +– 6 = 20 - - 6 = -20 - + 6 = Rules of Negatives Multiplying/Dividing Same sign + Positive Different sign – Negative 3 x 4 = -3 x -4 = -3 x 4 = 3 x -4 = Adding/Subtracting Look at “touching” signs Same sign + Positive Different sign – Negative 20 +– 6 = 20 - - 6 = -20 - + 6 = Start by asking pupils to simplify x + x + x + x + x. This is 5 lots of x, which is written as 5x. Next ask pupils how we could simplify x × x × x × x × x. Make sure there is no confusion between this repeated multiplication and the previous example of repeated addition. If x is equal to 2, for example, x + x + x + x + x equals 10, while x × x × x × x × x equals 32. Some pupils may suggest writing xxxxx. While this is not incorrect, neither has it moved us on very far. Point out the problems of readability, especially with high powers. When we write a number or term to the power of another number it is called index notation. The power, or index (plural indices), is the superscript number, in this case 5. The number or letter that we are multiplying successive times, in this case, x, is called the base. Practice the relevant vocabulary: x2 is read as ‘x squared’ or ‘x to the power of 2’; x3 is read as ‘x cubed’ or ‘x to the power of 3’; x4 is read as ‘x to the power of 4’.

5c 3x 4c + 5a c – x 5a + 2x 3c2 x2 a = 3, c = 2, x = -4 Substitution Example Practice: 4a + 3b 5c 3x 4c + 5a c – x 5a + 2x 3c2 x2 a = 5 b = -2 Start by asking pupils to simplify x + x + x + x + x. This is 5 lots of x, which is written as 5x. Next ask pupils how we could simplify x × x × x × x × x. Make sure there is no confusion between this repeated multiplication and the previous example of repeated addition. If x is equal to 2, for example, x + x + x + x + x equals 10, while x × x × x × x × x equals 32. Some pupils may suggest writing xxxxx. While this is not incorrect, neither has it moved us on very far. Point out the problems of readability, especially with high powers. When we write a number or term to the power of another number it is called index notation. The power, or index (plural indices), is the superscript number, in this case 5. The number or letter that we are multiplying successive times, in this case, x, is called the base. Practice the relevant vocabulary: x2 is read as ‘x squared’ or ‘x to the power of 2’; x3 is read as ‘x cubed’ or ‘x to the power of 3’; x4 is read as ‘x to the power of 4’.

Plotting graphs of linear functions y = 2x + 5 x y = 2x + 5 –3 –2 –1 1 2 3 1) Complete the table and plot the points y 2) Draw a line through the points 3) Use you graph to estimate: (i) y when x = - 1.5 (ii) x when y = 8 This slide summarizes the steps required to plot a graph using a table of values. 3 2 1 1 2 3 x

Use your graph to estimate the value of y = 2x + 2 Use your graph to estimate the value of y when x = -1.5

Linear Graphs – NO Table Given – Make one On the grid draw the graph of x + y = 4 for values of x from -2 to 5 Explain that when we construct a table of values, the value of y depends on the value of x. That means that we choose the values for x and substitute them into the equation to get the corresponding value for y. The minimum number of points needed to draw a straight line is two, however, it is best to plot several extra points to ensure that no mistakes have been made. The points given by the table can then be plotted to give the graph of the required function.

3(x + 5) 12(2x – 3) 4x(x + 1) 5a(4 – 7a) Expanding Brackets Look at this algebraic expression: 3(4x – 2) To expand or multiply out this expression we multiply every term inside the bracket by the term outside the bracket. 3(4x – 2) = 3(x + 5) 12(2x – 3) 4x(x + 1) 5a(4 – 7a) The lines shown in orange show which terms we are multiplying together.

Expanding Brackets and Simplifying Expand and simplify: 2(3n – 4) + 3(3n + 5) Expand and simplify: 3(3b + 2) - 3(2b - 5) In this example, we have two sets of brackets. The first set is multiplied by 2 and the second set is multiplied by 3. We don’t need to use a grid as long as we remember to multiply every term inside the bracket by every term outside it. Talk through the multiplication of (3n – 4) by 2 and (3n + 5) by 3. Let’s write the like terms next to each other. When we collect the like terms together we have 6n + 9n which is 15n and –8 + 15 = 7.

Expanding DOUBLE brackets (x + 4)(x + 2) x 4 2

Expanding two brackets Expand these algebraic expressions: (x + 5)(x + 2) = (x + 2)(x - 3) = In this example, we need to multiply everything in the second bracket by 3 and then everything in the second bracket by t. We can write this as 3(4 – 2t) + t(4 – 2t). As pupils become more confident, they can leave this intermediate step out.

Indices a4 × a2 = 4a5 × 2a = a5 ÷ a2 = 4p6 ÷ 2p4 = (y3)2 = (q2)4 = When we multiply two terms with the same base the indices are added. a4 × a2 = 4a5 × 2a = When we divide two terms with the same base the indices are subtracted. a5 ÷ a2 = 4p6 ÷ 2p4 = When we have brackets you need to multiply the indices. Stress that the indices can only be added when the base is the same. (y3)2 = (q2)4 =

You Try a5 x a3 = a2 1) a2 x a3 = 2) m2 x m-4 = 3) 3h2 x 4h = 4) 3g-5 x 2g-3 = 5) a5 ÷ a3 = 6) m3 ÷ m = 7) 10h 2 ÷ 5h 3 = 8) 12g5 ÷ 3g-3 = a5 x a3 = You may wish to ask pupils to complete this exercise individually before talking through the answers. 9) 10) (a2)3 = a2 11) (m3)-4 = 12) (g-5)-3 =

Session 3 - Shape Transformations Pythagoras’ Theorem

There are two ways you have to answer this question: Pythagoras There are two ways you have to answer this question: (1) Finding the longest side (2) Finding a shorter side Stress that the indices can only be added when the base is the same.

Pythagoras Stress that the indices can only be added when the base is the same.

Draw and label these lines Stress that the indices can only be added when the base is the same.

Transformations Stress that the indices can only be added when the base is the same.

Find Reflections State pairs of triangles and the equation of the line Stress that the indices can only be added when the base is the same. Now reflect the black triangle in the line x = y

Translation Can describe in words: Or as a VECTOR Stress that the indices can only be added when the base is the same.

Translations Stress that the indices can only be added when the base is the same.

Rotations Rotate triangle T 90 anti-clockwise about the point (0,0). Label your new triangle U Rotate triangle T 180 about point (2,0). Label your new triangle V

Describe fully the single transformation which maps triangle Transformations Describe fully the single transformation which maps triangle T to triangle U 3 Marks = 3 THINGS

Describe fully the single transformation which maps triangle Transformations Describe fully the single transformation which maps triangle A to triangle B 3 Marks = 3 THINGS

DESCRIBING Rotations Stress that the indices can only be added when the base is the same.

Describe (3 marks)

Describe fully the single transformation which maps shape P to shape Q Enlargements Describe fully the single transformation which maps shape P to shape Q

Enlargements Describe fully the single transformation which maps triangle S to triangle T Stress that the indices can only be added when the base is the same.

Session 4 - Number BIDMAS Long Multiplication Place Value Estimating Fractions

B ( ) I x2 D ÷ M x A + S - 6 x 5 +2 6 + 5 x 2 48 ÷ (14 – 2) 2 + 32 BIDMAS 6 x 5 +2 6 + 5 x 2 48 ÷ (14 – 2) 2 + 32 6 x 4 – 3 x 5 35 – 4 x 3 B ( ) I x2 D ÷ M x A + S - Stress that the indices can only be added when the base is the same.

Long Multiplication Stress that the indices can only be added when the base is the same.

One more for you to try….. 46 x 129 =

Long Multiplication – Embedded into a word problem I buy 135 tickets costing £12 each. How much do I spend?

Using this information 46 x 129 = Calculate: 4600 x 129 = 46 x 12.9 = 460 x 1290 = 4.6 x 1290 = 4.6 x 0.129 = Stress that the indices can only be added when the base is the same.

Using this information 46 x 129 = 5934 Calculate: 5934 ÷12.9 = Estimate: Stress that the indices can only be added when the base is the same.

Using this information 97.6 x 370 = 36112 Calculate: 9.76 x 37 9760 x 3700 361.12 ÷ 97.6 Stress that the indices can only be added when the base is the same.

Rounding to ONE significant figure to 1 s. f. 4 890 351 4 890 351 6.3528 34.026 0.0007506 0.005708 150.932 Discuss each example, including the use of zero place holders and zeros that are significant figures. The numbers can be modified as required. 0.00007835

Estimate: 43 x 2.6 = (3.01 + 8.7)2.2 =

Estimate:

What if you need to divide by a decimal?

Work out an estimate for the value of 6.37 x 1.9 0.145

Multiplying Fractions 3 8 What is × ? 4 5 5 6 What is × ? 2 Point out that we could also cancel before multiplying.

Dividing Fractions 2 3 4 5 What is ÷ ? 3 5 6 7 What is ÷ ? Explain that when we are dividing by a fraction we can write an equivalent calculation by swapping the numerator and the denominator around (turning the fraction upside-down) and multiplying. This works because when we multiply by a fraction we multiply by the numerator and divide by the denominator. Multiplying by a fraction is straight forward because we simply multiply the numerators together and multiply the denominators together.

Adding and Subtracting Fractions What is + 1 2 3 ? What is 3 5 + 4 ? Stress that the indices can only be added when the base is the same.

Fractions Stress that the indices can only be added when the base is the same.

Where to start with topics……. How to score HIGH marks Where to start with topics……. 2nd March NON Calculator Estimating (round to 1 significant figure) Place Value Solving Linear Equations Long Multiplication and Division Fractions Operations (+, - , x, ÷) Indices Substitution Transformations (doing and describing) Expanding Brackets and factorising Angles (parallel lines, special triangles) Simple percentage increase/decrease Plans and Elevations (& planes of symmetry) Writing and using formulae Questionnaires 5th March CALCULATOR Trial and Improvement Use your calculator to work out…… Rounding - decimal places and sig figs Area and circumference of a circle Volume and surface area of cylinders Pythagoras’ Theorem Currency Conversions

How to score HIGH marks What should be my strategy in the exam hall for MATHS? Depends if you are higher or foundation If you are entered for higher – it is worth revising some “easy” B grade topics Tree Diagrams Cumulative Frequency Basic Circle Theorems Right – angle Triangle Trigonometry Standard Form

How to score HIGH marks If the question asks you to calculate: AREA – immediately write ……… on the answer line VOLUME – immediately write …… on the answer line Factorise “fully” – clue that there is more than one factor e.g. Factorise fully 8x + 12x2 Trial and Improvement - Once you have the this situation…. X 2.7 ----- Too small 2.8 ----- Too big

Circles x 9.72 = 295.5924528

Pythagoras 82 + 112 = 64 +121 = 185 √185 = 13.60147051

1.962631579 Write down all the figures on your calculator display. Use your calculator to work out the value of Write down all the figures on your calculator display. .......................... (2) (b) Write your answer to part (a) to 3 decimal places ..........................(1) (Total 3 marks) 1.962631579