For use with the Edexcel 2010 Mathematics B Foundation Specification Unit 1 Unit 2 Unit 3 Random © DBr 2011

Unit 1 Statistics Number Probability Algebra Random Geometry and Measures Probability Algebra Random © DBr 2011

Unit 1: Statistics SP a Understand and use statistical problem solving processes/Handling data cycle SP b Identify possible sources of bias SP d Design data collection sheets distinguishing between different types of data SP c Design and experiment or survey SP e Extract data from printed tables and lists SP f Design and use two way tables for discrete and grouped data SP g Produce charts and diagrams for various data types SP h Calculate mean, median, mode, range and modal class SP i Interpret a wide range of graphs and diagrams to draw conclusions SP j Look at data to find patterns and exceptions SP k Recognise correlation and draw and use lines of best fit SP l Compare distributions and make inferences SP u Use calculators efficiently and effectively – including statistical functions © DBr 2011

Unit 1: Number N a Add, Subtract, Multiply and Divide any number N h Understand equivalent fractions and simplifying a fraction N j Use decimal notation and recognise that each terminating decimal is a fraction N l Understand that percentage means per 100 and use this in proportion calculations N m Use percentage N o Interpret fractions, decimals and percentages as operators N p Use ratio notation, including simplifying and its various links to fraction notation N q Understand and use a number of operations and the relationships between them N t Divide a quantity by a given ration N u Approximate to a specified or appropriate degree of accuracy N v Use calculators effectively and efficiently © DBr 2011

Unit 1: Geometry and Measures GM a Recall and use properties of angles at a point GM o Interpret scales on a range of measuring instruments and recognise the inaccuracy of measurements GM p Convert measurements from one unit to another GM q Make sensible estimates of a range of measurements GM t Measure and draw lines and angles © DBr 2011

Unit 1: Probability SP m Understand and use the vocabulary of probability and the probability scale SP n Understand and use estimates or measures of probability from theoretical models or from relative frequency SP o List all outcomes for single events, and for two successive events in a systematic way and derive relative probabilities SP p Identify different mutually exclusive outcomes and know that the sum of these probabilities is 1 SP s Compare experimental data and theoretical probabilities SP t Understand that if they repeat and experiment they may – and usually will – get different outcomes, and that increasing sample size generally leads to better estimates of probability. © DBr 2011 © DBr 2011

Unit 1: Algebra A a Distinguish the different roles played by letter symbols in algebra, using the correct notation A b Distinguish in meaning between the words ‘equation’, ‘formula’ and ‘expression’ A l Recognise and plot equations that correspond to straight line graphs in the coordinate plane, including finding gradients A s Discuss, plot and interpret graphs (which may be non-linear) modelling real situations © DBr 2011

Unit 2 Algebra Number Geometry Measures Random © DBr 2011

Unit 2: Algebra A a Distinguish the different roles played by letter symbols in algebra using correct notation A b Distinguish in meaning between the words ‘equations’, ‘formula’ and ‘expression’ A c Manipulate algebraic expressions by collecting like terms, multiplying a single term over a bracket and by taking out common factors A f Derive a formula, substitute numbers in to formula A i Generate terms of a sequence using term-to-term and position-to-term definitions A j Use linear expressions to describe the nth term of an arithmetic sequence A k Use the conventions for coordinates in the plane and in all 4 quadrants A l Recognise and plot equations that correspond to straight line graphs including finding gradients A r Construct linear functions from real life problems and plot their corresponding graphs A s Discuss, plot and interpret graphs (that may be non-linear) modelling real life situations © DBr 2011

Unit 2: Number N a Add, subtract, multiply and divide any number N b order rational numbers N c Use the concepts of factor, multiple, HCF, LCM, prime and prime factor N d Use the terms square, square root (+ and - ), cube and cube root N e Use index notation for squares, cubes and powers of 10 N f Use index laws for multiplication and division of integer powers N h Understand equivalent fractions and simplifying a fraction N i Add and subtract fractions N j Use decimal notation and recognise that each terminating decimal is a fraction N k Recognise that recurring decimals are exact fractions, and visa versa NEXT PAGE © DBr 2011

Unit 2: Number N l Understand that percentage means per 100 and use to compare proportions N o Interpret fractions, decimals and percentages as operators N p Use ratio notation, including simplifying and its various links to fraction notation N q Understand and use a number of operations and the relationships between them N t Divide a quantity in a given ration N u Approximate to a specified or appropriate degree of accuracy PREVIOUS PAGE © DBr 2011

Unit 2: Geometry GM a Recall and use properties of angles at a point, angles on a straight line, perpendicular lines and opposite angles at a vertex GM b Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals GM d Recall the properties and definitions of special types of quadrilateral, parallelogram, trapezium, kite and rhombus GM e Recognise reflection and rotation symmetry of 2D shapes GM f Understand congruence and similarity GM i Distinguish between centre, radius, chord, diameter, circumference, tangent, arc, sector and segment GM k Use 2D representations of 3D shapes GM x Calculate perimeters and areas of shapes made from triangles and rectangles GM aa Calculate volumes of right prisms and shapes made from cubes and cuboids © DBr 2011

Unit 2: Measures GM o Interpret scales on a range of measuring instruments and recognise the inaccuracy of measurements GM p Convert measurements from one unit to another GM q Make sensible estimates of a range of measures GM s Understand and use compound measures GM t Measure and draw lines and angles © DBr 2011

Unit 3 Algebra Number Geometry Measures Random © DBr 2011

Unit 3: Algebra A c Manipulate algebraic expressions by collecting like terms, by multiplying over a single bracket and by taking out common factors A d Set up and solve simple equations A f Derive a formula, substitute numbers in to a formula and change the subject of a formula A g Solve linear equations in one variable, and represent the solution on a number line A h Use systematic trial and improvement to find approximate solutions of equations where there is no simple analytical method of solving them A k Use the conventions for coordinates in the plane and plot points in all four quadrants A s Discuss, plot and interpret graphs (which may be non-linear) modelling real situations A t Generate points and plot graphs of simple quadratic functions, and use these to find approximate solutions © DBr 2011

Unit 3: Number N a Add, Subtract, Multiply and Divide any number N m Use percentage N o Interpret fractions, decimals and percentages as operators N l Understand that percentage means per 100 and use this in proportion calculations N q Understand and use a number of operations and the relationships between them N v Use calculators effectively and efficiently © DBr 2011

Unit 3: Geometry GM c Calculate and use the sums of interior and exterior angles in polygons GM f Understand congruence and similarity GM g Use Pythagoras’ theorem in 2D GM k Use 2D representations of 3D shapes GM l Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that are preserved under particular transformations GM v Use straight edge and a pair of compasses to do constructions GM w Construct Loci GM z Find circumferences and areas of circles GM aa Calculate volumes of right prisms and shapes made from cubes and cuboids © DBr 2011

Unit 3: Measures GM m Use and interpret maps and scale drawings GM n Understand the effect of enlargement for perimeter, area and volume of shapes GM p Convert measurements from one unit to another GM r Understand and use bearings GM u Draw triangles and other 2D shapes using a ruler and protractor © DBr 2011

SP a Understand and use statistical problem solving processes/Handling data Cycle Maria is playing a game with two fair dice. Dice A has six faces numbered 5 to 10. Dice B has four faces numbered 1 to 4. She throws the two dice. She subtracts the number on dice B from the number on dice A to get her score. (a)Complete the table below to show all her possible scores. Three have been done for you. [2] (b) What is the probability that her score is (i) 9, ....................................... [1] (ii) a factor of 14? ....................................... [2]   © DBr 2011

SP b Identify possible sources of bias © DBr 2011

SP c Design an experiment or survey © DBr 2011

SP d Design data collection sheets distinguishing between different types of data Some pupils wanted to find out how pupils in certain year groups got to school. Design a questionnaire to find this out. [4] © DBr 2011

SP e Extract data from printed tables and lists [2] © DBr 2011

SP f Design and use two way tables for discrete and grouped data © DBr 2011

SP g Produce charts and diagrams for various data types Bar Chart Pie Chart Stem and Leaf Pictogram © DBr 2011

SP g Produce charts and diagrams for various data types Bar Chart Pie Chart Stem and Leaf Pictogram [3] © DBr 2011

SP g Produce charts and diagrams for various data types Bar Chart Pie Chart Stem and Leaf Pictogram [2] © DBr 2011

SP g Produce charts and diagrams for various data types Bar Chart Pie Chart Stem and Leaf Pictogram [2] © DBr 2011

SP h Calculate mean, median, mode, range and modal class © DBr 2011

SP i Interpret a wide range of graphs and diagrams to draw conclusions © DBr 2011

SP j Look at data to find patterns and exceptions (b)Describe the correlation shown on the scatter diagram. .......................................................................................................[1] (c)(i)Draw a line of best fit on the diagram.[1] (ii)Lorenzo scored 48% on Paper 1, but was absent for Paper 2. Use your line of best fit to estimate his percentage on Paper 2. . ...........................% [1] (d)Rosie scored 72% in a test. Francine scored 52 out of 75 marks in the same test. Who did better in the test? Give a reason for your answer. ............................. because .............................................................…. ............................................................................................................. [2] © DBr 2011

SP k Recognise correlation and draw and use lines of best fit (b) What does the diagram show about the relationship between thumb and wrist measurements?............................................................................................................................................................................................................................ (c) Show this relationship on the graph. [2] [1] © DBr 2011

SP l Compare distributions and make inferences © DBr 2011

SP m Understand and use the vocabulary of probability and the probability scale © DBr 2011

SP n Understand and use estimates or measures of probability from theoretical models or from relative frequency © DBr 2011

SP o List all outcomes for single events, and for two successive events in a systematic way and derive relative probabilities © DBr 2011

SP p Identify different mutually exclusive outcomes and know that the sum of these probabilities is 1 © DBr 2011

SP s Compare experimental data and theoretical probabilities © DBr 2011

SP t Understand that if they repeat and experiment the may – and usually will – get different outcomes, and that increasing sample size generally leads to better estimates of probability John was conducting an experiment to see if a dice was fair. He knows that if it is fair, the probability of rolling a number is John rolled the dice 6 times. Below are his results. Number Frequency 1 2 2 1 3 0 4 0 5 1 6 2 John concluded that his dice was not fair. Is John’s conclusion correct? Explain your answer 1 6 © DBr 2011

SP u Use calculators efficiently and effectively – including statistical functions © DBr 2011

N a Add, subtract, multiply and divide any number © DBr 2011

N b Order rational numbers © DBr 2011

N c Use the concepts of factor, multiple, HCF, LCM, prime and prime factor © DBr 2011

N d Use the term square, square root (+ and -), cube and cube root © DBr 2011

N e Use index notation for squares, cubes and powers of 10 Fill in the missing gaps (a) 7 = 49 (b) √121 = (c) 3√ 8 = (d) 3 = 27 [1] [1] [1] [1] © DBr 2011

N f Use index laws for multiplication and division of integer powers © DBr 2011

N h Understand equivalent fractions and simplifying a fraction © DBr 2011

N i Add and Subtract fractions © DBr 2011

N j Use decimal notation and recognise that each terminating decimal is a fractions © DBr 2011

N k Recognise that recurring decimals are exact fractions and visa versa . . Change 0.42 in to a fraction. You should write your answer in its simplest form [3] © DBr 2011

N l Understand that percentage means per 100 and use this in proportion calculations © DBr 2011

N m Use percentage © DBr 2011

N o Interpret fractions, decimals and percentages as operations © DBr 2011

N p Use ratio notation, including simplifying and its various links to fraction notation A piece of wood 240cm long is to be split in to the ratio 3:5:8. What fraction of the whole piece of wood will be the smallest? [3] © DBr 2011

N q Understand and use a number of operations and the relationships between them [2] [2] © DBr 2011

N t Divide a quantity by a given ratio © DBr 2011

N u Approximate to a specified or appropriate degree of accuracy © DBr 2011

N v Use calculators efficiently and effectively © DBr 2011

GM a Recall and use properties of angles at a point © DBr 2011

GM b Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals Q1 Q2 Q3 © DBr 2011

GM b Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals Q1 Q2 Q3 © DBr 2011

GM b Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals Q1 Q2 Q3 © DBr 2011

GM c Calculate and use the sums of interior and exterior angles in polygons © DBr 2011

GM d Recall the properties and definitions of special types of quadrilateral, parallelogram, trapezium, kite and rhombus © DBr 2011

GM e Recognise reflection and rotation symmetry of 2D shapes © DBr 2011

GM f Understand congruence and similarity © DBr 2011

GM g Use Pythagoras’ theorem in 2D © DBr 2011

GM i Distinguish between centre, radius, chord, diameter, circumference, tangent, arc, sector and segment You should show all of your answers on the diagram Draw and label a radius Draw and label a diameter Draw and label a chord Draw and label a sector x C © DBr 2011

GM k Use 2D representations of 3D shapes Nets Plans © DBr 2011

GM k Use 2D representations of 3D shapes Nets Plans © DBr 2011

GM l Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that are preserved under particular transformations Q1 Q2 Q3 Q4 © DBr 2011

GM l Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that are preserved under particular transformations Q1 Q2 Q3 Q4 © DBr 2011

GM l Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that are preserved under particular transformations Q1 Q2 Q3 Q4 © DBr 2011

GM l Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that are preserved under particular transformations Q1 Q2 Q3 Q4 © DBr 2011

GM m Use and interpret maps and scale drawings Scale: 2cm to 1km © DBr 2011

GM n Understand the effect of enlargement for perimeter, area and volume of shapes Enlarge the shape ABCD with centre O and scale factor 3. The perimeter of ABCD is 11×21 cm to 2 decimal places. Without measuring, write down the perimeter of the enlarged shape. .................................... cm [1] © DBr 2011

GM o Interpret scales on a range of measuring instruments and recognise the inaccuracy of measurements Then I weigh an apple and a melon © DBr 2011

GM p Convert measurements from one unit to another © DBr 2011

GM q Make sensible estimates of a range of measurements © DBr 2011

GM r Understand and use bearings © DBr 2011

GM s Understand and use compound measures © DBr 2011

GM t Measure and draw lines and angles © DBr 2011

GM u Draw triangles and other 2D shapes using a ruler and protractor © DBr 2011

GM v Use straight edge and a pair of compasses to do constructions © DBr 2011

GM w Construct Loci Q1 Q2 © DBr 2011

GM w Construct Loci Q1 Q2 © DBr 2011

GM x Calculate perimeters and areas of shapes made from triangles and rectangles © DBr 2011

GM z Find circumferences and areas of circles © DBr 2011

GM aa Calculate volumes of right prisms and shapes made from cubes and cuboids © DBr 2011

A a Distinguish the different roles played by letter symbols in algebra, using the correct notation © DBr 2011

A b Distinguish in meaning between the words ‘equation’, ‘formula’ and ‘expression’ Put a tick in the correct box © DBr 2011

A c Manipulate algebraic expressions by collecting like terms, multiplying a single term over a bracket and by taking out common factors © DBr 2011

A d Set up and solve simple linear equations © DBr 2011

A f Derive a formula, substitute numbers in to formula © DBr 2011

A g Solve linear equations in one variable, and represent the solution on a number line © DBr 2011

A h Use systematic trial and improvement to find approximate solutions of equations where there is no simple analytical method of solving them © DBr 2011

A i Generate terms of a sequence using term-to-term and position-to-term definitions © DBr 2011

A j Use linear expressions to describe the nth term of an arithmetic sequence © DBr 2011

A k Use the conventions for coordinates in the plane and in all 4 quadrants Write down the coordinates of the point A. (............... , ...............) [1] Plot the point (1, –6) and label it C. [1]   ABCD is a rectangle. Plot point D. Write down the coordinates of D. (............... , . ..............) [2] © DBr 2011

A l Recognise and plot equations that correspond to straight line graphs in the coordinate plane, including finding gradients © DBr 2011

A r Construct linear functions from real life problems and plot their corresponding graphs © DBr 2011

A s Discuss, plot and interpret graphs (which may be non-linear) modelling real situations © DBr 2011

A t Generate points and plot graphs of simple quadratic functions, and use these to find approximate solutions (b)Use your graph to find approximate solutions to the equation x2 – 2 = 2 .................. and .................. [2] © DBr 2011