# HYC GCSE Foundation

**Y9F Unit 1a – Integers and place value - Mathswatch**

Use and order positive and negative numbers. - 2

Order integers and decimals using the symbols < and >. - 5

Add and subtract positive and negative integers. - 17, 18

Recall all multiplication facts to 10×10 and derive corresponding division facts. - 18

Multiply or divide any number by powers of 10. - 30

Multiply and divide negative numbers. - 68b

Recall and apply BIDMAS (not including powers). - 75

Round numbers to a given power of 10. - 31

**Y9F Unit 1b – Decimals**

Use decimal notation and place value. - 1

Identify the value of digits in a decimal or whole number. - 1

Compare and order decimals using the < and > symbols. Understand the ≠ symbol. - 5

Add, subtract, multiply and divide decimals, including calculations involving money. - 17, 18, 66, 67

Multiply or divide by any number between 0 and 1. - 66

Round to the nearest integer, decimal places and significant figures. - 31, 32, 90

Estimate answers to calculations by rounding to 1SF. - 91

Use one calculation to find the answer to another. - 92

**Y9F Unit 1c – Indices, powers and roots**

Find and recall the square numbers up to 10×10 and their corresponding roots. - 81

Understand the difference between positive and negative square roots. - 81

Recall the cubes of 1, 2, 3, 4, 5 and 10. - 81

Evaluate expressions involving squares, cubes and roots (and know how to do this on a calculator). - 81

Use index notation for powers of 10 including negative powers. - 82

Use the laws of indices to multiply and divide numbers written in index form. - 131

Use BIDMAS including with powers. - 131

**Y9F Unit 1d – Factors, multiples and primes**

List all three-digit integers than can be made from three given integers. - 1

Recognise odd and even numbers. - 1

Identify factors, multiples and prime numbers. - 28

List factors and multiples systematically. - 28

Express a number as a product of prime factors in index form. - 78

Find common factors and multiples of two numbers. - 79, 80

Find the HCF and LCM of two numbers by listing, using Venn diagrams and using prime factors. - 79, 80, 127a

Solve simple problems using HCF, LCM and prime numbers. - 79, 80

**Y9F Unit 2a - Algebra: the basics**

Use notation and symbols correctly and write expressions. - 7

Identify different types of algebra. - 7

Simplify expressions by collecting like terms. - 33

Multiply two simple algebraic expressions. - 34

Simplify expressions by cancelling. - 34

Use index notation when multiplying or dividing algebraic terms - 82

Use index laws in algebra. - 131

**Y9F Unit 2b – Expanding and factorising single brackets**

Multiply a single number term over a bracket. - 93

Write and simplify expressions using squares and cubes - 33,34,35

Expand and simplify expressions involving brackets. - 93

Argue mathematically to show two expressions are equivalent.

Recognise factors of algebraic terms involving single brackets. - 94

Factorise algebraic expressions by taking out common factors. - 94

**Y9F Unit 2c - Expressions and substitution into formulae**

Write expressions to solve problems representing a situation. - 137

Substitute numbers into simple algebraic expressions - 95

Substitute numbers into expressions involving brackets and powers. - 95

Substitute positive and negative numbers into expressions. - 95

Derive a simple formula. - 137

Substitute numbers into a worded formula. - 95

Substitute numbers into a formula. - 95

**Y9F Unit 3a – Tables**

Design and use data-collection sheets for grouped, discrete and continuous data, use inequalities for grouped data, and introduce ≤ and ≥ signs. - 63

Sort, classify and tabulate data, both discrete and continuous quantitative data, and qualitative data. - 63

Construct tables for time–series data. - 153

Extract data from lists and tables.

Use correct notation for time, 12- and 24-hour clock. Work out time taken for a journey from a timetable. - 6a/b

Design and use two-way tables for discrete and grouped data. - 61

Construct and read frequency tables, including identifying the mode/modal class. - 65a,62

**Y9F Unit 3b – Charts and graphs**

Plot coordinates in the first quadrant and read graph scales in multiples. - 8

Draw and interpret pictograms and bar charts. - 16,15

Draw and interpret dual bar charts and vertical line charts. - 64

Draw and interpret line graphs including for time series data. - 153

Draw and interpret histograms with equal class intervals. - 205

Draw and interpret stem and leaf diagrams, including back-to-back. - 128b

**Y9F Unit 3c – Pie charts**

Know how many degrees there are in a full turn, half turn and quarter turn.

Measure and draw angles, to the nearest degree. - 46a

Interpret simple pie charts using simple fractions and percentages. - 128a

Construct pie charts for categorical data and discrete/ continuous numerical data. - 128a

Use a pie chart to find the mode and total frequency. - 128a,62

Understand that the frequency represented by corresponding sectors in two pie charts is dependent upon the total populations represented by each of the pie charts. - 128a

**Y9F Unit 3d – Scatter graphs**

Draw scatter graphs. - 129

Interpret points on a scatter graph and identify outliers. - 129

Draw the line of best fit on a scatter diagram by eye, and understand what it represents. - 129

Use the line of best fit make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing. - 129

Distinguish between positive, negative and no correlation using lines of best fit. Interpret correlation in terms of the problem. - 129

Understand that correlation does not imply causality. State how reliable their predictions are, i.e. not reliable if extrapolated. - 129

**Y9F Unit 4a - Fractions**

Use diagrams to find equivalent fractions or compare fractions and write fractions to describe shaded parts of diagrams. - 25

Express a given number as a fraction of another.

Write a fraction in its simplest form and find equivalent fractions. Order fractions. - 25.26

Convert between mixed numbers and improper fractions.(KS3) - N35

Add and subtract fractions, writing the answer as a mixed number where appropriate - .71

Multiply and divide a fraction by an integer and vice versa. - 73,74

Multiply and divide fractions. - 73,74

**Y9F Unit 4b – Fractions, decimals and percentages**

Convert between fractions and decimals. - 84

Recognise recurring decimals and convert fractions into recurring decimals, using correct notation. - 177

Compare and order fractions, decimals and integers, using inequality signs. - 3,73

Express a given number as a percentage of another number. - 89

Convert between fractions, decimals and percentages. - 85

Order fractions, decimals and percentages, including use of inequality signs. - 85

**Y9F Unit 4c – Percentages**

Find a percentage of a quantity using non-calculator methods. - 87

Find a percentage of a quantity using calculator methods. - 88

Calculate percentage change. - 109

Increase and decrease amounts by percentages using non-calculator methods. - 108

Use multipliers to increase and decrease amounts by percentages. - 108

**Y9F Unit 5a – Equations**

Write expressions and set up simple equations. - 137

Use function machines.

Solve simple equations.

Solve linear equations, with integer coefficients, in which the unknown appears on either side or on both sides of the equation. - 135

Solve linear equations which contain brackets, including those that have negative signs occurring anywhere in the equation, and those with a negative solution - .135

Rearrange simple equations. - 136

Substitute into a formula, and solve the resulting equation. - 95

Solve problems by setting up and solving equations, including involving angle or perimeter problems. - 137

**Y9F Unit 5b – Inequalities**

Show inequalities on number lines. - 138

Construct inequalities to represent a set shown on a number line. - 138

Write down whole number values that satisfy an inequality. - 138

Solve an inequality and show the solution set on a number line. - 139

Solve two inequalities in x, find the solution sets and compare them to see which value of x satisfies both. - 139

**Y9F Unit 5c – Sequences**

Recognise sequences of odd and even numbers, and other sequences including Fibonacci sequences. - 104,141

Write the term-to-term definition of a sequence in words.

Generate arithmetic sequences of numbers, triangular number, square and cube integers and sequences derived from diagrams. - 37

Find the next term in a sequence, including negative values. - 37

Find the nth term of a linear sequence. - 103

Use the nth term of an arithmetic sequence to generate terms. - 103

Use the nth term of an arithmetic sequence to decide if a given number is a term in the sequence or to find the first term that is less than/greater than a certain value. - 102

Continue a geometric progression and find the term-to-term rule, including negatives, fraction and decimal terms. - 163

Continue a quadratic sequence and use the nth term to generate terms. - 213

**Y10F Unit 6a – Properties of shapes, parallel lines and angle factsMathswatch**

Measure angles using a protractor. - 46a

Use correct notation to identify sides and angles. - 9, 122

Identify types of lines and special types of triangle and quadrilateral.

Recall and use the angle sum of triangles and quadrilaterals. - 121, 123

Solve angle problems involving intersecting lines.

Understand and use the angle properties of parallel lines. - 120

Calculate interior and exterior angles of triangles. - 120

**Y10F Unit 6b – Interior and exterior angles of polygons**

Recognise and name the polygons up to 10 sides. - 10

Identify regular and irregular polygons. - 10

Calculate and use the interior angle sum of polygons. - 123

Calculate and use the angles of regular polygons. - 123

Use the sum of exterior angles of a polygon. - 123

Use the sum of the interior and exterior angle. - 123

Identify shapes which are congruent. - 12b

Explain why some polygons fit together and some do not - .12a

**Y10F Unit 7a – Statistics and sampling**

Plan an investigation, deciding what data to collect and how to analyse it. Understand how sources of data may be biased.

Recognise types of data: primary secondary, quantitative and qualitative. - 63

Identify which primary data they need to collect and in what format, including grouped data.

Explain why a sample may not be representative of a whole population. - 152

**Y10F Unit 7b – The averages**

Calculate the mean, mode, median and range for discrete data. - 62

Interpret and find the median, mean and range from a (discrete) frequency table. - 130a

Interpret and find the range, modal class, interval containing the median, and estimate of the mean from a grouped data frequency table. - 130b

Interpret and find the mode, mean and range from a bar chart, the median, mode and range from stem and leaf diagrams. - 62, 128b

Compare the mean, median, mode and range. - 62

Recognise the advantages and disadvantages between measures of average.

**Y10F Unit 8a – Perimeter and area**

Convert between units of measure within one system, including time. - 112

Make sensible estimates of a range of measures in everyday settings.

Measure shapes to find perimeters and areas using a range of scales.

Find the perimeter of rectangles, triangles, parallelograms, trapezia and compound shapes. - 52

Recall and use the formula for the area of rectangles and triangles. - 53, 54

Recall and use the formula for the area of a trapezium and parallelogram. - 55, 56

Find the surface area of a prism. - 114

Convert between metric area measures. - 112

**Y10F Unit 8b – 3D forms and volume**

Identify and name common solids. - 43

Sketch nets of cuboids and prisms. - 44

Recall and use the formula for the volume of a prism. - 115, 119

Convert between metric units of volume (and capacity). - 112

**Y10F Unit 9a – Real-life graphs**

Use input/output diagrams. - 36

Use co-ordinates in all four quadrants. - 8

Find the co-ordinates of the midpoint of a line segment. - 133

Draw and interpret straight line graphs representing real-life situations. - 96

Draw distance-time graphs and velocity-time graphs. - 143

Calculate speed for a section of a distance-time graph. - 142, 143

**Y10F Unit 9b – Straight line graphs**

Draw and recognise graphs of y=a, x=a, y=x and y=-x. - 96

Use a table of values to plot graphs of the form y=mx+c. - 96

Sketch the graph of a linear function directly from the gradient and y-intercept. - 97

Identify parallel lines from their equations. - 97

Draw graphs of the form ax+by=c. - 96

Find the equation of a straight line. - 159a

Find the equation of the line through one point with a given gradient. - 159b

**Y10F Unit 10a – Transformations 1: rotations and translations**

Describe rotations. Accurately rotate shapes - 49

Accurately rotate shapes. - 49

Understand how vectors work. Translate a given shape by a vector. - 50

Describe translations. - 50

**Y10F Unit 10b – Transformations 2: reflections and enlargements**

Describe reflections including stating the equation of the line of reflection. - 48

Reflect shapes in horizontal and vertical lines. - 48

Reflect shapes in diagonal lines. - 48

Describe and perform enlargements using a positive integer scale factor. - 148

Describe and perform enlargements using a positive fractional scale factor. - 148

**Y10F Unit 11a – Ratio**

Write ratios in their simplest form. - 38

Share a quantity in a given ratio. - 106

Solve ratio problems in context. - 106

Compare ratios, including writing them in the form 1:n and n:1. - 38

Write a ratio as a fraction or linear function. - 107

Write lengths, areas and volumes of two shapes as ratios in simplest form. - 200

**Y10F Unit 11b – Proportion**

Solve word problems involving direct and inverse proportion. - 42

Work out which product is best value. - 41

Solve proportion problems involving recipes. - 39

Convert between currencies. - 105

Solve proportion problems using the unitary method. - 106

Identify values that are in direct and inverse proportion including from graphs. - 107

**Y10F Unit 12 – Pythagoras and trigonometry**

Recall and apply Pythagoras’ Theorem to calculate the length of the hypotenuse, including in applied problems. - 150

Recall and apply Pythagoras’ Theorem to calculate the length a shorter side, including in applied problems. - 150

Use Pythagoras’ Theorem to justify if a triangle is right angled or not. - 150

Recall the trigonometric ratios sin, cos and tan and apply them to calculate sides in right angled triangles. - 168

Recall the trigonometric ratios sin, cos and tan and apply them to calculate angles in right angled triangles. - 168

Use trigonometry to solve applied problems in 2D. - 168

Know exact trigonometric values. - 173

**Y10F Unit 13a – Probability 1**

Use the language of probability and position events on the probability scale. - 14

Find theoretical probabilities and express them as fractions, decimals or percentages. - 59

Work out probabilities from frequency tables and two-way tables. - 61

Identify mutually exclusive events and know that the sum of the probabilities of all outcomes is 1. - 60

Use 1 – p as the probability of an event not occurring where p is the probability of the event occurring. - 60

**Y10F Unit 13b – Probability 2**

Find the probability of an event happening using relative frequency. - 125

Estimate the number of times an event will occur, given the probability and the number of trials – for both experimental and theoretical probabilities.

List all outcomes for combined events systematically. - 58, 126

Work out probabilities from Venn diagrams including using union and intersection. - 127, 185

Use tree diagrams to calculate the probability of two independent events. - 151

Use tree diagrams to calculate the probability of two dependent events. - 151

**Y10F Unit 14 – Multiplicative reasoning**

Understand and use speed. - 142

Understand and use density. - 142

Understand and use pressure. - 142

Calculate percentage profit or loss. - 87, 109

Make calculations involving repeated percentage change. - 109

Calculate compound interest. - 164

Solve reverse percentage problems. - 110

**Y11F Unit 15a – Plans and elevationsMathswatch**

Measure and draw lines, to the nearest mm and measure and draw angles to the nearest degree. - 46a/b

Know and use compass directions.

Draw sketches of 3D solids. - 43

Know and use the terms face, edge and vertex (vertices). - 43

Identify and sketch planes of symmetry of 3D solids. - 11

Draw plans and elevations of 3D shapes. - 51

Given the plans and elevations, sketch the 3D solid. - 51

**Y11F Unit 15b – Construction, loci and bearings**

Visually identify shapes which are congruent. - 12b

Use bearings to specify direction. - 124

Use a ruler and compass to construct perpendicular bisectors (including from a point), angle bisectors and angles of 90° and 45°.146a/b, - 145

Draw and construct diagrams from given instructions to show a region bounded by a circle and a line, a given distance from a point/line, equal distances from 2 points/lines. - 165

Use constructions to solve loci problems. - 165

Draw and use accurate scale diagrams. - 38

Solve problems involving bearings. - 124

**Y11F Unit 16a – Quadratic equations: expanding and factorising**

Define a quadratic expression.

Expand double brackets. - 134b

Square a linear expression. - 134b

Factorise quadratics of the form x2+bx+c. - 157

Factorise quadratics of the form x2-a2 using the difference of two squares. - 158

Solve quadratic equations by factorising. - 157

**Y11F Unit 16b – Quadratic equations: graphs**

Generate points and plot graphs of simple quadratic functions. - 98

Generate points and plot graphs of more general quadratic functions. - 98

Identify the line of symmetry of a quadratic graph. - 96

Find approximate solutions to quadratic equations using a graph. - 160

Interpret graphs of quadratic functions from real-life problems - .160

Identify and interpret roots, intercepts and turning points of quadratic graphs. - 160

**Y11F Unit 17 – Perimeter, area and volume 2**

Identify and name parts of a circle. - 116

Recall and use the formulae for area and circumference of circles. Give answers in terms of π - 117, 118

Find the radius or diameter when given the area or circumference of a circle. - 117, 118

Calculate the perimeter or area of composite shapes made from parts of circles. - 17, 118

Calculate arc length and sector area - 149

Calculate the volume and surface area of a cylinder. - 119, 114b

Calculate the surface area and volume of spheres, cones and pyramids. - 169, 170, 171

**Y11F Unit 18a – Fractions**

Add and subtract mixed number fractions. - 71a

Multiply mixed number fractions. - 73

Divide mixed numbers by whole numbers and vice versa.7 - 4

Find the reciprocal of an integer, decimal or fraction. Understand ‘reciprocal’ as multiplicative inverse, knowing that any non-zero number multiplied by its reciprocal is 1. - 76

**Y11F Unit 18b – Indices and standard form**

Use index laws to simplify and calculate the value of numerical expressions involving multiplication and division of integer powers, fractions and powers of a power. - 82

Use numbers raised to the power of zero. - 82

Convert large and small numbers into standard form. - 83

Convert large and small numbers out of standard form. - 83

Add and subtract numbers in standard form. - 83

Multiply and divide numbers in standard form. - 83

**Y11F Unit 19a – Similarity and congruence in 2D**

Use the basic congruence criteria for triangles (SSS, SAS, ASA and RHS). - 166

Solve angle problems involving congruence. - 166

Identify shapes which are similar; including all circles or all regular polygons with equal number of sides. - 144

Identify the scale factor of an enlargement of a shape as the ratio of the lengths of two corresponding sides. - 144, 48

Solve problems to find missing lengths in similar shapes. - 144

Know that scale diagrams, including bearings and maps are ‘similar’ to the real-life examples. - 38, 144

**Y11F Unit 19b – Vectors**

Understand and use column notation in relation to vectors. - 174

Be able to represent information graphically given column vectors. - 174

Identify two column vectors which are parallel. - 174

Calculate using column vectors, and represent graphically, the sum of two vectors, the difference of two vectors and a scalar multiple of a vector. - 219

**Y11F Unit 20 – Rearranging equations, graphs and simultaneous equations**

Change the subject of a formula involving the use of square roots and squares. - 136

Answer ‘show that’ questions using consecutive integers (n, n + 1), squares a2, b2, even numbers 2n, and odd numbers 2n +1.

Find the equation of the line through two given points. - 159b

Recognise, sketch and interpret graphs of simple cubic and reciprocal functions. - 161, 99

Write simultaneous equations to represent a situation. - 162

Solve simultaneous equations (linear/linear) algebraically and graphically - .162