# 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

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

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

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