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# Mathematics GCSE

A layout of all the components of a Foundation Mathematics GCSE course (based on Edexcel Linear)

by

Tweet## Oliver Offord

on 3 March 2011#### Transcript of Mathematics GCSE

Maths GCSE Statistics Shape Algebra Whole Numbers Decimals Properties of numbers Fractions Percentages Ratio & Proportion Powers & Brackets Number Coordinates Introduction to Algebra Patterns & Sequences Linear Equations Linear Graphs

Formula Quadratic Graphs Trial & Improvement Angles Drawing 2D Shapes Reading Scales Angle Properties of

Triangles & Quadrilaterals 3D Shapes Perimeter & Area Volume Angle Properties of Polygons Transformations Scale Factors Circles Compound Measures Collecting Data Charts & Graphs Small Data Sets Probability Pie Charts Time Series Scatter Graphs & Correlation Large Data Sets a. Understand and order whole numbers

b. Add, subtract, multiply and divide whole numbers

c. Add, subtract, multiply and divide negative numbers

d. Understand the meaning of BIDMAS, e.g. work out 12 5 – 24 8

e. Round whole numbers to the nearest 10, 100, 1000, …

f. Multiply and divide whole numbers by a given multiple of 10

g. Check calculations by rounding, e.g. 29 31 30 30

h. Check answers by reverse calculation, e.g. if 9 23 = 207 then 207 9 = 23 a.Put digits in the correct place in a decimal number

b.Write decimals in ascending order of size

c.Approximate decimals to a given number of decimal places or significant figures

d.Multiply and divide decimal numbers by whole numbers and decimal numbers (up to 2 decimal places), e.g. 266.22 0.34

e.Know that e.g. 13.5 0.5 = 135 5 a.Understand and use negative numbers in context, eg thermometers

b.Find: squares; cubes; square roots; cube roots of numbers, with and without a calculator (including the use of trial and improvement)

c.Understand odd and even numbers, and prime numbers

d.Find the HCF and the LCM of numbers

e.Write a number as a product of its prime factors, eg 108 = 2 2 3 3 3

f.Interpret standard index form from a calculator display a.Visualise a fraction on a diagram

b.Understand a fraction as part of a whole

c.Recognise and write fractions in everyday situations

d.Write a fraction in its simplest form and recognise equivalent fractions

e.Compare the sizes of fractions using a common denominator

f.Add and subtract fractions by using a common denominator

g.Write an improper fraction as a mixed fraction

h.Multiply and divide a number with a fraction, and a fraction with a fraction (expressing the answer in its simplest form)

i.Simplify multiplication of fractions by first cancelling common factors

j.Convert a fraction to a decimal, or a decimal to a fraction

k.Convert a fraction to a recurring decimal

l.Find the reciprocal of whole numbers, fractions, and decimals, e.g. find the reciprocal of 0.4

m.Know that 0 does not have reciprocal, and that a number multiplied by its reciprocal is 1

n.Use fractions in contextualised problems a.Understand that a percentage is a fraction in hundredths

b.Write a percentage as a decimal; or as a fraction in its simplest terms

c.Write one number as a percentage of another number

d.Calculate the percentage of a given amount

e.Find a percentage increase/decrease, of an amount

f.Calculate simple and compound interest for two, or more, periods of time

g.Calculate an index number a.Understand what is meant by ratio

b.Write a ratio in its simplest form; and find an equivalent ratio

c.Share a quantity in a given ratio

d.Understand and use examples in direct proportion

e.Interpret map/model scales as a ratio a.Multiply and divide powers of the same number

b.Understand and use the index rules to simplify algebraic expressions, e.g. 55 52 = 53

c.Use brackets to expand and simplify simple algebraic expressions

d.Solve linear equations involving a single pair of brackets a. Design a suitable question for a questionnaire

b. Understand the difference between: primary and secondary data; discrete and continuous data

c. Design suitable data capture sheets for surveys and experiments

d. Understand about bias in sampling Represent data as:

a.Bar charts (including dual bar charts)

b.Pictograms

c.Line graphs

d.Histograms (intervals with equal width)

e.Frequency polygons

f.Choose an appropriate way to display discrete, continuous and categorical data a.Find the mode or the median for (small) sets of data

b.Find the mean and the range for (small) sets of data

c.Use a stem and leaf diagram to sort data

d.Know the advantages/disadvantages of using the different measure of average a.Use the language of probability to describe the likelihood of an event

b.Represent and compare probabilities on a number scale

c.List outcomes for single mutually exclusive events and write down their probability

d.Write down the theoretical probability for an equally likely event

e.Estimate a probability by relative frequency

f.Know that a better estimate for a probability is achieved by increasing the number of trials a.Represent categorical data in a pie chart

b.Interpret categorical data in a pie chart a.Represent data as a time series

b.Identify trends in data over time

c.Identify exceptional periods by comparison with similar previous periods a.Draw and produce a scatter graph

b.Appreciate that correlation is a measure of the strength of association between two variables

c.Distinguish between positive, negative and zero correlation using a line of best fit

d.Appreciate that zero correlation does not necessarily imply ‘no correlation’ but merely ‘no linear relationship’

e.Draw lines of best fit by eye and understand what it represents

f.Find the equation of the line of best and use it to interpolate/extrapolate a.Identify the modal class interval in grouped and ungrouped frequency distributions

b.Find the class interval containing the median value

c.Find the mean of an ungrouped frequency distribution

d.Find an estimate for the mean of a grouped frequency distribution by using the mid-interval value

e.Use the statistical functions on a calculator or a spreadsheet to calculate the mean for discrete data a. Plot and read coordinates on a coordinate grid (in all four quadrants)

b. Understand that one coordinate identifies a point on a line, two coordinates identify a point in a plane and three coordinates identify a point in space, and use the terms ‘1-D’, ‘2-D’ and ‘3-D’

c. Find the coordinates of the fourth vertex of a parallelogram

d. Identify the coordinates of the vertex of a cuboid on a 3-D grid

e. Writing down the coordinates of the midpoint of the line connecting two points

f. Calculate the length of the line segment joining two points in the plane (all four quadrants)

a.Simplify algebraic expressions in one, or more like terms, by adding and subtracting

b.Multiply and divide with letters and numbers a.Find the missing numbers in a number pattern or sequence

b.Find the nth term of a number sequence

c.Find whether a number is part of a given sequence

d.Use a calculator to produce a sequence of numbers a.Solve linear equations with one, or more, operations

b.Solve linear equations involving a single pair of brackets

c.Solve linear inequalities in one variable and present the solution set on a number line a.Draw linear graphs from tabulated data, including real-world examples

b.Interpret linear graphs, including conversion graphs and distance-time graphs

c.Understand the difference between a line and a line segment

d.Draw and interpret graphs in the form y = mx + c (when values for m and c are given)

e.Understand that lines are parallel when they have the same value of m

f.Solve graphically simultaneous equations, e.g. find when/where the car overtakes the bus a.Use letters or words to state the relationship between different quantities

b.Substitute positive and negative numbers into simple algebraic formulae

c.Substitute positive and negative numbers into algebraic formulae involving powers

d.Find the solution to a problem by writing an equation and solving it

e.Change the subject of a formula, e.g. change the formula for converting Centigrade into Fahrenheit into a formula that converts Fahrenheit into Centigrade a.Substitute values of x into a quadratic function to find the corresponding values of y

b.Draw graphs of quadratic functions such as y=x2+2

c.Draw graphs of quadratic functions such as y=2x2-6x+5

d.Use quadratic graphs to solve quadratic equations

e.Expand and simplify expressions with two pairs of brackets a.Solve cubic functions by successive substitution of values of x a. Distinguish between acute, obtuse, reflex and right angles

b. Estimate the size of an angle in degrees

c. Measure and draw angle to the nearest degree

d. Use angle properties on a line and at a point to calculate unknown angles

e. Measure a bearing (acute and obtuse)

f. Measure a bearing (reflex)

g. Calculate bearings

a.Use a ruler and compass to draw accurate triangles, and other 2-D shapes, given information about their side lengths and angles.

b.Use straight edge and compass to construct: an equilateral triangle; the midpoint and perpendicular bisector of a line segment; the bisector of an angle

c.Find the locus of points e.g. the locus of points equidistant to two given points

d.Understand, by their experience of constructing them, that triangles satisfying SSS, SAS, ASA and RHS are unique, but SSA triangles are not

e.Recall and use angle properties of equilateral, isosceles and right-angled triangles

f.Recall and use the properties of squares, rectangles, parallelograms, trapeziums and rhombuses

g.Recall and use properties of circles

h.Appreciate why some shapes tessellate and why some shapes do not tessellate a.Make estimates of: length; volume and capacity; weights

b.Make approximate conversions between metric and imperial units

c.Decide on the appropriate units to use in real life problems

d.Read measurements from instruments: scales; analogue and digital clocks; thermometers, etc

e.Do calculations involving time, including the use of time tables and calendars a.Mark parallel lines in a diagram

b.Use angle properties of triangles and quadrilaterals to find missing angles

c.Prove that the angle sum of a triangle is 180 degrees

d.Explain why the angle sum of a quadrilateral is 360 degrees

e.Find missing angles using properties of corresponding angles and alternate angles, giving reasons

f.Find the three missing angles in a parallelogram when one of them is given

g.Identify and list the properties of quadrilaterals (including kites)

h.Name all quadrilaterals that have a pair of opposite sides that are equal a.Count the vertices, faces and edges of 3-D shapes

b.Draw nets of solids and recognise solids from their nets

c.Draw and interpret plans and elevations

d.Draw planes of symmetry in 3-D shapes

e.Recognise and name examples of solids, including prisms, in the real world a.Find the perimeters and areas of shapes made up from triangles and rectangles

b.Find areas of shapes by counting squares

c.Use formulae to find the area of shapes made up of rectangles and triangles

d.Find the surface area of cuboids and prisms

e.Solve a range of problems involving areas

f.Convert between units of area a.Find volumes of shapes by counting cubes

b.Use formulae for the volume of cuboids

c.Solve a range of problems involving volume

d.Convert between units of volume a.Calculate and use the sums of the interior angles of convex polygons of sides 3, 4, 5, 6, 8, 10

b.Know, or work out, the relationship between the number of sides of a polygon and the sum of its interior angles

c.Know that the sum of the exterior angles of any polygon is 360 degrees

d.Find the size of each exterior/interior angle of a regular polygon a.Transform triangles and other shapes by translation, rotation and reflection (including combinations of transformations)

b.Understand translation as a combination of a horizontal and vertical shift (including vector notation)

c.Understand rotation as a (clockwise) turn about a given origin

d.Reflect shapes in a given mirror line. Initially line parallel to the coordinate axes and then y = x or y = –x

e.Enlarge shapes by a given scale factor from a given point; using positive whole number scale factors, then positive fractional scale factors

f.Distinguish properties that are preserved under transformations, e.g. write down the angles of a triangle that has been enlarged a.Use integer and non-integer scale factors to find the length of a missing side in each of two similar shapes, given the lengths of a pair of corresponding sides

b.Know the relationship between linear, area and volume scale factors of similar shapes

c.Deduce the areas and volumes of similar shapes after they have been enlarged by simple scale factors

d.Read and construct scale drawing, e.g. work out the real distance if the map distance is 6cm scale 1:25000 a.Solve problems involving the circumference and area of a circle (and simple fractional parts of a circle)

b.Solve problems involving the volume of a cylinder

c.Find exact answers by leaving answers in terms of pi a.Understand formulae by considering its dimensions, e.g. identify formulae that represent area from a list

b.Use the relationship between distance, speed and time to solve problems

c.Convert between metric units of speed e.g. km/h to m/s

d.Know that density is found by mass ÷ volume

e.Use the relationship between density, mass and volume to solve problems

f.Convert between metric units of density e.g. kg/m to g/cm

Full transcriptFormula Quadratic Graphs Trial & Improvement Angles Drawing 2D Shapes Reading Scales Angle Properties of

Triangles & Quadrilaterals 3D Shapes Perimeter & Area Volume Angle Properties of Polygons Transformations Scale Factors Circles Compound Measures Collecting Data Charts & Graphs Small Data Sets Probability Pie Charts Time Series Scatter Graphs & Correlation Large Data Sets a. Understand and order whole numbers

b. Add, subtract, multiply and divide whole numbers

c. Add, subtract, multiply and divide negative numbers

d. Understand the meaning of BIDMAS, e.g. work out 12 5 – 24 8

e. Round whole numbers to the nearest 10, 100, 1000, …

f. Multiply and divide whole numbers by a given multiple of 10

g. Check calculations by rounding, e.g. 29 31 30 30

h. Check answers by reverse calculation, e.g. if 9 23 = 207 then 207 9 = 23 a.Put digits in the correct place in a decimal number

b.Write decimals in ascending order of size

c.Approximate decimals to a given number of decimal places or significant figures

d.Multiply and divide decimal numbers by whole numbers and decimal numbers (up to 2 decimal places), e.g. 266.22 0.34

e.Know that e.g. 13.5 0.5 = 135 5 a.Understand and use negative numbers in context, eg thermometers

b.Find: squares; cubes; square roots; cube roots of numbers, with and without a calculator (including the use of trial and improvement)

c.Understand odd and even numbers, and prime numbers

d.Find the HCF and the LCM of numbers

e.Write a number as a product of its prime factors, eg 108 = 2 2 3 3 3

f.Interpret standard index form from a calculator display a.Visualise a fraction on a diagram

b.Understand a fraction as part of a whole

c.Recognise and write fractions in everyday situations

d.Write a fraction in its simplest form and recognise equivalent fractions

e.Compare the sizes of fractions using a common denominator

f.Add and subtract fractions by using a common denominator

g.Write an improper fraction as a mixed fraction

h.Multiply and divide a number with a fraction, and a fraction with a fraction (expressing the answer in its simplest form)

i.Simplify multiplication of fractions by first cancelling common factors

j.Convert a fraction to a decimal, or a decimal to a fraction

k.Convert a fraction to a recurring decimal

l.Find the reciprocal of whole numbers, fractions, and decimals, e.g. find the reciprocal of 0.4

m.Know that 0 does not have reciprocal, and that a number multiplied by its reciprocal is 1

n.Use fractions in contextualised problems a.Understand that a percentage is a fraction in hundredths

b.Write a percentage as a decimal; or as a fraction in its simplest terms

c.Write one number as a percentage of another number

d.Calculate the percentage of a given amount

e.Find a percentage increase/decrease, of an amount

f.Calculate simple and compound interest for two, or more, periods of time

g.Calculate an index number a.Understand what is meant by ratio

b.Write a ratio in its simplest form; and find an equivalent ratio

c.Share a quantity in a given ratio

d.Understand and use examples in direct proportion

e.Interpret map/model scales as a ratio a.Multiply and divide powers of the same number

b.Understand and use the index rules to simplify algebraic expressions, e.g. 55 52 = 53

c.Use brackets to expand and simplify simple algebraic expressions

d.Solve linear equations involving a single pair of brackets a. Design a suitable question for a questionnaire

b. Understand the difference between: primary and secondary data; discrete and continuous data

c. Design suitable data capture sheets for surveys and experiments

d. Understand about bias in sampling Represent data as:

a.Bar charts (including dual bar charts)

b.Pictograms

c.Line graphs

d.Histograms (intervals with equal width)

e.Frequency polygons

f.Choose an appropriate way to display discrete, continuous and categorical data a.Find the mode or the median for (small) sets of data

b.Find the mean and the range for (small) sets of data

c.Use a stem and leaf diagram to sort data

d.Know the advantages/disadvantages of using the different measure of average a.Use the language of probability to describe the likelihood of an event

b.Represent and compare probabilities on a number scale

c.List outcomes for single mutually exclusive events and write down their probability

d.Write down the theoretical probability for an equally likely event

e.Estimate a probability by relative frequency

f.Know that a better estimate for a probability is achieved by increasing the number of trials a.Represent categorical data in a pie chart

b.Interpret categorical data in a pie chart a.Represent data as a time series

b.Identify trends in data over time

c.Identify exceptional periods by comparison with similar previous periods a.Draw and produce a scatter graph

b.Appreciate that correlation is a measure of the strength of association between two variables

c.Distinguish between positive, negative and zero correlation using a line of best fit

d.Appreciate that zero correlation does not necessarily imply ‘no correlation’ but merely ‘no linear relationship’

e.Draw lines of best fit by eye and understand what it represents

f.Find the equation of the line of best and use it to interpolate/extrapolate a.Identify the modal class interval in grouped and ungrouped frequency distributions

b.Find the class interval containing the median value

c.Find the mean of an ungrouped frequency distribution

d.Find an estimate for the mean of a grouped frequency distribution by using the mid-interval value

e.Use the statistical functions on a calculator or a spreadsheet to calculate the mean for discrete data a. Plot and read coordinates on a coordinate grid (in all four quadrants)

b. Understand that one coordinate identifies a point on a line, two coordinates identify a point in a plane and three coordinates identify a point in space, and use the terms ‘1-D’, ‘2-D’ and ‘3-D’

c. Find the coordinates of the fourth vertex of a parallelogram

d. Identify the coordinates of the vertex of a cuboid on a 3-D grid

e. Writing down the coordinates of the midpoint of the line connecting two points

f. Calculate the length of the line segment joining two points in the plane (all four quadrants)

a.Simplify algebraic expressions in one, or more like terms, by adding and subtracting

b.Multiply and divide with letters and numbers a.Find the missing numbers in a number pattern or sequence

b.Find the nth term of a number sequence

c.Find whether a number is part of a given sequence

d.Use a calculator to produce a sequence of numbers a.Solve linear equations with one, or more, operations

b.Solve linear equations involving a single pair of brackets

c.Solve linear inequalities in one variable and present the solution set on a number line a.Draw linear graphs from tabulated data, including real-world examples

b.Interpret linear graphs, including conversion graphs and distance-time graphs

c.Understand the difference between a line and a line segment

d.Draw and interpret graphs in the form y = mx + c (when values for m and c are given)

e.Understand that lines are parallel when they have the same value of m

f.Solve graphically simultaneous equations, e.g. find when/where the car overtakes the bus a.Use letters or words to state the relationship between different quantities

b.Substitute positive and negative numbers into simple algebraic formulae

c.Substitute positive and negative numbers into algebraic formulae involving powers

d.Find the solution to a problem by writing an equation and solving it

e.Change the subject of a formula, e.g. change the formula for converting Centigrade into Fahrenheit into a formula that converts Fahrenheit into Centigrade a.Substitute values of x into a quadratic function to find the corresponding values of y

b.Draw graphs of quadratic functions such as y=x2+2

c.Draw graphs of quadratic functions such as y=2x2-6x+5

d.Use quadratic graphs to solve quadratic equations

e.Expand and simplify expressions with two pairs of brackets a.Solve cubic functions by successive substitution of values of x a. Distinguish between acute, obtuse, reflex and right angles

b. Estimate the size of an angle in degrees

c. Measure and draw angle to the nearest degree

d. Use angle properties on a line and at a point to calculate unknown angles

e. Measure a bearing (acute and obtuse)

f. Measure a bearing (reflex)

g. Calculate bearings

a.Use a ruler and compass to draw accurate triangles, and other 2-D shapes, given information about their side lengths and angles.

b.Use straight edge and compass to construct: an equilateral triangle; the midpoint and perpendicular bisector of a line segment; the bisector of an angle

c.Find the locus of points e.g. the locus of points equidistant to two given points

d.Understand, by their experience of constructing them, that triangles satisfying SSS, SAS, ASA and RHS are unique, but SSA triangles are not

e.Recall and use angle properties of equilateral, isosceles and right-angled triangles

f.Recall and use the properties of squares, rectangles, parallelograms, trapeziums and rhombuses

g.Recall and use properties of circles

h.Appreciate why some shapes tessellate and why some shapes do not tessellate a.Make estimates of: length; volume and capacity; weights

b.Make approximate conversions between metric and imperial units

c.Decide on the appropriate units to use in real life problems

d.Read measurements from instruments: scales; analogue and digital clocks; thermometers, etc

e.Do calculations involving time, including the use of time tables and calendars a.Mark parallel lines in a diagram

b.Use angle properties of triangles and quadrilaterals to find missing angles

c.Prove that the angle sum of a triangle is 180 degrees

d.Explain why the angle sum of a quadrilateral is 360 degrees

e.Find missing angles using properties of corresponding angles and alternate angles, giving reasons

f.Find the three missing angles in a parallelogram when one of them is given

g.Identify and list the properties of quadrilaterals (including kites)

h.Name all quadrilaterals that have a pair of opposite sides that are equal a.Count the vertices, faces and edges of 3-D shapes

b.Draw nets of solids and recognise solids from their nets

c.Draw and interpret plans and elevations

d.Draw planes of symmetry in 3-D shapes

e.Recognise and name examples of solids, including prisms, in the real world a.Find the perimeters and areas of shapes made up from triangles and rectangles

b.Find areas of shapes by counting squares

c.Use formulae to find the area of shapes made up of rectangles and triangles

d.Find the surface area of cuboids and prisms

e.Solve a range of problems involving areas

f.Convert between units of area a.Find volumes of shapes by counting cubes

b.Use formulae for the volume of cuboids

c.Solve a range of problems involving volume

d.Convert between units of volume a.Calculate and use the sums of the interior angles of convex polygons of sides 3, 4, 5, 6, 8, 10

b.Know, or work out, the relationship between the number of sides of a polygon and the sum of its interior angles

c.Know that the sum of the exterior angles of any polygon is 360 degrees

d.Find the size of each exterior/interior angle of a regular polygon a.Transform triangles and other shapes by translation, rotation and reflection (including combinations of transformations)

b.Understand translation as a combination of a horizontal and vertical shift (including vector notation)

c.Understand rotation as a (clockwise) turn about a given origin

d.Reflect shapes in a given mirror line. Initially line parallel to the coordinate axes and then y = x or y = –x

e.Enlarge shapes by a given scale factor from a given point; using positive whole number scale factors, then positive fractional scale factors

f.Distinguish properties that are preserved under transformations, e.g. write down the angles of a triangle that has been enlarged a.Use integer and non-integer scale factors to find the length of a missing side in each of two similar shapes, given the lengths of a pair of corresponding sides

b.Know the relationship between linear, area and volume scale factors of similar shapes

c.Deduce the areas and volumes of similar shapes after they have been enlarged by simple scale factors

d.Read and construct scale drawing, e.g. work out the real distance if the map distance is 6cm scale 1:25000 a.Solve problems involving the circumference and area of a circle (and simple fractional parts of a circle)

b.Solve problems involving the volume of a cylinder

c.Find exact answers by leaving answers in terms of pi a.Understand formulae by considering its dimensions, e.g. identify formulae that represent area from a list

b.Use the relationship between distance, speed and time to solve problems

c.Convert between metric units of speed e.g. km/h to m/s

d.Know that density is found by mass ÷ volume

e.Use the relationship between density, mass and volume to solve problems

f.Convert between metric units of density e.g. kg/m to g/cm