# Topics

Every topic here listed in order.

1a - expand a single bracket

1b - factorise a single bracket

2a - expand two brackets & simplify

2b - factorise a quadratic into two brackets

2c - factorise to simplify algebraic fractions

2d - Solve a quadratic equation by factorising

2e - Use the quadratic formula to solve a quadratic equation

3a - Use an inequality sign

3b - solve a simple inequality & find the integer values

3c - Solve a harder inequality & find the integer values

3d - Plot and shade the regions of an inequality question

4a - solve a basic equation

4b - convert a number machine into an equation

4c - solve an equation with x on one side

4d - Solve an equation with x on both sides

4e - Solve an equation with prior simplification (such as expanding brackets)

4f - Solve a fractional equation

5 - solve an equation using trial and improvement

6a - solve a simultaneous equation algebraically

6b - Solve simultaneous equations graphically

6c - Calculate where a straight line meets a circle

6d - Solve a linear & quadratic simultaneous equation

7a - Use simple formulae in words

7b - Derive an algebraic expression from a formula in words

8a - Substitute numbers into a formula

8b - Substitute numbers into a harder formula (e.g. by squaring)

8c - Substitute fractions or decimals in a formula

9a - Rearrange the subject of a simple formula

9b - Rearrange a formula where the subject occurs more than once

10 - Plot co-ordinates in all four quadrants

11a - Interpret & draw a conversion or travel graph

11b - Calculate speed, distance & time from a travel graph

11c - Sketch a graph of a real life situation (e.g. a water container)

12a - Plot, write & recognise a basic straight line graph

12b - Plot a straight line from its equation

12c - Recognise & calculate the gradient, y-intercept & equation of a line

12d - Plot a quadratic, cubic, reciprocal or difficult linear graph

12e - Calculate the equation of a line from its coordinates

13a - Find the graphical solutions to equations (using meeting lines)

13b - Sketch & find the solution to a trigonometric curve

13c - Apply transformations to y=f(x)

14a - Add, subtract, multiply & divide an algebraic expression

14b - Simplify algebra using the rules for indices

14c - Simplify an algebraic expression with negative or fractional indices

14d - Simplify an algebraic expression with fractions

15a - Find the output of a number machine

15b - Continue a sequence of numbers or pattern of shapes

15c - Generate a sequence from a given rule

15d - Find a number machine input from a given output

15e - Find a specific sequence term from a given worded or nth term rule

15f - Find the nth term formula for a (linear) expression

16a - Calculate the mode from a list of data

16b - Calculate the range from a list of data

16c - Calculate the mean from a list of data

16d - Calculate the mean from a list of data

16e - Choose the best average to use and explain your decision

16f - Compare the averages from different data

17a - Calculate the averages from a frequency table

17b - Calculate the averages from a grouped frequency table

18a - Design and complete a cumulative frequency table

18b - Draw a cumulative frequency curve

18c - Draw a box plot

18d - Interpret a cumulative frequency curve and box plot

19 - Calculate and interpret the moving average

20a - Collect and sort discrete data into a frequency table

20b - Collect and sort continuous data into groups within a frequency table

20c - Distinguish between qualitative, quantitative, discrete & continuous data

20d - Design or correct a questionnaire

20e - Write a hypothesis and test it

20f - Understand what makes good and bad sampling

20g - Understand sampling techniques and justify their choice

21a - Draw a simple line graph

21b - Interpret a line graph or bar chart

22a - Draw a pie chart and calculate the angles

22b - Interpret a pie chart

23a - Draw a histogram with equal widths

23b - Interpret a histogram with equal widths

24a - Draw a frequency polygon

24b - Interpret a frequency polygon

25a - Draw a stem and leaf diagram

25b - Interpret a stem and leaf diagram

26a - Plot a scatter graph and draw the line of best fit

26b - Describe correlation and use the line of best fit for predictions

27a - Draw a histogram using different widths and frequency density

27b - Interpret a histogram using frequency density and different widths

28a - Use probability words like fair and likely

28b - Use the probability scale from 0 to 1

28c - Calculate the theoretical probability of an event happening

28d - Calculate the probability of an event not happening

28e - Estimate the relative frequency of an event happening

28f - Predict the exected number of outcomes for an event

29a - Calculate the probability of two events happening in a table

29b - Calculate the probability of combined events using a tree diagram

29c - Calculate the probabilities of exclusive events from sample data

29d - Calculate the probabilities of compound events from sample data

30a - Find the place value of a digit

30b - Put decimals in order

31a- Add and subtract decimals

31b - Multiply & divide decimals by 10, 100, 1000 etc.

31c - Multiply & divide decimals (and whole numbers) together

31d - Multiply and divide numbers by decimals between 0 and 1

32a - Convert between fractions, decimals and percentages

32b - Change a recurring fraction into a decimal

33a - Find a simple fraction of an amount or shape

33b - Calculate the fraction of a quantity or measurement

33c - Write one amount as a fraction of another

34a - Simplify and find equivalent fractions

34b - Convert between mixed numbers and improper fractions

35a - Add and subtract fractions

35b - Multiply and divide fractions

36a - Write numbers multiplied together in index form

36b - Simplify numbers with powers using the rules of indices

36c - Evaluate numbers with fractional or negative indices

37 - Solve problems involving standard form

38a - Recognise & find multiples, factors & primes

38b - Recognise & find square & cube numbers & roots

38c - Find the lowest common multiple (LCM)

38d - Find the prime factors and highest common factor (HCF)

39a - Add and subtract

39b - Multiply and divide small numbers

39c - Solve problems with money

39d - Multiply two numbers using long multiplication

39e - Divide two numbers using long division

40a - Add, subtract and order negative numbers

40b - Multiply and divide negative numbers

41a - Follow the correct order of operations using BODMAS

41b - Use BODMAS in longer questions

42a - Find a percentage of an amount

42b - Find one amount as a percentage of another

42c - Calculate percentage profit or loss

43a - Calculate harder percentage change (e.g. VAT, tax & credit)

43b - Calculate simple interest

43c - Calculate the original amount before a percentage change

43d - Calculate repeated percentage change (e.g. interest & depreciation)

44a - Solve problems using simple ratio & proportion

44b - Compare & simplify numbers in a given ratio

44c - Find fractions of items in proportion to each other (e.g. recipes)

44d - Divide or share an amount in a ratio

44e - Find a missing constant & variable for direct or inverse proportion

44f - Use scale factors with a map or a scale drawing

45a - Check a solution by simple approximating

45b - Check a solution using inverse operations

45c - Round a number to decimal places or significant figures

45d - Check a solution to a harder question by approximating

45e - Find the upper and lower bounds of a rounded number

46a - Calculate the rational answer to a surd question

46b - Simplify a surd, usually leaving your answer in surd form

47 - Use a protractor to measure & draw angles correctly

48a - Calculate the missing angle(s) in a triangle and quadrilateral

48b - Calculate the missing angle(s) on a straight line

48c - Calculate the missing angle(s) at a point

48d - Calculate the missing angles in parallel lines

48e - Calculate the interior & exterior angles of polygons

48f - Provide the proof for an angle problem

49a - Measure & draw bearings

49b - Calculate the bearings of two objects from each other

50 - Calculate angles using circle theorems

51a - Calculate the area and circumference of a circle

51b - Calculate the area of compound shapes from circles

51c - Calculate the length of an arc, & area of a sector & segment

52a - Calculate the volume and surface area of a cylinder

52b - Calculate the volume & surface area of a cone & pyramid

52c - Calculate the volume & surface area of a sphere

53a - Calculate the area of a shape by counting squares

53b - Calculate the volume of a shape by counting cubes

53c - Calculate the perimeter of a simple shape

53d - Calculate the area of a rectangle & a triangle

53e - Calculate parallelogram, trapezium, kite & compound shape area

54a - Calculate the volume of a cuboid or cube

54b - Calculate the volume & surface area of a prism

54c - Recognise whether a formula is length, area or volume

55a - Draw all the points a given distance from a point or line

55b - Draw an angle or perpendicular bisector

55c - Draw a shape accurately from its description (e.g. a triangle)

55d - Draw loci with more than one condition

56a - Write time in the 12 & 24 hour clock

56b - Use suitable units, measuring scales & instruments

56c - Convert between metric units of length, mass & capacity

56e - Convert between metric & imperial units

56f - Convert between units of length, area & volume

56g - Convert between units of currency

57a - Solve a simple problem involving speed, distance or time

57b - Solve a problem involving a combination of speed, distance & time

57c - Solve a problem involving a combination of density, mass & volume

58a - Calculate the length of a missing side using Pythagoras

58b - Apply Pythagoras theorem to a complicated question

59a - Recognise the properties of 2D and 3D shapes

59b - Identify all the lines of symmetry of 2D shapes

59c - Identify the order of rotational symmetry of 2D shapes

59d - Learn & distinguish the properties of every 2D shape

59e - Identify all the planes of symmetry of a 3D shape

60a - Draw or recognise a sketch or net of a 3D shape

60b - Learn & draw 3D shapes on isometric (dotted) paper

60c - Draw & recognise the plans & elevations of 3D shapes

60d - Draw tesselation & know why it is sometimes impossible

61a - Recognise & draw congruent 2D shapes

61b - Calculate the lengths of missing sides in simple similar shapes

61c - Prove that shapes are congruent or similar

61d - Calculate the lengths of missing sides in harder similar shapes

61e - Solve a problem with similar figures involving area & volume

62a - Reflect a simple shape in a one-way mirror line

62b - Reflect any shape in a one- & two-way mirror line

62c - Solve a problem involving positive enlargement

62d - Solve a problem involving translation using vectors

62e - Recognise & describe a combination of transformations

62f - Solve a problem involving fractional enlargement

62g - Rotate a shape, or state the angle, direction & centre of rotation

62h - Reflect in a diagonal mirror line or find the equation of the mirror line

62i - Solve a problem involving negative enlargement

63a - Find missing angles or sides in a right angled triangle with trigonometry

63b - Solve a trigonometry problem with an angle of elevation or depression

63c - Solve a problem involving trigonometry & pythagoras

64a - Use the sine rule to find a missing side or angle

64b - Use the cosine rule to find a missing side or angle

64c - Solve a problem involving surds in Pythagoras & trigonometry

64d - Solve a problem involving Pythagoras and trigonometry in 3D

64e - Calculate the area of a triangle using Sin C

65a - Calculate the sum, difference & multiple of vectors

65b - Draw the sum, difference or multiple of vectors

65c - Solve other problems using vectors