Year 11 GCSE Higher Tier Maths Revision Checklist

Number Topics

• Number problems and reasoning: Work out the total number of ways of performing a series of tasks.
• Place value and estimating: Estimate an answer using place value; use place value to answer questions.
• HCF and LCM: Write a number as the product of its prime factors; find the HCF and LCM of two numbers.
• Calculating with powers (indices): Use powers and roots in calculations; multiply and divide using index laws; work out a power raised to a power.
• Zero, negative and fractional indices: Use negative indices; use fractional indices.
• Powers of 10 and standard form: Write a number in standard form; calculate with numbers in standard form.
• Surds: Simplify a surd; rationalise a denominator; understand the difference between rational and irrational numbers.

Fractions, Ratio and Percentages

• Fractions: Add, subtract, multiply and divide fractions and mixed numbers; find the reciprocal of an integer, decimal or fraction.
• Ratios: Write ratios in the form 1 : n or n : 1; compare ratios; find quantities using ratios; solve problems involving ratios.
• Ratio and proportion: Convert between currencies and measures; recognise and use direct proportion; solve problems involving ratios and proportion.
• Percentages: Work out percentage increases and decreases; solve real-life problems involving percentages.

Algebra Topics

• Algebraic indices: Use the rules of indices to simplify algebraic expressions.
• Expanding and factorising: Expand brackets; factorise algebraic expressions.
• Equations: Solve equations involving brackets and numerical fractions; use equations to solve problems.
• Formulae: Substitute numbers into formulae; rearrange formulae; distinguish between expressions, equations, formulae and identities.
• Linear sequences: Find a general formula for the nth term of an arithmetic sequence; determine whether a particular number is a term of a given arithmetic sequence.

Graphs Topics

• Linear graphs: Find the gradient and y-intercept from a linear equation; rearrange an equation into the form y = mx + c; compare two graphs from their equations.
• More linear graphs: Sketch graphs using the gradient and intercepts; find the equation of a line, given its gradient and one point on the line.
• Graphing rates of change: Draw and interpret distance–time graphs; calculate average speed from a distance–time graph; understand velocity–time graphs.
• Real-life graphs: Draw and interpret real-life linear graphs; recognise direct proportion; draw and use a line of best fit.
• Line segments: Find the coordinates of the midpoint of a line segment; find the gradient and length of a line segment.

Equations and Inequalities Topics

• Solving quadratic equations: Find the roots of quadratic functions; solve more complex quadratic equations.
• Completing the square: Complete the square for a quadratic expression; solve quadratic equations by completing the square.
• Solving simple simultaneous equations: Solve simple simultaneous equations; solve simultaneous equations for real-life situations.

More Algebra Topics

• Rearranging formulae: Change the subject of a formula where the power of the subject appears.
• Algebraic fractions: Add and subtract algebraic fractions; multiply and divide algebraic fractions.
• Simplifying algebraic fractions: Simplify algebraic fractions; expand expressions involving surds.
• More algebraic fractions: Add and subtract more complex algebraic fractions; multiply and divide more complex algebraic fractions.
• Surds: Simplify expressions involving surds; expand expressions involving surds; rationalise the denominator of a fraction.

Geometry Topics

• Angles and trigonometry: Derive and use the sum of angles in a triangle and in a quadrilateral.
• Interior angles of a polygon: Calculate the sum of the interior angles of a polygon; use the interior angles of polygons to solve problems.
• Exterior angles of a polygon: Know the sum of the exterior angles of a polygon; use the angles of polygons to solve problems.
• Pythagoras’ theorem: Calculate the length of the hypotenuse in a right-angled triangle; solve problems using Pythagoras’ theorem.
• Trigonometry: Use trigonometric ratios to find lengths in a right-angled triangle; use trigonometric ratios to solve problems.

Area and Volume Topics

• Perimeter and area: Find the perimeter and area of compound shapes; recall and use the formula for the area of a trapezium.
• Units and accuracy: Convert between metric units of area; calculate the maximum and minimum possible values of a measurement.
• Prisms: Convert between metric units of volume; calculate volumes and surface areas of prisms.

Transformations and Constructions Topics

• 3D solids: Draw plans and elevations of 3D solids.
• Reflection and rotation: Reflect a 2D shape in a mirror line; rotate a 2D shape about a centre of rotation.
• Enlargement: Enlarge shapes by fractional and negative scale factors about a centre of enlargement.
• Transformations and combinations: Translate a shape using a vector; carry out and describe combinations of transformations.

Similarity and Congruence Topics

• Congruence: Show that two triangles are congruent; know the conditions of congruence.
• Geometric proof and congruency: Prove shapes are congruent; solve problems involving congruence.

More Trigonometry Topics

• Accuracy: Understand and use upper and lower bounds in calculations involving trigonometry.
• Graph of the sine function: Understand how to find the sine of any angle; know the graph of the sine function and use it to solve equations.

Circle Theorems Topics

• Radii and chords: Solve problems involving angles, triangles and circles; understand and use facts about chords and their distance from the centre of a circle.
• Tangents: Understand and use facts about tangents at a point and from a point; give reasons for angle and length calculations involving tangents.

Probability Topics

• Interpreting and representing data: Construct and use back-to-back stem and leaf diagrams; construct and use frequency polygons and pie charts.
• Time series: Plot and interpret time series graphs; use trends to predict what might happen in the future.
• Scatter graphs: Plot and interpret scatter graphs; determine whether or not there is a linear relationship between two variables.

Ratio & Proportion Topics

• Growth and decay: Find an amount after repeated percentage changes; solve growth and decay problems.

• Compound measures: Calculate rates; convert between metric speed measures; use a formula to calculate speed and acceleration.### Statistical Diagrams

• Two-way tables can be constructed and used to display data.

• Appropriate diagrams can be chosen to display data.

• Misleading graphs can be recognized.

Probability

• The product rule can be used to find the number of outcomes for two or more events.
• All possible outcomes of two events can be listed in a sample space diagram.
• Mutually exclusive outcomes and events can be identified.
• The probabilities of mutually exclusive outcomes and events can be found.
• The probability of an event not happening can be found.
• Expected results for experimental and theoretical probabilities can be worked out.
• Real results can be compared with theoretical expected values to see if a game is fair.
• Independent events and tree diagrams can be used to calculate probabilities of repeated events.
• Conditional probability can be calculated using tree diagrams.
• Two-way tables can be used to calculate conditional probability.
• Venn diagrams and set notation can be used to calculate conditional probability.

Further Statistics

• Simple random samples can be taken.
• Stratified samples can be taken.
• Cumulative frequency tables and diagrams can be drawn and interpreted.
• The median, quartiles, and interquartile range can be worked out from cumulative frequency tables and diagrams.
• Box plots can be drawn and interpreted.
• Quartiles and the interquartile range can be found from stem-and-leaf diagrams.
• Histograms can be drawn and interpreted.
• Frequency density can be understood.
• Two sets of data can be compared and populations can be described.

Revision checklist for Year 11 GCSE Higher Tier Maths, covering number topics including number problems, place value, HCF, and LCM.