Year 10 Higher Maths
Curriculum:
Click to Expand Autumn Content:
Equations & Inequalities
Probability
Multiplicative Reasoning
Prior Knowledge:
Prior Knowledge:
Prior Knowledge:
- Recall the two possible square roots of a given square number.
- Recall the factors of 15.
- Understand the term ‘quadratic’.
- Find positive and negative square roots.
- Expand and simplify a bracket squared.
- Substitute into simple algebraic expressions.
- Recall the equation of a straight line.
- Identify different types of equation.
- Understand inequality signs.
- Identify correct inequalities from given information.
- List all the possible outcomes for a single event systematically.
- Add decimals.
- Subtract decimals and fractions from 1.
- Simplify fractions.
- Add fractions.
- Know that the probability of something not happening is 1 minus the probability of the event happening.
- Interpret inequalities.
- Understand the use of indices.
- Calculate simple rates.
- Convert between metric units of area and volume.
- Recall the formulae for the area of a circle and the volume of a prism.
- Rearrange formulae.
Teaching Content:
Teaching Content:
Teaching Content:
- Find the roots of quadratic functions.
- Rearrange and solve simple quadratic equations.
- Solve more complex quadratic equations.
- Use the quadratic formula to solve a quadratic equation.
- Complete the square for a quadratic expression.
- Solve quadratic equations by completing the square.
- Solve simple simultaneous equations.
- Solve simultaneous equations for real-life situations.
- Use simultaneous equations to find the equation of a straight line.
- Solve linear simultaneous equations where both equations are multiplied.
- Interpret real-life situations involving two unknowns and solve them.
- Solve simultaneous equations with one quadratic equation.
- Use real-life situations to construct quadratic and linear equations and solve them.
- Solve inequalities and show the solution on a number line and using set notation.
- Use the product rule for finding the number of outcomes for two or more events.
- List all the possible outcomes of two events in a sample space diagram.
- Identify mutually exclusive outcomes and events.
- Find the probabilities of mutually exclusive outcomes and events.
- Find the probability of an event not happening.
- Work out the expected results for experimental and theoretical probabilities.
- Compare real results with theoretical expected values to decide if a game is fair.
- Draw and use frequency trees.
- Calculate probabilities of repeated events.
- Draw and use probability tree diagrams.
- Decide if two events are independent.
- Draw and use tree diagrams to calculate conditional probability.
- Draw and use tree diagrams without replacement.
- Use two-way tables to calculate conditional probability.
- Use Venn diagrams to calculate conditional probability.
- Use set notation.
- Find an amount after repeated percentage changes.
- Solve growth and decay problems.
- Calculate rates.
- Convert between metric speed measures.
- Use a formula to calculate speed and acceleration.
- Solve problems involving compound measures.
- Use relationships involving ratio.
- Use direct and indirect proportion.
Keywords:
Keywords:
Keywords:
Solving, roots, quadratic formula, perfect squares, completing the square, simultaneous equations, inequalities, set notation
Sample space diagram, mutually exclusive, experimental probability, theoretical probability, frequency tree, independent, tree diagram, dependent events, conditional probability, Intersection, union
Annual, depreciate, compound interest, total interest, compound measures, velocity, initial velocity, acceleration, mass, volume, force, area
Click to Expand Spring Content:
Similarity and Congruence
Further Trigonometry
Further Statistics
Prior Knowledge:
Prior Knowledge:
Prior Knowledge:
- Know the angle sum of interior angles of a triangle.
- Use correct mathematical notation for equal angles and sides.
- Use geometric properties to find similarities and differences between given polygons.
- Find area scale factor, given length scale factor.
- Work out the volume and surface area of a cube.
- Recognise when to use the sine rule and when to use the cosine rule.
- Applying simple transformations to coordinates
- Calculate the upper and lower bounds of a measurement.
- Know the values of the sine function for key angles.
- Know the values of the cosine function for key angles.
- Know the exact value of the tangent function for key angles.
- Use A = ½bh to find the area of a triangle.
- Evaluate expressions using the priority of operations.
- Simplify fractions.
- Find a fraction of an amount.
- Read and interpret a frequency table for grouped continuous data.
- Identify the median value.
- Calculate the interquartile range.
- Division by whole numbers and decimals.
- List the measures of spread and average.
Teaching Content:
Teaching Content:
Teaching Content:
- Show that two triangles are congruent.
- Know the conditions of congruence.
- Prove shapes are congruent.
- Solve problems involving congruence.
- Use the ratio of corresponding sides to work out scale factors.
- Find missing lengths on similar shapes.
- Use similar triangles to work out lengths in real life.
- Use the link between linear scale factor and area scale factor to solve problems.
- Use the link between scale factors for length, area and volume to solve problems.
- Understand and use upper and lower bounds in calculations involving trigonometry.
- Understand how to find the sine of any angle.
- Know the graph of the sine function and use it to solve equations.
- Understand how to find the cosine of any angle.
- Know the graph of the cosine function and use it to
solve equations. - Understand how to find the tangent of any angle.
- Know the graph of the tangent function and use it to
solve equations. - Find the area of a triangle and a segment of a circle.
- Use the sine rule to solve 2D problems.
- Use the cosine rule to solve 2D problems.
- Solve bearings problems using trigonometry.
- Use Pythagoras’ theorem in 3D.
- Use trigonometry in 3D.
- Recognise how changes in a function affect trigonometric graphs.
- Understand how to take a simple random sample.
- Understand how to take a stratified sample.
- Draw and interpret cumulative frequency tables and diagrams.
- Work out the median, quartiles and interquartile range from a cumulative frequency diagram.
- Find the quartiles and the interquartile range from stem-and-leaf diagrams.
- Draw and interpret box plots.
- Understand frequency density.
- Draw histograms.
- Interpret histograms.
- Compare two sets of data.
Keywords:
Keywords:
Keywords:
Congruence, similar, Scale Factor
Accuracy, sine, cosine, tangent, area, sine rule, cosine rule, plane, diagonal
Population, census, sample, bias, random, strata, stratified sample, box plot, box-and-whisker diagram, summary statistics, comparative box plots, histogram, outliers
Click to Expand Summer Content:
Equations and Graphs
GCSE Exams
Circle Theorems
Prior Knowledge:
At this time in the Summer term, students have covered enough of the syllabus to access a grade 9 on the GCSE exams.
Time in lessons is now given to preparation and revision for the Early Entry GCSE examination.
All students will be sitting an exam, either as a certificated, external GCSE examination, or as a “mock” internal End of Year exam.
Prior Knowledge:
- Write the equation of a circle, centre at the origin, from its graph.
- Find integer values to satisfy inequalities.
- Describe the shape of a quadratic graph.
- Determine if a quadratic graph will have a maximum or a minimum point from the equation.
- Find the points where quadratic graphs cross the x-axis.
- Know properties of isosceles triangles.
- Define the chord of a circle.
- Know that a line from the centre of a circle to the midpoint of a chord is perpendicular to the chord.
- Know that angles round a point add to 360°.
- Recall the sum of angles of a quadrilateral.
- Use correct mathematical vocabulary for parts of a circle.
- Understand that x² + y² = r² is the equation of a circle with centre at the origin.
- Find the gradient of a line from its equation and know the gradient of a line perpendicular to it.
Teaching Content:
Teaching Content:
- Solve simultaneous equations graphically.
- Represent inequalities on graphs.
- Interpret graphs of inequalities.
- Recognise and draw quadratic functions.
- Find approximate solutions to quadratic equations graphically.
- Solve quadratic equations using an iterative process.
- Find the roots of cubic equations.
- Sketch graphs of cubic functions.
- Solve cubic equations using an iterative process.
- Solve problems involving angles, triangles and circles.
- Understand and use facts about chords and their distance from the centre of a circle.
- Solve problems involving chords and radii.
- Understand and use facts about tangents at a point and from a point.
- Give reasons for angle and length calculations involving tangents.
- Understand, prove and use facts about angles subtended at the centre and the circumference of circles.
- Understand, prove and use facts about the angle in a semicircle being a right angle.
- Find missing angles using these theorems and give reasons for answers.
- Understand, prove and use facts about angles subtended at the circumference of a circle.
- Understand, prove and use facts about cyclic quadrilaterals.
- Prove the alternate segment theorem.
- Solve angle problems using circle theorems.
- Give reasons for angle sizes using mathematical language.
- Find the equation of the tangent to a circle at a given point.
Keywords:
Keywords:
Simultaneous, roots, maximum, minimum, iterative, iteration
Subtended, segment, alternate segment, cyclic quadrilateral
Subject Overview:
In Year 10 our Higher students are stretched even further. We cover as much of the curriculum as possible and all our students cover enough material to access a grade 9 at the end of Year 10.
Students who gain the top grades will be able to do a 1-year GCSE in Further Maths in Year 11. Others will get the opportunity to improve their GCSE grade at the end of Year 11.
This approach to Early Entry and using it as a 'springboard' into Year 11 has proven very successful over the years.
Assessments:
In Year 10 there are end of unit assessments and in the summer students will either sit the Early Entry Higher GCSE maths exam or will sit an internal End of Year exam.
