# Year 09 Higher Maths

##### Curriculum:

*Multiply numbers in a similar format to questions later in the lesson.**Estimate the value of a square root.**Multiply prime factors together.**Work out simple powers.**Work out roots.**Convert a decimal to a fraction.**Multiply by powers of 10 when the number is written as an ordinary number and not an index.**Review different ways to divide by 10.**Review the meaning of the dot in the notation for recurring decimals.**Identify the missing multiple which practices the skills of searching for a perfect square factor.*

*Recognise that squaring and taking the square root and cubing and taking the cube root are inverse operations.**Simplify algebraic terms, including index notation.**Solve a simple equation expressed in words.**Substitute values into a one-step formula.**Find the next term of a given arithmetic sequence.**Substitute values in a simple linear expression.**Find the next term of given sequences.**Identify arithmetic and geometric sequences.**Recalling a square root.**Finding the factor pairs of small integers.*

- Work out the total number of ways of performing a series of tasks.
- Estimate an answer.
- Use place value to answer questions.
- Write a number of the product of its prime factors.
- Find the HCF and LCM of two numbers.
- Use powers and roots in calculations.
- Multiply and divide using index laws.
- Work out a power raised to a power.
- Use negative indices.
- Use fractional indices.
- Write a number in standard form.
- Calculate with numbers in standard form.
- Understand the difference between rational and irrational numbers.
- Simplify a surd.
- Rationalise a denominator.

- Use the rules of indices to simplify algebraic expressions.
- Expand brackets.
- Factorise algebraic expressions.
- Solve equations involving brackets and numerical fractions.
- Use equations to solve problems.
- Substitute numbers into formulae.
- Rearrange formulae.
- Distinguish between expressions, equations, formulae and identities.
- Find a general formula for the
*nt*h term of an arithmetic sequence. - Determine whether a particular number is a term of a given arithmetic sequence.
- Solve problems using geometric sequences.
- Work out terms in Fibonacci-like sequences.
- Find the
*n*th term of a quadratic sequence. - Expand the product of two brackets.
- Use the difference of two squares.
- Factorise quadratics of the form
*x*^{2}+*bx*+*c*

*Work out mode, median and range from a list of numbers.**Identify trends by noticing whether sequences of numbers increase, decrease or oscillate.**Recognise when a line has a positive, negative or zero gradient.**Plot points on a coordinate grid, and identify points that do not lie on a straight line.**Understand and be able to define the meaning of correlation.**Read values from graphs.**Find the range of a list of numbers.**Find the midpoint of two numbers.**Use subtraction to find missing values.**Draw a bar chart.**Draw a pie chart.*

*Identify unit fractions, improper fractions and mixed numbers.**Multiply a whole number by a fraction.**Know the priority of operations.**Multiply a fraction by its reciprocal for a product of 1.**Simplify ratios.**Write ratios in the form n : 1.**Write one number as a proportion of the total.**Identify equivalent ratios.**Find a percentage of a given amount.**Work out percentage multipliers.**Convert between fractions, decimals and percentages.**Solve simple equations.*

*Recognise special types of triangle and quadrilateral.**Recall basic angle facts.**Name polygons and understand the meaning of ‘regular polygon’.**Substitute numbers into an expression.**Find missing angles in triangles, quadrilaterals and at a point.**Find missing angles on a straight line.**Calculate the sum of interior angles of a polygon.**Recall square numbers and square roots.**Find the area of a square.**Find square roots.**Recognise perfect squares.**Use Pythagoras' theorem to find the length of the hypotenuse.**Convert fractions to decimals.**Identify the hypotenuse.**Use the angle sum of a triangle to work out missing angles.**Identify the opposite and adjacent sides of a given angle in right-angled triangles.**Use the trigonometric ratios to find lengths in right-angled triangles.*

- Construct and use back-to-back stem and leaf diagrams.
- Construct and use frequency polygons and pie charts.
- Plot and interpret time series graphs.
- Use trends to predict what might happen in the future.
- Plot and interpret scatter graphs.
- Determine whether or not there is a linear relationship between two variables.
- Draw a line of best fit on a scatter graph.
- Use the line of best fit to predict values.
- Decide which average is best for a set of data.
- Estimate the mean and range from a grouped frequency table.
- Find the modal class and the group containing the median.
- Construct and use two-way tables.
- Choose appropriate diagrams to display data.
- Recognise misleading graphs.

- Add, subtract, multiply and divide fractions and mixed numbers.
- Find the reciprocal of an integer, decimal or fraction.
- Write ratios in the form 1 : n or n : 1.
- Compare ratios.
- Find quantities using ratios.
- Solve problems involving ratios.
- Convert between currencies and measures.
- Recognise and use direct proportion.
- Solve problems involving ratios and proportion.
- Work out percentage increases and decreases.
- Solve real-life problems involving percentages.
- Work out percentage increases and decreases.
- Solve real-life problems involving percentages.

- Derive and use the sum of angles in a triangle and in a quadrilateral.
- Derive and use the fact that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.
- Calculate the sum of the interior angles of a polygon.
- Use the interior angles of polygons to solve problems.
- Know the sum of the exterior angles of a polygon.
- Use the angles of polygons to solve problems.
- Calculate the length of the hypotenuse in a right-angled triangle.
- Solve problems using Pythagoras’ theorem.
- Calculate the length of a shorter side in a right-angled triangle.
- Solve problems using Pythagoras’ theorem.
- Use trigonometric ratios to find lengths in a right-angled triangle.
- Use trigonometric ratios to solve problems.
- Use trigonometric ratios to calculate an angle in a right-angled triangle.
- Find angles of elevation and angles of depression.
- Use trigonometric ratios to solve problems.
- Know the exact values of the sine, cosine and tangent of some angles.

*Identify positive and negative gradients and intercepts from graphs.**Rearrange equations.**Identify lines with the same gradient or y-intercept from their equations.**Write the equation of a line from a graph.**Find speed from given distance and time.**Find the area of triangles and rectangles.**Write the equation of a line from a sketch graph.**Plot a graph using values given in a table.**Identify parallel and perpendicular lines**Know properties of gradients of parallel lines.**Identify the gradient and intercept from an equation in the form y = mx + c.**Identify quadratic expressions.**Write the equation of a line from a graph.**Know the shape of linear and quadratic graphs.**Match the shape of a container to the graph of depth of water against time.*

*Recognising units of length (perimeter) and area.**Work out the area and perimeter of rectangles, triangles and parallelograms.**Recall the formulae for the area of quadrilaterals and triangles. Identify the possible integer values of x from an inequality.**Round numbers to a specified degree of accuracy.**Work out percentages of quantities.**Calculate the volume and surface area of a cuboid.**Calculate the volume of a shape made from cuboids.**Understand ‘radius’ and ‘diameter’.**Solve and rearrange simple equations.**Work out fractions of a circle given the angle of a sector.**Simplify equations.**Find the area and circumference of a circle in terms of π.**Sketch a net of a cylinder.**Solve simple equations.**Find the volume of a cube.**Find the side length of a cube given its volume.**Calculate the area of a triangle.**Use Pythagoras' theorem to work out the length of the hypotenuse.*

*Draw 3D shapes on an isometric grid.**Recognise dimensions of a cuboid.**Draw simple straight lines on a coordinate grid.**Know whether the image is congruent to the original following a reflection or a rotation.**Enlarge shapes on a coordinate grid in one quadrant.**Describe translations.**Convert metric measures and apply to scales.**Accurate drawing of right-angled triangle.**Accurate drawings of triangles given SSS and ASA.**Know the meaning of the terms perpendicular, bisect, arc.**Draw angles with a protractor.*

- 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.
- Plot graphs with equations ax + by = c.
- Sketch graphs using the gradient and intercepts.
- Find the equation of a line, given its gradient and one point on the line.
- Find the gradient of a line through two points.
- Draw and interpret distance–time graphs.
- Calculate average speed from a distance–time graph.
- Understand velocity–time graphs.
- Find acceleration and distance from velocity–time graphs.
- Draw and interpret real-life linear graphs.
- Recognise direct proportion.
- Draw and use a line of best fit.
- Find the coordinates of the midpoint of a line segment.
- Find the gradient and length of a line segment.
- Find the equations of lines parallel or perpendicular to a given line.
- Draw quadratic graphs.
- Solve quadratic equations using graphs.
- Identify the line of symmetry of a quadratic graph.
- Interpret quadratic graphs relating to real-life situations.
- Draw graphs of cubic functions.
- Solve cubic equations using graphs.
- Draw graphs of reciprocal functions.
- Recognise a graph from its shape.
- Interpret linear and non-linear real-life graphs.
- Draw the graph of a circle.

- Find the perimeter and area of compound shapes.
- Recall and use the formula for the area of a trapezium.
- Convert between metric units of area.
- Calculate the maximum and minimum possible values of a measurement.
- Convert between metric units of volume.
- Calculate volumes and surface areas of prisms.
- Calculate the area and circumference of a circle.
- Calculate area and circumference in terms of π.
- Calculate the perimeter and area of semicircles and quarter circles.
- Calculate arc lengths, angles and areas of sectors of circles.
- Calculate volume and surface area of a cylinder and a sphere.
- Solve problems involving volumes and surface areas.
- Calculate volume and surface area of pyramids and cones.

- Draw plans and elevations of 3D solids.
- Reflect a 2D shape in a mirror line.
- Rotate a 2D shape about a centre of rotation.
- Describe reflections and rotations.
- Enlarge shapes by fractional and negative scale factors about a centre of enlargement.
- Translate a shape using a vector.
- Carry out and describe combinations of transformations.
- Draw and use scales on maps and scale drawings.
- Solve problems involving bearings.
- Construct triangles using a ruler and compasses.
- Construct the perpendicular bisector of a line.
- Construct the shortest distance from a point to a line using a ruler and compasses.
- Bisect an angle using a ruler and compasses.
- Construct angles using a ruler and compasses.
- Construct shapes made from triangles using a ruler and compasses.
- Draw a locus.

##### Subject Overview:

Our Higher students follow the Edexcel GCSE Higher course which covers the following areas:

Number, Algebra, Ratio, Proportion and Rates of Change, Geometry and Measures, Probability and Statistics

The qualification consists of three equally-weighted written examination papers.

Paper 1 is a non-calculator assessment. Calculators are required for paper 2 and paper 3.

Each paper is 1 hour and 30 minutes long and is worth 80 marks.

##### Assessments:

In Year 9 students are assessed at the end of each unit. There are also End of Term assessments and an End of Year assessment.