# Stage 5 content (Yr. 9 & 10)

### **Mathematics - Year 9 | Stage 5.1**

**Term 1**

The first term re-establishes a student's confidence with numbers, before applying similar rules in algebra.

__Students learn about:__

Review Computing with Integers, Fractions, Decimal

- Compares, orders and calculates with integers, applying a range of strategies to aid computation
- Operates with fractions, decimals and percentages

__Algebraic Techniques__

- Generalises number properties to operate with algebraic expressions

__Indices__

- Operates with algebraic expressions involving positive-integer and zero indices, and establishes the meaning of negative indices for numerical bases.

__Term 2__

Students continue to build their knowledge of geometrical shapes and algebraic techniques for solving equations and inequations.

__Students learn about:__

Properties of Geometrical Figures

- Describes and applies the properties of similar figures and scale drawings

- Uses algebraic techniques to solve simple linear and quadratic equations

__Term 3__

Students begin learning about trigonometry and continue to build their knowledge and skills in area and number plane calculations.

__Students learn about:__

- Applies trigonometry, given diagrams, to solve problems, including problems involving angles of elevation and depression.

__Measurement__

- Calculates the areas of composite shapes, and the surface areas of rectangular and triangular prisms

__Linear Relationships__

- Determines the midpoint, gradient and length of an interval, and graphs linear relationships.

__Term 4__

Students continue to develop their knowledge, skills and understanding in data analysis and probability as well as establishing new knowledge in financial mathematics and the properties of shapes.

__Students learn about:__

__Single Variable Data Analysis__

- Uses statistical displays to compare sets of data, and evaluates statistical claims made in the media

__Financial Mathematics__

- Solves financial problems involving earning, spending and investing money

__Congruence and Similarity__

- Describes and applies the properties of similar figures and scale drawings

__Probability__

- Calculates relative frequencies to estimate probabilities of simple and compound events

### **Mathematics - Year 9 | Stage 5.2**

**Term 1**

The first term re-establishes a student's confidence with numbers, before applying similar rules in algebra.

__Students learn about:__

Review Computing with Integers, Fractions, Decimal

- Compares, orders and calculates with integers, applying a range of strategies to aid computation
- Operates with fractions, decimals and percentages

__Algebraic Techniques__

- Simplifies algebraic fractions and expands and factorises quadratic expressions

__Indices__

- Applies index laws to operate with algebraic expressions involving integer indices

__Term 2__

Students continue to build their knowledge of geometrical shapes and algebraic techniques for solving equations and inequations and begin learning about trigonometry.

__Students learn about:__

Properties of Geometrical Figures

- Describes and applies the properties of similar figures and scale drawings

Equations and Inequations

- Solves linear and simple quadratic equations, linear inequalities and linear simultaneous equations using analytical and graphical techniques

__Trigonometry__

- applies trigonometry to solve problems, including problems involving bearings

__Term 3__

Students and continue to build their knowledge and skills in measurement, algebra and data.

__Students learn about:__

Perimeter,__Area and Volume__

- Calculates the surface area of right prisms, cylinders and related composite solids¿
- applies formulas to calculate the volumes of compositesolids composed of right prisms and cylinders

__Linear Relationships__

- Uses the gradient-intercept form to interpret and graph linear relationships

__Data Analysis__

- Uses quartiles and box plots to compare sets of data, and evaluates sources of data.

__Term 4__

Students continue to develop their knowledge, skills and understanding in probability as well as establishing new knowledge in financial mathematics and the properties of shapes.

__Students learn about:__

__Financial Mathematics__

- Solves financial problems involving compounding interest

__Congruence and Similarity__

- Calculates the angle sum of any polygon and uses minimum conditions to prove triangles are congruent or similar.

__Probability__

- Describes and calculates probabilities in multi-step chance experiments.

**Mathematics - Year 9 | Stage 5.3**

**Term 1**

The first term re-establishes a student's confidence with numbers, before applying similar rules in algebra and with indices.

__Students learn about:__

Review Computing with Integers, Fractions, Decimal

- Compares, orders and calculates with integers, applying a range of strategies to aid computation
- Operates with fractions, decimals and percentages

__Algebraic Techniques__

- Selects and applies appropriate algebraictechniques tooperate with algebraic expressions

__Indices and Surds__

- Performs operations with surds and indices.

__Term 2__

Students continue to build their knowledge of geometrical shapes and algebraic techniques for solving equations and inequations before applying their knowledge to trigonometry.

__Students learn about:__

Properties of Geometrical Figures

- Proves triangles are similar, and uses formal geometric reasoning to establish properties of triangles and quadrilaterals

- Solves complex linear, quadratic, simple cubic and simultaneous equations, and rearranges literal equations.

__Trigonometry __

- Applies Pythagoras' theorem, trigonometric relationships, the sine rule, the cosine rule and the area rule to solve problems, including problems involving three dimensions.

__Term 3__

Students continue learning about measurement and build their knowledge and skills in algebra and data analysis.

__Students learn about:__

Perimeter,__Area and Volume__

- applies formulas to find the volumes of right pyramids, right cones, spheres and related composite solids¿
- applies formulas to find the surface areas of right pyramids, right cones, spheres and related composite solids

__Linear Relationships__

- Uses formulas to find midpoint, gradient and distance on the Cartesian plane and applies standardforms of the equation of a straight line

__Data Analysis__

- Uses standard deviation to analyse data.

__Term 4__

Students continue to develop their knowledge, skills and understanding in probability as well as establishing new knowledge in financial mathematics and the properties of shapes.

__Students learn about:__

__Financial Mathematics__

- Solves financial problems involving compounding interest

__Congruence and Similarity__

- Calculates the angle sum of any polygon and uses minimum conditions to prove triangles are congruent or similar.

__Probability__

- Describes and calculates probabilities in multi-step chance experiments.

**Mathematics - Year 10 | Stage 5.1**

**Term 1**

The first term re-establishes a student's confidence with numbers, before applying similar rules in algebra and building knowledge in data analysis.

__Students learn about:__

__Rational Numbers__

- Applies index laws to simplify and evaluate arithmetic expressions and uses scientific notation to write large and small numbers

__Data Representation & Analysis__

- Groups data to aid analysis and constructs frequency and cumulative frequency tables and graphs

__Indices__

- Applies the index laws to simplify algebraic expressions

__Term 2__

Students continue to build their knowledge of geometrical shapes, financial mathematics and probability.

__Students learn about:__

__Perimeter & Area__

- Uses formulae to calculate the area of quadrilaterals and finds areas and perimeters of simple composite figures

__Earning & Spending Money__

- Solves consumer arithmetic problems involving earning and spending money

__Probability__

- Determines relative frequencies and theoretical probabilities

__Term 3__

Students begin learning about trigonometry and continue to build their knowledge and skills in area and number plane calculations.

__Students learn about:__

- Applies trigonometry, given diagrams, to solve problems, including problems involving angles of elevation and depression.

__Coordinate Geometry__

Determines the midpoint, gradient and length of an interval, and graphs linear relationships.

__Surface Area & Volume__

- Applies formulae to find the surface area of right cylinders and volume of right pyramids, cones and spheres and calculates the surface area and volume of composite solids

__Term 4__

Students continue to develop their knowledge, skills and understanding in algebra and geometry as well as establishing new knowledge in data analysis.

__Students learn about:__

__Equations & Inequalities__

- Solves linear and simple quadratic equations, solves linear inequalities

__Polygons__

- Develops and applies results related to the angle sum of interior and exterior angles for any convex polygon

__Data Analysis & Evaluation__

- Uses the interquartile range and standard deviation to analyse data

**Mathematics - Year 10 | Stage 5.2**

**Term 1**

The first term begins with students developing their knowledge of financial applications, before applying trigonometrical rules and building knowledge in algebra.

__Students learn about:__

__Consumer Arithmetic__

- Solves consumer arithmetic problems involving compound interest, depreciation, and successive discounts

__Trigonometry__

- Applies trigonometry to solve problems including those involving bearings

__Simultaneous Equations__

- Solves linear and simple quadratic equations, solves linear inequalities and solves simultaneous equations using graphical and analytical methods

__Term 2__

Students continue to build their knowledge of algebra, geometrical shapes and data analysis.

__Students learn about:__

__Number Plane Graphs__

- Draws and interprets graphs including simple parabolas and hyperbolas
- Draws and interprets graphs of physical phenomena

__Surface Area & Volume__

- Applies formulae to find the surface area of right cylinders and volume of right pyramids, cones and spheres and calculates the surface area and volume of composite solids

__Data Analysis & Evaluation__

- Uses the interquartile range and standard deviation to analyse data

__Term 3__

Students continue to build their knowledge of geometry and algebra.

__Students learn about:__

__Congruence & Similarity__

- Develops and applies results for proving that triangles are congruent or similar

__Products & Factors __

- Uses algebraic techniques to simplify expressions, expand binomial products and factorise quadratic expressions

__Surds__

- Performs operations with surds and indices

__Term 4__

Students establishing new knowledge, skills and understanding in algebra and trigonometry.

__Students learn about:__

__Quadratic Equations__

- Solves linear, quadratic and simultaneous equations, solves and graphs inequalities, and rearranges literal equations

__Further Trigonometry__

- Applies trigonometric relationships, sine rule, cosine rule and area rule in problem solving

__Further Coordinate Geometry__

- Uses various standard forms of the equation of a straight line and graphs regions on the number plane

**Mathematics - Year 10 | Stage 5.3**

**Term 1**

The first term begins with students developing their knowledge of financial applications, before applying trigonometrical rules and building knowledge in algebra.

__Students learn about:__

__Consumer Arithmetic__

- Solves consumer arithmetic problems involving compound interest, depreciation, and successive discounts

__Trigonometry__

- Applies trigonometry to solve problems including those involving bearings

__Surface Area & Volume__

Applies formulae to find the surface area of right cylinders and volume of right pyramids, cones and spheres and calculates the surface area and volume of composite solids

__Term 2__

Students continue to build their knowledge of data analysis, chance and algebra.

__Students learn about:__

__Data Analysis & Evaluation__

- Uses the interquartile range and standard deviation to analyse data

__Probability__

- Solves probability problems involving compound events

__Factorisation & Algebraic Fractions__

- Uses algebraic techniques to simplify expressions, expand binomial products and factorise quadratic expression

__Term 3__

Students continue to build their knowledge of geometry, algebraic equations and associated graphs.

__Students learn about:__

__Deductive Geometry__

- Constructs arguments to prove geometrical results
- Determines properties of triangles and quadrilaterals using deductive reasoning

__Quadratic Equations__

- Solves linear, quadratic and simultaneous equations, solves and graphs inequalities, and rearranges literal equations

__Number Plane Graphs__

- Draws and interprets a variety of graphs including parabolas, cubics, exponentials and circles and applies coordinate geometry techniques to solve problems
- Analyses and describes graphs of physical phenomena

__Term 4__

Students establishing new knowledge, skills and understanding in trigonometry, geometry and algebra.

__Students learn about:__

__Further Trigonometry__

- Applies trigonometric relationships, sine rule, cosine rule and area rule in problem solving

__Similarity__

- Develops and applies results for proving that triangles are congruent or similar
- Constructs geometrical arguments using similarity tests for triangles

__Functions & Logarithms__

- Describes, interprets and sketches functions and uses the definition of a logarithm to establish and apply the laws of logarithms

*Please note, the information contained on these pages is subject to change. Whilst every effort is made to ensure the content is updated and correct we recommend you consult the Head Teacher of each faculty to ensure up to date and accurate information.