﻿ Mathematics - Subjects - Wilmington Grammar School for Girls

# Mathematics

Department vision

Mathematics is important in our everyday life, allowing us to make sense of the world around us and to manage our lives. Using mathematics enables us to model real-life situations and make connections and informed predictions. It equips us with the skills we need to interpret and analyse information, simplify and solve problems, assess risk and make informed decisions.”

We aim to encourage students to develop lively, creative and enquiring minds.  To be capable of independent thought and to enjoy Mathematics through problem solving and perseverance.  To appreciate that Mathematics is inherent to everyday life.

### Year 8

 Topic Learning Outcomes Term 1 Factors and Powers;              Working with powers (Algebra);                Graphs. – Write the prime factor decomposition of a number.  Use prime factor decomposition to find the HCF and LCM of two numbers.  – Use the laws of indices for positive powers for multiplying and dividing.  – Use and understand powers of 10.  Understand the effect of multiplying and dividing by any integer power of 10.  – Round to a number of significant figures.    2.1 – Simplify expressions involving powers and brackets.  Understand the meaning of an identity.  2.2 – Use the index laws in algebraic calculations and expressions.  Simplify expressions with powers.  2.3 – Write and simplify expressions involving brackets and powers.  Factorise an algebraic expression.  2.4 – Substitute integers into expressions.  Construct and solve equations.    10.1 – Plotting straight line graphs.  Finding the y-intercept of a straight-line graph.  10.2 – Find the gradient of a straight-line graph.  Plotting graphs using the gradient and y-intercept.  10.3 – Use y = mx + c.  Find the equation of a straight-line graph.  10.4 – Identify parallel and perpendicular lines.  10.5 – Find the inverse of a linear function. Term 2 Graphs (cont.);    Real-life Graphs;                Transformations. 10.6 – Plot and use non-linear graphs.    4.1 – Recognise when values are in direct proportion.  Plot graphs and read values to solve problems.  4.2 – Interpret graphs from different sources.  Understand financial graphs.  4.3 – Draw and interpret distance-time graphs.  Use distance-time graphs to solve problems.  4.4 – Interpret graphs that are curved.  Interpret real-life graphs.  4.5 – Understand when graphs are misleading.    5.1 – Describe and carry out translations and reflections.  5.2 – Describe and carry out rotations.  5.3 – Describe and carry out enlargements.  5.4 – Enlarge a shape using a negative or fractional scale factor.  5.5 – Transform 2D shapes using a combination of reflection, rotation, enlargement and translation. Term 3 Transformations (cont);        Fractions, Decimals and Percentages;              Probability. 5.6 – Identify planes of reflection symmetry in 3D solids.  Find the perimeter and area of 2D shapes after enlargements.  Find the volume of 3D solids after enlargements.  6.1 – Recognise fractional equivalents to some recurring decimals.  Change a recurring decimal into a fraction.  6.2 – Calculate percentages.  Calculating an original quantity before a percentage increase or decrease.  6.3 – Calculate percentage change.  6.4 – Calculate the effect of repeated percentage changes.    8.1 – Calculate and compare probabilities.  Decide if a game is fair.  8.2 – Identify mutually exclusive outcomes and events.  Find the probability of mutually exclusive outcomes and events.  Find the probability of an event not happening.  8.3 – Calculate the relative frequency of a value.  Use relative frequency to estimate the probability of an event.  Use estimated probability to calculate expected frequencies.  8.4 – Carry out a probability experiment.  Estimate probability using data from an experiment.  Work out the expected results when an experiment is repeated.  8.5 – List all the possible outcomes in sample space diagrams or Venn diagrams.  Calculate probabilities of repeated events. Term 4 Probability;    Scale Drawings and Measures; 8.6 – Use tree diagrams to find the probabilities of two or more events.    9.1 – Use scales in maps and plans.  Use and interpret maps.  9.2 – Measure and use bearings.  Draw diagrams to scale using bearings.  9.3 – Draw diagrams to scale.  Use and interpret scale drawings.  9.4 – Identify congruent and similar shapes.  Use congruence to solve problems in triangles and quadrilaterals.  9.5 – Use similarity to solve problems in 2D shapes. Term 5 Constructions and Loci                    2D Shapes and 3D Solids 7.1 – Draw triangles accurately using a ruler and protractor.  Draw diagrams to scale.  7.2 – Draw accurate nets of 3D solids.  Construct triangles using a ruler and compasses.  Construct nets of 3D solids using a ruler and compasses.  7.3 – Bisect a line using a ruler and compasses.  Construct perpendicular lines using a ruler and compasses.  7.4 – Bisect angles using a ruler and compasses.  Draw accurate diagrams to solve problems.  7.5 – Draw a locus.  Use loci to solve problems.    3.1 – Use 2D representations of 3D solids.  3.2 – Sketch nets of 3D solids.  Calculate the surface area of prisms. Term 6 2D Shapes and 3D Solids                Revision and preparation for the PPE’s.     Consolidation for work completed and areas of weakness identified from the PPE’s.    Time allowed for those topics not completed during Terms 1-5. 3.3 – Calculate the volume of prisms.  3.4 – Name different parts of a circle.  Calculate the circumference of a circle or arc length.  Calculate the radius or diameter given the circumference.  3.5 – Calculate the area of a circle or sector.  Calculate the radius or diameter when given the area.  3.6 – Calculate the volume and surface area of a cylinder.  3.7 – Use Pythagoras’ Theorem in right-angled triangles.

Year 10

Year 11

### Post 16 at WG6

Year 12

Year 13

Topic

Learning Outcomes

Term 1

Pure 2: Functions and Graphs

Pure 3: Sequences and Series

Pure 4: Binomial Expansion

Mechs 5: Forces and Friction

Mechs 6: Projectiles

Pure 6: Trigonometric Functions

2.1 The Modulus Function

2.2 Functions and Mapping

2.3 Composite Functions

2.4 Inverse Functions

2.5

y=|f(x)|y=f(x)

and

y=f(|x|)y=f(x)

2.6 Combining Transformations

2.7 Solving Modulus Problems

3.1 Arithmetic Sequences

3.2 Arithmetic Series

3.3 Geometric Sequences

3.4 Geometric Series

3.5 Sum to Infinity

3.6 Sigma Notation

3.7 Recurrence Relations

3.8 Modelling with Series

4.1 Expanding

(1+x)n(1+x)n

4.2 Expanding

(a+bx)n(a+bx)n

4.3 Using Partial Fractions

5.1 Resolving Forces

5.2 Inclined Planes

5.3 Friction

6.1 Horizontal Projection

6.2 Horizontal and Vertical Components

6.3 Projection at any Angle

6.4 Projectile motion formulae

6.1 Secant, cosecant and cotangent

6.2 Graphs of sec x, cosec x and cot x

6.3 Using sec x, cosec x and cot x

6.4 Trigonometric Identities

6.5 Inverse Trigonometric Functions

Term 2

Pure 7: Trigonometry and Modelling

Pure 8: Parametric Equations

Pure 9: Differentiation

Stats 1: Regression, correlation and hypothesis testing

Stats 2: Conditional Probability

7.2 Using the angle addition formulae

7.3 Double-angle formulae

7.4 Solving Trigonometric Equations

7.5 Simplifying

acosx ±bsinxacosâ¡x ±bsinâ¡x

7.6 Proving Trigonometric Identities

7.7 Modelling with Trigonometric Functions

8.1 Parametric Equations

8.2 Using Trigonometric Identities

8.3 Curve Sketching

8.4 Points of Intersection

8.5 Modelling with Parametric Equations

9.1 Differentiating

sinx andcosxsinâ¡x andcosâ¡x

9.2 Differentiation exponentials and logarithms

9.3 The chain rule

9.4 The product rule

9.5 The quotient rule

9.6 Differentiating trigonometric functions

9.7 Parametric differentiation

9.8 Implicit differentiation

9.9 Using second derivatives

9.10 Rates of change

1. Exponential models

1. Measuring correlation

1. Hypothesis testing for zero correlation

2.1 Set Notation

2.2 Conditional Probability

2.3 Conditional Probabilities in Venn Diagrams

2.4 Probability Formulae

2.5 Tree Diagrams

Term 3

Stats 3: The Normal Distribution

3.1 The normal distribution

3.2 Finding probabilities for normal distributions

3.3 The inverse normal distributions

3.4 The standard normal distribution

3.5 Finding

μ

### Related Careers

Mathematics has applications in many other subjects including Science, Business Studies, Economics, Geography, Computing, Design and Psychology.  Careers such as Engineering, Architecture, Accountancy and Actuarial Science will require strong Mathematical skills whilst Mathematics is a valued supporting subject for many other degrees and careers.

• Accountancy

• Actuarial Science

• Architecture

• Engineering

• Financial consultant

• Computer systems analyst

• Insurance Broker

• Marketing Executive