Module 5 Equations & Formulae
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Module Grade Topic

Description

5

2

1

Derive and use a simple formula expressed in words

 

 

 

Use letters to represent Simple Formulae

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5

2

2

Understand the use of symbols to represent unknowns; use simple function machines to deal with inputs and outputs, recognising basic inverse functions.

 

 

 

Function Machines

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5

3

3

In context, use formulae expressed in words or symbols; substitute positive numbers into the formula to find the value of the subject.

 

 

 

Substitution

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5

3

4

Solve simple linear equations in which the unknown appears on one side including the use of a bracket, including by using inverse operations and by transforming both sides in the same way.

 

 

 

Solving One-Step Equations

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Solving Two-Step Equations

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5

3

5

Manipulate algebraic expressions by collecting like terms, including expanding brackets such as 3(x+2)

 

 

 

Collecting Like Terms

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Expanding Single Brackets

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5

4

6

Distinguish in meaning between the words: ‘equation’, ‘formula’, ‘identity’ and ‘expression’. Understand the ≠ (not equal) symbol.

 

 

 

Understanding Identities

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5

4

7

Manipulate algebraic expressions by multiplying a single letter term over a bracket a(2a + 5) and by taking out single term common factors.

 

 

 

Factorising Expressions

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5

4

8

Use systematic trial and improvement methods and ICT tools to find approximate solutions to equations such as x3 + x = 20

 

 

 

Trial and Improvement

 

 

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5

4

9

Form and solve linear equations including those with unknowns on both sides, including non integer coefficients.  Solve linear equations with integer coefficients in which the unknown appears on both sides of the equation, or with brackets, including by using inverse operations and by transforming both sides in the same way.

 

 

 

Form and Solve Linear Equations (Geometry Context)

 

 

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Solve Equations with x on both sides

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Solving Equations including the use of Brackets

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Solving Equations Mixed

 

 

 

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5

5

10

Use and generate formulae in context; substitute positive and negative numbers into a formula.

 

 

 

Substitution into more complex formulae

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5

5

11

Change the subject of a formula in cases where the subject only appears once.

 

 

 

Change the Subject of a Formula

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5

5

12

Expand the product of two linear expressions and simplify (x+2)(x-5)  Factorise simple quadratics

 

 

 

Expanding Double Brackets with a = 1

 

 

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Factorising Quadratics where a = 1 (inc Difference of 2 Squares)

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5

5

13

Form and Solve Simple Linear Inequalities in one Variable and represent the solution set on a number line.  Use inequaity notation and specify simple error intervals due to truncation or rounding.

 

 

 

Inequalities on the Number Line

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Solving Linear Inequalities

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Homework 1

 

5

5

14

Factorise and Solve quadratic expressions where a = 1, including the difference of two squares.

 

 

 

Expanding Two Brackets resulting in a > 1

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Solve Quadratics by Factorising (a = 1)

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5

6

15

Find the exact solution of two simultaneous equations in two unknowns by eliminating a variable algebraically.

 

 

 

Setting Up and Solving Simultaneous Equations

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Solving Simultaneous Equations involving Negatives

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Solving Simultaneous Equations non Integer Solutions

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5

6

16

Multiply expressions of the form (2x + 3)(3x – 7) and simplify the resulting expression, Factorise Quadratics where a>1

 

 

 

 

 

 

 

 

 

 

5

6

17

Factorise and Solve quadratic expressions where a = 1, including the difference of two squares.

 

 

 

 

 

 

 

 

 

 

5

6

18

Solve quadratic equations by drawing a graph and cubic equations graphically when the graph is given.

 

 

 

 

 

 

 

 

 

 

5

7

19

Use and generate formulae; change the subject of a formula, including simple cases where the subject appears twice or where a power of the subject appears.

 

 

 

 Change the Subject of a Formula where subject appears Twice

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5

7

20

Factorise and Solve quadratic expressions where a > 1, including the difference of two squares.

 

 

 

Factorising Quadratics where a > 1

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Solve Quadratics by Factorising (a > 1)

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5

7

21

Solve harder linear equations including those with fractional coefficients.

 

 

 

 

 

 

 

 

 

 

5

8

22

Solve quadratic equations by completing the square and using the quadratic formula.

 

 

 

The Quadratic Formula

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5

8

23

Locate turning points of a quadratic function by completing the square.

 

 

 

 

 

 

 

 

 

 

5

8

24

Solving Algebraic problems, e.g. explain why (n+1)(n+20) is an even number.   Proof by induction n(n + 1)(n + 2) is a multiple of 6

 

 

 

Cancelling Algebraic Fractions

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Adding Algebraic Fractions

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Multiplying Algebraic Fractions

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5

9

25

Manipulate algebraic expressions including fractions; solve related equations.

 

 

 

Equations Involving Algebraic Expressions

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5

9

26

Rearrange harder formulae, including cases where the subject appears twice, or where a power of the subject appears.

 

 

 

Rearranging harder Formulas

 

 

 

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5

9

27

Solve exactly, by elimination of an unknown, two simultaneous equations in two unknowns, one of which is linear, the other equation quadratic in one unknown or of the form x2 + y2 = r2.

 

 

 

Solving Simultaneous Equations involving Non Linear

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5

9

28

Expand the products of more than two binomials

 

 

 

 

 

 

 

 

 

 

5

9

29

Find approximate solutions using iteration

 

 

 

Iterative Methods

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5

9

30

Solve Quadratic Inequalities

 

 

 

 

 

 

 

 

 

 

5

9

31

Find Inverse and Composite Functions

 

 

 

Introduction to Functions

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