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AM3 Further Algebraic Skills and Techniques

Basic Concepts: Manipulating algebra

Adding and subtracting algebraic fractions Using index laws Expand brackets and simplify expressions

Substitutions Solving equations, including simultaneous equations

Change the subject of a formula

Revision of Preliminary work:

Algebraic Fractions

Index Laws As you hopefully remember from stage 5 work

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1 Look to perform the opposite operation (+ is opposite to -, is opposite to ). 2 Add or subtract the same number to both sides of the

equation OR 3 Multiply or divide both sides of the equation by the same number.

4 To solve harder equations, repeat these steps as required. It is often easier to first add or subtract the same number to both sides of the equation.

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Formulae A formula is a mathematical relationship between two or more variables. To solve:

1 Write the formula. 2 Replace the variables in the formula with the numbers given in the question.

3 If the unknown is not the subject of the equation, solve the equation. 4 Evaluate using the calculator.

5 Write the answer to the specified level of accuracy and correct units if necessary.

Step it up Changing the Subject of a

Formula Move the other pronumerals and numbers, except the pronumeral you want as the subject, to the right-hand side of

the equation. To move any term or number: 1 Look to perform the opposite operation (+ is opposite to -,

is opposite to ). 2 Add or subtract the same term or number to both sides of the equation OR

3 Multiply or divide both sides of the equation by the same number.

=

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Solving Simultaneous Equations Graphica This is done by graphing equations and observing where they

cross each other. Solving Simultaneous

Solving simultaneous equations involves substituting one Equations

equation into the other and solving for the remaining variable. There are two ways to solve: Method A)

Substitution 1 Make one pronumeral the subject in one of the equations. 2 Substitute the expression for this subject into the other

equation. 3 Solve this new equation to find the value of one y =2 x 11 1

pronumeral. 2 to find the =19

4 Substitute this value into one of+ the equations

1 value of the second pronumeral. h

+ ( 2 11 )=19 e.g. solve simultaneously:

3 +11=19 =10 h1

y =2(10)11 2

y =9

. 2

Method B) Elimination 1 Make sure that the two coefficients of one pronumeral are

the same. This may require multiplying or dividing one or both equations by a number. 2 Eliminate one pronumeral by adding or subtracting the two

equations. 3 Solve this new equation to find the value of one pronumeral.

4 Substitute this value into one of the equations to find the value of the second pronumeral.

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