Transcript File

3. Further algebraic skills and
techniques
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Adding and subtracting like terms
To add and subtract algebraic terms:
1. Find the like terms.
2. Only like terms can be added or subtracted.
3. Add
or subtract the coefficients or numbers before the
pronumeral of the like terms.
To add and subtract algebraic fractions
1. Find a common denominator, preferably the lowest.
Express each fraction as an equivalent fraction with the
common denominator.
3. Simplify the numerator by adding/subtracting like terms
2.
HSC Hint – Circle like terms, including the sign in front of the
term. Add or subtract the circled like terms.
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Index laws
Index form or index notation is used to write expressions
in a shorter way such as a × a = a2.
1.
a m ´ a n = a m+n
2.
a m ¸ a n = a m-n
3.
(a m ) n = a mn
a0 = 1
Use the index laws when multiplying and dividing
algebraic terms to form a single algebraic expression.
4.
HSC Hint – When multiplying − add the index.
When dividing − subtract the index.
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Equations
Look to perform the opposite operation.
 + is opposite to −
 × is opposite to ÷
2. Add or subtract the same number to both sides.
1.
3.
4.
Multiply or divide the same number to both sides.
To solve two- or three-step equations repeat the
above steps. It is often easier to first add or subtract
the same number to both sides of the equation.
HSC Hint – Do one step at a time and set work out down
the page. One equal sign per line.
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Solving equations after substitution
4.
Write the formula.
Replace the variables in the formula with the numbers
given in the question.
Solve the equation if the unknown is not the subject.
Evaluate using the calculator.
5.
Write the answer to the specified level of accuracy.
1.
2.
3.
HSC Hint – Check your solution to the equation by
substituting the answer back into the equation.
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Changing the subject of the 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.
HSC Hint – Circle the pronumeral that needs to be made
the subject. Use the same techniques you use
for solving an equation and solve for this
pronumeral.
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Simultaneous equations – 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
pronumeral.
4. Substitute this value into one of the equations to find
the value of the second pronumeral.
HSC Hint – Use the substitution method if one
pronumeral is the subject of the equation.
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Simultaneous equations – Elimination
1. Make sure that the two coefficients of one pronumeral
are the same. This may require multiplying and
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.
HSC Hint – Do not forget to find the value of both
pronumerals (step 4).
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