3. Further algebraic skills and techniques Cambridge University Press 1 G K Powers 2013 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 Find a common denominator, preferably the lowest. Express each fraction as an equivalent fraction with the common denominator. Simplify the numerator by adding/subtracting like terms
HSC Hint Circle like terms, including the sign in front of the term. Add or subtract the circled like terms. Cambridge University Press 2 G K Powers 2013 Index laws Index form or index notation is used to write expressions in a shorter way such as a a = a2. 1. am an =am+n 2. am an =am- n 3.
(am) n =amn 4. a0 =1 Use the index laws when multiplying and dividing algebraic terms to form a single algebraic expression. HSC Hint When multiplying add the index. When dividing subtract the index. Cambridge University Press 3 G K Powers 2013 Equations 1.
2. 3. 4. Look to perform the opposite operation. + is opposite to is opposite to Add or subtract the same number to both sides. 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. Cambridge University Press 4 G K Powers 2013
Solving equations after substitution 1. 2. 3. 4. 5. 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. Write the answer to the specified level of accuracy. HSC Hint Check your solution to the equation by substituting the answer back into the equation. Cambridge University Press 5
G K Powers 2013 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. Cambridge University Press 6
G K Powers 2013 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. Cambridge University Press 7 G K Powers 2013
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). Cambridge University Press 8 G K Powers 2013
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