A1. Formulae & Equations Flashcards
Manipulate algebraic expressions & solve equations
Pronumerals
A pronumeral (or variable) is a letter in an equation or formula which represents a number.
Like Terms
Like Terms contain the same pronumeral(s) and indices
- 3ab, 10ab and 2ba are like terms
- 5b2 and -b2 are like terms
- 3m2 and 2m are unlike terms
Collecting Like Terms
Like terms can be collected (added or subtracted)
[1] 3a2 + 4a2 =
[2] 5mn - 2nm =
[3] 2a + 3b =
Like terms can be collected (added or subtracted)
[1] 3a2 + 4a2 = 7a2
[2] 5mn - 2nm = 3mn
[3] 2a + 3b = 2a + 3b
Indices and Index Laws
An index (or power or exponent) is used to abbreviate repeated multiplication.
Index Laws are rules for combing terms with indices.
Multiplying Terms
Like or unlike terms can be multiplied.
[1] 3ab × 5c =
[2] 4ab × 2a2c =
When multiplying terms, multiply the numbers and then multiply the variables.
[1] 3ab × 5c = 15abc
When multiplying the same pronumerals ADD their indicies.
[2] 4ab × 2a2c = 8a2bc
Dividing Terms
Like or unlike terms can be divided.
[1] 24abc ÷ 6ab =
[2] 15a5bc ÷ 3a2b =
Dividing Terms
When dividing terms, divide the numbers and then divide the pronumerals.
[1] 24abc ÷ 6ab = 4c
When dividing the same pronumerals, SUBTRACT their indicies.
[2] 15a5bc ÷ 3a2b = 5a3c
Raising Powers to Powers
• (2a5b2)3 =
When raising terms with powers to powers, MULTIPLY the powers.
• (2a5b2)3 = 23a15b<span>6</span> = 8a15b<span>6</span>
Don’t forget to raise the constant term in the brackets to the power as well.
Expanding Brackets
Expand 4(b + 6)
Expanding brackets means removing the brackets (grouping symbols) by multiplying each term inside the brackets by the term outside of the brackets.
Formula
A formula is a rule that describes a relationship between 2 or more variables.
The variable on the LHS is callled the SUBJECT of the formula.
Formula Applications - Medicine Dosage
The correct dosage of medicine for infants (babies up to 2 years) depends on the child’s age or weight.
Fried’s, Young’s or Clark’s rules can be used to convert an adult dosage to a child’s dosage. These formulas when required will be provided in the question.
Solving Equations
Solving equations require a series of ‘undo’ operations.
- Subtraction undoes _______
- Addition undoes _______
- Multiplication undoes _______
- Division undoes _______
- Square rooting undoes _______
- Squaring undoes _______
- Subtraction undoes Addition_
- Addition undoes Subtraction
- Multiplication undoes Division
- Division undoes Multiplication
- Square rooting undoes Squaring
- Squaring undoes Square Rooting
Two Step Equations
A 2-step requires two ‘undo’ steps to solve.
- Show all ‘undo’ steps on both sides of equation.
- Check answer by subsitution.
Equations With Brackets
First step - expand all brackets by multipllying each term inside the brackets by the term outside of the brackets.
Equations With Fractions
First Step - eliminate fractions by multiplying EVERY term on both sides of the equation by the lowest common multiple of the denominators.
Equations With Pronumerals on Both Sides
First Step - move the smallest pronumeral term first.