A1. Formulae & Equations Flashcards

Manipulate algebraic expressions & solve equations

1
Q

Pronumerals

A

A pronumeral (or variable) is a letter in an equation or formula which represents a number.

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2
Q

Like Terms

A

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
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3
Q

Collecting Like Terms

Like terms can be collected (added or subtracted)

[1] 3a2 + 4a2 =

[2] 5mn - 2nm =

[3] 2a + 3b =

A

Like terms can be collected (added or subtracted)

[1] 3a2 + 4a2 = 7a2

[2] 5mn - 2nm = 3mn

[3] 2a + 3b = 2a + 3b

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4
Q

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.

A
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5
Q

Multiplying Terms
Like or unlike terms can be multiplied.

[1] 3ab × 5c =

[2] 4ab × 2a2c =

A

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

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6
Q

Dividing Terms

Like or unlike terms can be divided.

[1] 24abc ÷ 6ab =

[2] 15a5bc ÷ 3a2b =

A

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

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7
Q

Raising Powers to Powers

• (2a5b2)3 =

A

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.

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8
Q

Expanding Brackets

Expand 4(b + 6)

A

Expanding brackets means removing the brackets (grouping symbols) by multiplying each term inside the brackets by the term outside of the brackets.

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9
Q

Formula

A

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.

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10
Q

Formula Applications - Medicine Dosage

The correct dosage of medicine for infants (babies up to 2 years) depends on the child’s age or weight.

A

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.

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11
Q

Solving Equations

Solving equations require a series of ‘undo’ operations.

  • Subtraction undoes _______
  • Addition undoes _______
  • Multiplication undoes _______
  • Division undoes _______
  • Square rooting undoes _______
  • Squaring undoes _______
A
  • Subtraction undoes Addition_
  • Addition undoes Subtraction
  • Multiplication undoes Division
  • Division undoes Multiplication
  • Square rooting undoes Squaring
  • Squaring undoes Square Rooting
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12
Q

Two Step Equations

A 2-step requires two ‘undo’ steps to solve.

A
  • Show all ‘undo’ steps on both sides of equation.
  • Check answer by subsitution.
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13
Q

Equations With Brackets

A

First step - expand all brackets by multipllying each term inside the brackets by the term outside of the brackets.

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14
Q

Equations With Fractions

A

First Step - eliminate fractions by multiplying EVERY term on both sides of the equation by the lowest common multiple of the denominators.

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15
Q

Equations With Pronumerals on Both Sides

A

First Step - move the smallest pronumeral term first.

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16
Q

Formulas & Equations

Sometimes after a value is subsituted into a formula the result is an equation which must be solved.

A

Find the value of a if S = 14.

17
Q

Changing the Subject

Some formulas can be rearranged to make another variable the new subject of the formula.

A

To change the subject use the same ‘undo’ steps as for solving an equation.

18
Q

Speed, Distance & Time

A
19
Q

BAC Formulas

The Blood Alcohol Content is the concentration of alcohol (in mg) per 100 mL of blood.

A

Different formulas are used to calculate BAC in males and females because of their different body builds.

20
Q

Returning BAC to Zero

A normal body can only reduce the BAC by about 0.015 to 0.020 per hour.

A
21
Q

Converting Units of Speed

It is necessary to convert speed measured in km/h into m/s to calculate Reaction Time Distance.

A

1 hour = 60 × 60 s = 3600 s

22
Q

Reaction Time Distance

A

Reaction Time Distance is the distance a car travels in the time between the decision to stop and applying the brakes.

Use Distance = Speed × Time

23
Q

Braking Distance

A

Braking Distance is the distance a car travels before coming to a stop after the brakes have been applied. Using the braking distance formula usually involves finding the value of the constant k.

24
Q

Stopping Distance

A

Stopping distance is the sum of the Reaction Time Distance (RTD) and the Braking Distance.