Year 9 Maths Mid-Year Exam Revision

Comprehensive practice flashcards covering Financial Mathematics, Algebra, Linear Equations, and Geometry based on Year 9 Mid-Year Exam revision notes.

How do you calculate a percentage increase of 15% using a single multiplier?

$$Original \times 1.15$$

When finding the original price (going backwards) after a percentage discount, which operation should be used?

Division (divide the new price by the decimal equivalent of the percentage paid)

What are the standard conversion values for Yearly to Weekly and Yearly to Fortnightly income?

Yearly = Weekly $\times 52$; Fortnightly = Yearly $\div 26$

In financial mathematics, what is the formula for Gross Pay when overtime is involved?

$$\text{Gross pay} = (\text{Normal hours} \times \text{Rate}) + (\text{Overtime hours} \times \text{Overtime rate})$$

What is the formula for income tax for the $120,001–$180,000 bracket according to the provided lecture notes?

$$29,467 + 0.37 \times (\text{Taxable Income} - 120,000)$$

How is GST calculated on a price that already includes it to find the GST amount alone?

Divide the GST-inclusive price by $11$

What is the Simple Interest formula, and what do the variables represent?

$I = \frac{P \times r \times t}{100}$, where $P$ is Principal, $r$ is rate (% per year), and $t$ is time (years)

What does the FOIL method stand for when expanding binomial products?

First terms, Outer, Inner, Last

What are the two Perfect Square identities?

$(a + b)^2 = a^2 + 2ab + b^2$ and $(a - b)^2 = a^2 - 2ab + b^2$

According to the Difference of Two Squares identity, what does $(a + b)(a - b)$ expand to?

$$a^2 - b^2$$

What is the Highest Common Factor (HCF) of $15a^2b$ and $10ab^2$?

$$5ab$$

What is the 'Keep, Change, Flip' rule for algebraic fractions?

Keep the first fraction, change the division sign to multiplication, and flip the second fraction

What is the golden rule for solving linear equations using the balance method?

Whatever you do to one side, you must do to the other

On a number line, when should you use an open circle versus a closed circle for inequalities?

Open circle for $<$ or $>$ (value not included); closed circle for $\leq$ or $\geq$ (value included)

What must you do to the inequality sign when multiplying or dividing by a negative number?

Flip the sign (e.g., $\leq$ becomes $\geq$)

What are the three main methods discussed for solving simultaneous equations?

Graphical, elimination, and substitution

What does the symbol $\cong$ represent in geometry?

Congruent (identical in shape and size)

List the four tests for triangle congruence.

SSS (Side-Side-Side), SAS (Side-Angle-Side), AAS (Angle-Angle-Side), and RHS (Right-Hypotenuse-Side)

Why is AAA (Angle-Angle-Angle) not enough to prove congruence?

It only proves similarity (same shape) but does not guarantee the same size; at least one matching side is needed to anchor the size

How do you calculate the scale factor between two similar triangles?

$$\text{Scale factor} = \frac{\text{side of new}}{\text{side of original}}$$