Maths 2025 Notes

Products and Factors

Binomial

• Algebraic expression with 2 terms
  • Example: 4a + 9, + 5x

Binomial Product

• Expression with 2 or more binomials multiplying together
  • Example: (4a + 9)(5a - 3)

Expand

• Rewrite an expression without grouping
  • Example: 5(3a - 10) = 15a - 50

Factorise

• Rewrite expression with grouping by taking out the highest common factor
  • Example: 5 + 125x = 5x(x + 25)

Perfect Square

• A square number or expression representing one

Quadratic Expression

• Highest power of variable is 2

Quadratic Trinomial

• Quadratic expression with 3 terms

Important Points:

• BODMAS is crucial in solving and factorizing algebraic expressions.
• Only like terms can be added or subtracted.
• Terms with indices can only be multiplied or divided with like terms.
• Use HCF for factorizing coefficients.
• FOIL method: Multiply first, outside, inside, last terms.

Trigonometry

Triangle Sides

• Opposite Side: Directly opposite a given angle in a right-angled triangle.
• Adjacent Side: Directly adjacent to a given angle in a right-angled triangle.
• Hypotenuse: Longest side of a right-angled triangle, opposite the 90-degree angle.

Angle Concepts

• Angle of Elevation: Angle of looking up from the horizon.
• Angle of Depression: Angle of looking down from the horizontal.

Bearing

• Angle showing direction from one location to another.

Important Points:

• Pythagoras Theorem: a² + b² = c²
• Hypotenuse is always opposite the right angle.
• Trigonometry applies only to right-angled triangles.

Bearings

• True Bearings: Measured from true north, written with 3 digits.
• Compass Bearings: Based on angle from North or South.

Equations

Key Concepts

• Consecutive Numbers: 3, 4, 5, 6, etc.
• Equation: Mathematical statement that two quantities are equal.
• Formula: Rule written as an algebraic expression.
• Inverse Operation: Opposite used in solving equations; e.g., inverse of multiplication is division.
• Linear Equation: Involves a variable not raised by a power.
• Quadratic Equation: Involves a squared variable.

Simplifying Surds

• Square Root: Simplify by finding factors where one is a perfect square.
• Cube Root: Simplify similarly but with a perfect cube.

Important Points:

• Always substitute the variable with your answer to verify correctness.
• Use inverse trig ratios (sin-1, cos-1, tan-1) for unknown angles.

Numeracy and Calculations

Financial Concepts

• Cost Price: Retailer cost price.
• GST: 10% tax added to the original price.
• Loss and Profit: Amounts lost or made when selling items.
• Principal: Amount of money invested or borrowed.
• Recurring Decimal: Decimal with repeating digits.

Important Points:

• Percentages are reversible (x% of y = y% of x).
• Simplifying ratios and rates is crucial.
• Unitary method is effective for finding amounts through percentages.

Earning Money

Financial Terms

• Allowable Deduction: Part of income not taxed.
• Annual Leave Loading: Extra payment based on 17.5% of 4 weeks leave.
• Income Tax: Tax based on gross income.
• Net Pay: Pay after deductions.
• Overtime Pay: Higher rate for time beyond normal hours.

Important Concepts

• Simple Interest Formula: I = Prn where I = Interest, P = Principal, r = interest rate, n = years.
• Salary vs. Wage: Salary is fixed annually; wage depends on hours worked.
• Commission and Royalties: Calculated as a percentage of sales or use of work.

These notes cover essential concepts in algebra, trigonometry, and financial mathematics, providing a structured overview of key formulae and methods used in solving mathematical problems.