Math Essentials Cheat Sheet

A quick reference for fundamental Year 9 Victorian Curriculum math concepts including interest, ratios, 2D shapes, Pythagoras' theorem, algebra, and scientific notation.

Core Principles

• Understanding and applying simple and compound interest formulas.
• Calculating and simplifying ratios for comparison and scaling.
• Identifying properties and calculating areas/perimeters of common 2D shapes.
• Using Pythagoras' theorem to find unknown sides in right-angled triangles.
• Manipulating algebraic expressions and solving linear equations.
• Converting between standard form and scientific notation.

Action Steps

• 1. Identify the type of interest (simple/compound) and relevant variables (Principal, Rate, Time).
• 2. Calculate interest earned or total amount.
• 3. Simplify ratios by dividing by the greatest common divisor.
• 4. Determine the shape and its dimensions.
• 5. Apply the correct area or perimeter formula.
• 6. For right-angled triangles, identify the hypotenuse (c).
• 7. Substitute known sides into Pythagoras' theorem to solve for the unknown.
• 8. Simplify algebraic expressions by combining like terms.
• 9. Solve linear equations by isolating the variable.
• 10. Convert large numbers to scientific notation by moving the decimal and counting places.
• 11. Convert small numbers to scientific notation using negative exponents.
• 12. Convert from scientific notation back to standard form.

Formulas

• Simple Interest: $I = PRT$
• Compound Interest: $A = P(1 + R/n)^{nt}$
• Ratio Simplification: $a:b$ to lowest terms
• Pythagoras' Theorem: $a^2 + b^2 = c^2$
• Area of Rectangle: $A = lw$
• Area of Triangle: $A = 1/2 bh$
• Scientific Notation: $a \times 10^b$ where $1 \le |a| < 10$

Key Terms

• Interest: The cost of borrowing money or the return on investment.
• Ratio: A comparison of two or more quantities.
• 2D Shapes: Flat shapes with length and width, like squares, circles, and triangles.
• Pythagoras' Theorem: Relates the sides of a right-angled triangle.
• Algebra: Using symbols and letters to represent numbers and quantities.
• Scientific Notation: A way to express very large or very small numbers concisely.

Timeline

• Ancient Greece: Pythagoras and his theorem developed.
• 15th Century: Early forms of compound interest calculations emerge in banking.
• 17th Century: Algebraic notation and methods significantly advanced by mathematicians like Descartes.
• 18th Century: Development of standardized mathematical notation, including scientific notation.
• Modern Era: Integration of these concepts into school curricula worldwide, including Victoria.

People

• Pythagoras: Ancient Greek mathematician credited with the Pythagorean theorem.
• René Descartes: French philosopher and mathematician who significantly advanced algebra and notation.