Year 8 Mathematics Half Yearly Assessment Study Guide

Chapter 1: Computation with Positive and Negative Integers

• 1A Adding and subtracting positive integers (Consolidating): Review of basic arithmetic operations with whole numbers greater than zero.
• 1B Multiplying and dividing positive integers (Consolidating): Review of product and quotient calculations for positive whole numbers.
• 1C Number properties (Consolidating): Review of fundamental properties such as commutativity, associativity, and identity.
• 1D Divisibility and prime factorisation (Consolidating): Determining factors of numbers and expressing integers as a product of their prime factors.
• 1E Negative integers (Consolidating): Introduction and review of numbers less than zero on the number line.
• 1F Adding and subtracting negative integers (Consolidating): Rules for directed number arithmetic, specifically addition and subtraction involving negatives.
• 1G Multiplying and dividing negative integers (Consolidating): Rules for signs in multiplication and division (e.g., a negative multiplied by a negative results in a positive).
• 1H Order of operations and substitution: Calculating expressions using the correct sequence (BODMAS/BIDMAS) and substituting integer values into algebraic expressions.

Chapter 4: Measurement and Pythagoras’ Theorem

• 4A Length and perimeter (Consolidating): Calculation of the total boundary distance of two-dimensional shapes.
• 4B Circumference of circles (Consolidating): Using the formulas $C = 2\pi r$ or $C = \pi d$ to find the boundary of a circle.
• 4C Area (Consolidating): Review of the space inside standard two-dimensional shapes.
• 4D Area of special quadrilaterals: Formulas and calculations for the area of parallelograms, trapeziums, rhombuses, and kites.
• 4E Area of circles: Using the formula $A = \pi r^2$ to calculate the area of a circle.
• 4F Area of sectors and composite figures: Calculating areas of circle fragments (sectors) and shapes composed of multiple standard figures.
• 4G Surface area of prisms (Extending): Calculating the total external area of all faces of a three-dimensional prism (extension level).
• 4H Volume and capacity: Understanding three-dimensional space occupancy and the volume of liquid a container holds.
• 4I Volume of prisms and cylinders: Calculating the volume using the formula $V = Ah$ (Area of cross-section $\times$ height) and $V = \pi r^2 h$ for cylinders.
• 4J Units of time and time zones (Consolidating): Conversions between time units and calculations involving different geographical time zones.
• 4K Introducing Pythagoras’ theorem: Understanding the relationship $a^2 + b^2 = c^2$ in right-angled triangles.
• 4L Using Pythagoras’ theorem: Applying the theorem to find the length of the hypotenuse ($c$).
• 4M Calculating the length of a shorter side: Rearranging the theorem to find lengths of legs ($a$ or $b$) where $a^2 = c^2 - b^2$.

Chapter 5: Algebraic Techniques and Index Laws

• 5A The language of algebra (Consolidating): Understanding and using technical terms such as term, coefficient, constant, and expression.
• 5B Substitution and equivalence: Replacing variables with numerical values and determining if two algebraic expressions are equivalent.
• 5C Adding and subtracting terms: Simplifying algebraic expressions by identifying and combining like terms.
• 5D Multiplying and dividing terms: Applying rules of multiplication and division to simplify algebraic terms and expressions.
• 5E Adding and subtracting algebraic fractions (Extending): Applying fractional arithmetic to expressions containing variables (extension level).
• 5F Multiplying and dividing algebraic fractions (Extending): Applying product and quotient rules to algebraic fractions (extension level).
• 5G Expanding brackets: Using the distributive law to multiply a single term over the terms inside a set of parentheses.
• 5H Factorising expressions: The reverse of expansion, identifying the highest common factor to rewrite expressions with brackets.
• 5I Applying algebra: Translating word problems into algebraic equations and using techniques to solve them.
• 5J Index laws for multiplication and division: Applying laws for powers with identical bases: $(a^m \times a^n = a^{m+n})$ and $(a^m \div a^n = a^{m-n})$.
• 5K The zero index and power of a power: Understanding the zero index law $(a^0 = 1, a \neq 0)$ and the power of a power law $((a^m)^n = a^{mn})$.