Maths Worksheets

Learning Objectives

• Understand and apply different methods—factoring, completing the square, and quadratic formula—to solve quadratic equations in practical contexts.
• Develop problem-solving skills for interpreting quadratic relations within real-world scenarios such as budgeting or measurements.
• Select the most efficient method based on data availability and problem complexity in applied situations.+ Show more

Learning Objectives

• Identify and analyze key attributes of two- and three-dimensional figures, including side lengths, angles, and symmetry.
• Apply geometric properties such as parallelism, perpendicularity, and congruence to classify shapes and solve problems.
• Use real-world scenarios to interpret and calculate measurements related to geometric figures.+ Show more

Learning Objectives

• Understand the concept of complex roots in quadratic and polynomial functions.
• Apply formulas to find complex roots of quadratic equations.
• Analyze how complex roots influence the graph and behavior of polynomial functions.+ Show more

Learning Objectives

• Find the conjugate of a complex number and use it to rationalise denominators in division
• Simplify complex-number quotients into standard form a+bi by eliminating the imaginary part of the denominator
• Identify the real and imaginary parts of a quotient after conjugate multiplication

Learning Objectives

• Understand how to formulate algebraic expressions and equations based on real-world data.
• Apply algebraic methods to interpret and analyze models of phenomena such as population growth and resource consumption.
• Evaluate the accuracy and limitations of algebraic models in practical contexts.+ Show more

Learning Objectives

• Identify proportional relationships of the form y = kx and the meaning of the constant of proportionality k
• Use plotted points on a coordinate grid to find k and write the rule y = kx
• Complete a ratio table for a proportional relationship and determine missing values+ Show more

Learning Objectives

• Understand the concept of ratios and how to compare quantities using proportional reasoning.
• Apply ratios to solve real-world problems such as scaling recipes and calculating speeds.
• Interpret and analyze proportional relationships in different contexts.+ Show more

Learning Objectives

• Identify proportional relationships on a coordinate grid by checking that the line passes through the origin.
• Use plotted points on a proportional graph to find the constant of proportionality k and the equation y = kx.
• Interpret proportional graphs using rate reasoning: compute and compare y/x values for nonzero points.+ Show more

Learning Objectives

• Use vertical angle relationships to set up equations that show two angles are equal
• Use linear pair (supplementary) relationships to set up equations that add to 180°
• Solve equations to find unknown angle measures and explain why the equation matches the diagram

Learning Objectives

• Apply volume formulas for prisms and related solids using correct base area and dimensions
• Solve measurement problems by finding missing dimensions or comparing volumes
• Use consistent units and interpret calculated volumes in context

Learning Objectives

• Translate contextual statements about input and output into correct function notation (e.g., f(a)=b).
• Interpret given function values to explain what the model says about inputs and outputs.
• Evaluate function expressions at specified inputs to find outputs.

Learning Objectives

• Interpret confidence levels as evidence from repeated sampling and avoid common misinterpretations.
• Use confidence intervals (and estimated margins of error) to justify conclusions about population parameters.
• Explain how sampling variability can produce different sample statistics while still being consistent with the same population.+ Show more

Learning Objectives

• Read dot plots, histograms, and box plots to identify key features such as shape, center, and spread
• Interpret one-to-one scales by connecting visual features (median, quartiles, bar heights) to quantitative meaning
• Distinguish typical values from extreme values (outliers) using graphical information and the 1.5×IQR rule

Learning Objectives

• Understand and calculate the mean, median, and mode of data sets.
• Interpret measures of central tendency in real-world contexts.
• Compare the usefulness and limitations of different measures considering data skewness and outliers.+ Show more

Learning Objectives

• Translate real situations into probability models using clear assumptions about the sample space and equally likely outcomes
• Use probability models to compute likelihoods, including complements
• Compare scenarios by using the probability model outcomes rather than intuition+ Show more

Learning Objectives

• Apply polynomial and rational functions to model real-world phenomena.
• Translate real-world situations into algebraic functions and interpret data.
• Solve problems involving function optimization, analysis, and parameter effects.+ Show more

Learning Objectives

• Recognize and create equivalent polynomial forms by expanding and factoring.
• Simplify equivalent rational expressions while correctly identifying excluded values.
• Use alternative forms (like vertex/standard forms or graph features) to reveal key properties without changing the represented values.

Learning Objectives

• Represent constraints using inequalities and boundary lines
• Interpret how the inequality direction determines the shaded solution region
• Use inequality substitution to test whether points satisfy a constraint+ Show more

Learning Objectives

• Understand the structure of polynomial expressions and identify individual terms.
• Apply rules for combining like terms and factorization to simplify polynomial expressions.
• Use polynomial expansion techniques to analyze the behavior of polynomial functions.+ Show more

Learning Objectives

• Translate a situation with constraints into an equation in one variable
• Solve equations by using algebraic steps and by interpreting solutions
• Use absolute value graphs to solve absolute value equations

Learning Objectives

• Understand the structure and properties of rational expressions
• Simplify rational expressions and identify their domain restrictions
• Apply rational expressions to solve real-world problems involving proportions and constraints+ Show more

Learning Objectives

• Understand methods for solving linear and quadratic equations.
• Apply algebraic manipulation and factoring techniques to find solutions.
• Represent systems of equations graphically and algebraically.+ Show more

Learning Objectives

• Understand and recall fundamental trigonometric identities including Pythagorean, angle sum, and double-angle identities.
• Apply identities to simplify complex trigonometric expressions and solve equations involving various angles.
• Interpret identities both geometrically and algebraically to enhance reasoning about function symmetries and transformations.+ Show more

Learning Objectives

• Rearrange algebraic formulas to make a chosen variable the subject using equivalent transformations.
• Use the rearranged form to interpret how changing one quantity affects another.
• Check that two formula forms are equivalent by substituting values.

Learning Objectives

• Multiply rational expressions by factoring and cancelling common factors efficiently
• Simplify products of rational expressions into equivalent rational expressions
• Identify restrictions on variables from denominator factors that cannot be zero

Learning Objectives

• Write function rules from verbal descriptions that describe how one quantity depends on another.
• Use patterns in data (constant difference vs constant ratio) to decide on a function type and write the correct model.
• Interpret parameters such as starting value and growth factor when writing exponential (ratio-based) functions.

Learning Objectives

• Compute conditional probabilities using P(A|B) = P(A ∩ B) / P(B).
• Translate situations into conditional-probability calculations from counts and tables.
• Interpret what conditional probability means and how it differs from P(B|A).

Learning Objectives

• Rewrite expressions to reveal structure, such as common factors and repeated terms, without changing the value.
• Use exponent and absolute value structure to produce equivalent forms that are easier to simplify or interpret.
• Connect different representations (graph form, vertex form, piecewise form) by rewriting expressions carefully.

Learning Objectives

• Translate real situations into equations/inequalities using two variables.
• Interpret how changing one variable affects the other in a two-variable model.
• Graph linear inequalities in two variables by describing which side of the boundary line to shade.+ Show more

Learning Objectives

• Recognize that similarity transformations keep angle measures the same while changing side lengths by a common scale factor.
• Use transformation sequences (dilations, rotations, reflections, translations) to map one figure to a similar figure on a coordinate grid.
• Find scale factors and corresponding lengths using ratios and proportional reasoning.

Learning Objectives

• Apply the distributive property to expand expressions with parentheses to form an equivalent equation.
• Combine like terms on each side to simplify to a linear equation in one variable.
• Solve the resulting linear equation by isolating the variable while keeping both sides balanced.+ Show more

Learning Objectives

• Use addition or subtraction to eliminate a variable when solving a system of two linear equations
• Solve the resulting one-variable linear equation after elimination
• Substitute back into an original equation to find the second variable and the ordered pair

Learning Objectives

• Rewrite expressions using the power of a power rule: (a^m)^n = a^(mn).
• Use the product of powers rule: a^m · a^n = a^(m+n) and the quotient rule: a^m ÷ a^n = a^(m−n).
• Solve exponent equations by rewriting both sides with the same base and equating exponents.

Learning Objectives

• Explain how integer exponents represent repeated multiplication and repeated division
• Use the exponent rules for integer powers (including zero and negative exponents) to find equivalent expressions
• Rewrite expressions with integer exponents as equivalent numerical values

Learning Objectives

• Solve linear equations with rational coefficients by eliminating fractions and isolating the variable
• Use equivalent transformations (same operation on both sides) to keep an equation balanced
• Verify solutions by substituting back into the original equation+ Show more

Learning Objectives

• Convert numbers between standard form and scientific notation
• Use exponent rules to multiply and divide numbers written in scientific notation
• Compare numbers in scientific notation using their powers of 10

Learning Objectives

• Solve linear equations in one variable using the properties of equality while keeping both sides balanced.
• Use inverse operations to isolate the variable, including when the equation has fractions or like terms.
• Check solutions by substituting the value back into the original equation.

Learning Objectives

• Solve a pair of simultaneous linear equations in two variables to find the ordered pair that satisfies both equations
• Connect the algebraic solution of a system to the intersection point of the graphs
• Identify whether a system has one solution, no solution, or infinitely many solutions

Learning Objectives

• Use substitution to rewrite one equation to express one variable in terms of the other
• Substitute that expression into the second equation to form and solve a one-variable equation
• Determine the corresponding value of the second variable and write the ordered pair solution

Learning Objectives

• Understand proportional relationships can be written in the form y = kx.
• Identify and interpret the constant of proportionality k as the unit rate.
• Solve simple equations of the form kx = y to find x or k.+ Show more

Learning Objectives

• Apply sequential percent changes using multiplicative factors (e.g., discount then tax).
• Represent percent change using parts of a 100% tape diagram model.
• Translate percent situations into equations and solve for the unknown original amount.+ Show more

Learning Objectives

• Use the distributive property with rational coefficients (fractions and negatives) to expand expressions with parentheses
• Rewrite equivalent expressions by distributing the same rational factor to every term inside parentheses
• Combine like terms after distribution to simplify correctly+ Show more

Learning Objectives

• Recognise that proportional relationships form straight lines that pass through the origin.
• Find the unit rate (slope) k from plotted points on a line through the origin.
• Use y = kx to predict y-values for new x-values and check whether a point fits the relationship.

Learning Objectives

• Use tape diagrams to interpret ratios and ratios that stay equivalent when quantities are scaled.
• Solve multi-step ratio scaling problems by applying proportional scale factors consistently across steps.
• Check that intermediate and final quantities keep the same ratio.

Learning Objectives

• Track units through multiplication and division to determine the unit of a derived quantity
• Identify the correct derived unit from a given formula and unit assignments
• Use unit checking to confirm whether an answer matches the situation

Learning Objectives

• Round measured or calculated values to the correct number of significant digits based on the precision of the measuring tool.
• Choose appropriate decimal places when adding or subtracting quantities measured with different accuracies.
• Use significant digits to make meaningful comparisons, including when values are written in scientific notation.+ Show more

Learning Objectives

• Use the rules for products involving rational numbers and irrational numbers
• Apply the “nonzero” condition when multiplying a rational number by an irrational number
• Classify expressions as rational or irrational without fully evaluating them

Learning Objectives

• Complete proportional tables by finding missing values using a constant ratio y/x
• Use the constant of proportionality y/x to extend patterns in tables
• Check whether a table represents a proportional relationship by comparing y/x across rows+ Show more