Maths Worksheets

Learning Objectives

• Use the Remainder Theorem to connect dividing by x-a to the value p(a).
• Use p(a)=0 to decide when x-a is a factor of p(x).
• Use non-zero remainders to rule out incorrect factors/roots.

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

• Write and interpret algebraic expressions using numbers, variables, and operation symbols.
• Use parentheses and order of operations to determine what an expression means.
• Evaluate expressions by substituting values for variables.

Learning Objectives

• Choose appropriate quantities and definitions so that a model’s calculated values represent the intended measurements.
• Read and interpret values accurately from absolute value graphs and linear inequality graphs used in quantity modeling.
• Justify whether a given point or computed value is consistent with a model (including strict vs inclusive conditions).

Learning Objectives

• Understand how geometric transformations affect the graphs of functions.
• Apply translation, stretching, and reflection concepts to analyze function graphs.
• Calculate the effects of transformations on key features such as domain, range, and symmetry.+ Show more

Learning Objectives

• Compare two data distributions using their center, spread, and shape.
• Interpret how differences in mean/median and measures of spread (range/IQR) affect conclusions.
• Use skewness and outliers to explain why summary statistics may differ between two data sets.

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

• Apply vector operations such as dot product and cross product to solve real-world physics and engineering problems.
• Interpret and model physical systems using vectors in multi-dimensional contexts.
• Perform multi-step calculations involving vector components, magnitudes, and angles with justified reasoning.+ Show more

Learning Objectives

• Write complex numbers in standard form a + bi and identify the real part a and imaginary part b
• Simplify expressions involving i using i^2 = -1
• Add and multiply complex numbers by combining real and imaginary parts correctly

Learning Objectives

• Learn to interpret solutions derived from mathematical models in real-world contexts.
• Evaluate the reasonableness and validity of solutions, including checking for extraneous solutions.
• Apply critical thinking to assess the practical relevance of solutions in everyday scenarios.+ Show more

Learning Objectives

• Use the proportional function rule y = kx to find unknown inputs or outputs
• Determine the constant of proportionality k from given values and apply it to new values
• Solve proportional relationships in context, interpreting the results as meaningful

Learning Objectives

• Interpret a quotient involving a fraction divided by a whole number using equal-size grouping.
• Interpret a quotient involving a whole number divided by a fraction as how many fractional-sized groups fit.
• Use multiplication to check division answers (divisor × quotient = dividend).+ Show more

Learning Objectives

• Understand how the second derivative determines the concavity of a function.
• Identify inflection points where the curvature changes sign.
• Apply second derivative tests to analyze the shape of graphs in real-world scenarios.+ Show more

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

• Interpret a fraction division statement (a/b) ÷ (c/d) as how many copies of (c/d) fit into (a/b)
• Use a tape diagram to represent fraction division and determine the quotient
• Solve simple equations that model fraction division as repeated equal-size pieces+ 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

• Interpret data from visual representations such as histograms and probability trees.
• Calculate combined probabilities in various scenarios.
• Apply probabilistic models to real-world decision-making situations.+ Show more

Learning Objectives

• Understand the algebraic computation of the dot product of vectors.
• Interpret the geometric meaning of the dot product in terms of vector magnitudes and angles.
• Apply the dot product to determine orthogonality and project vectors in real-world contexts.+ Show more

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

• Understand the formulas for simple and compound interest.
• Calculate interest accrued over different time periods.
• Apply interest concepts to real-world financial scenarios.+ Show more

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

• Understand and apply the product, quotient, and power rules of logarithms.
• Simplify logarithmic expressions and solve exponential equations using logarithmic properties.
• Relate logarithms to real-world contexts such as scientific measurements and financial calculations.+ Show more

Learning Objectives

• Identify the parameters a and b in an exponential function f(x)=a·b^x
• Construct an exponential model from initial value and growth/decay factor
• Use the model to make predictions by evaluating f(x) for given x

Learning Objectives

• Distinguish rational and irrational numbers using whether their decimal expansions terminate or repeat
• Convert between common fractions and decimals to determine if a decimal terminates or repeats
• Use number line and graphs to connect decimal behaviour to rational vs irrational classification

Learning Objectives

• Read a line plot to find key features such as the mode, range, and gaps.
• Describe the overall shape of a line plot by looking for clustering and spread.
• Use frequency information from stacked marks to support conclusions about where values concentrate and how values vary.

Learning Objectives

• Understand the concept of limits as the input approaches infinity and how functions behave at their end points.
• Calculate limits of polynomial and rational functions as x approaches infinity.
• Interpret horizontal asymptotes and relate them to the end behaviour of functions.+ Show more

Learning Objectives

• Apply mathematical reasoning to analyze financial data and marketing claims.
• Calculate percentages, discounts, and total costs in practical scenarios.
• Interpret data to make informed financial decisions based on mathematical analysis.+ Show more

Learning Objectives

• Understand strategies for maintaining perseverance in solving complex math problems.
• Apply goal setting and self-monitoring techniques during problem-solving tasks.
• Analyze how perseverance affects success in mathematical reasoning and real-world scenarios.+ Show more

Learning Objectives

• Construct linear models from real-world data and scenarios.
• Translate contextual information into algebraic expressions and graphs.
• Interpret the meaning of solutions within practical contexts.+ Show more

Learning Objectives

• Understand the principles of simple interest and how savings grow over time.
• Apply interest calculation formulas to real-world saving scenarios.
• Interpret data related to savings and interest to make financial decisions.+ Show more

Learning Objectives

• Understand how to calculate and interpret unit prices in shopping scenarios.
• Apply arithmetic operations to compare costs of different products or services.
• Develop skills to analyze and interpret real-world cost data for informed decision-making.+ Show more

Learning Objectives

• Understand how to represent real-world situations using algebraic and graphical models.
• Compare the effectiveness of different modeling methods in context-based problems.
• Justify appropriate modeling choices based on accuracy, clarity, and relevance.+ Show more

Learning Objectives

• Identify appropriate mathematical representations such as graphs, equations, and models for different types of problems.
• Analyze how choosing different representations can enhance understanding and problem-solving strategies.
• Apply various representations to interpret data, solve problems, and communicate mathematical ideas effectively.+ Show more

Learning Objectives

• Identify the rule that generates terms in a numeric pattern
• Use algebraic expressions to describe linear and geometric pattern rules
• Translate between a pattern rule and a condition using inequalities+ Show more

Learning Objectives

• Analyze marketing claims related to credit cards, loans, and savings plans.
• Calculate and compare interest rates and costs to evaluate financial benefits.
• Interpret advertised benefits using mathematical reasoning.+ Show more

Learning Objectives

• Understand how equations represent real-world physical situations in coordinate geometry.
• Apply algebraic and geometric methods to interpret and solve relation-based problems.
• Develop critical reasoning skills to verify solutions and assess the accuracy of models in practical contexts.+ Show more

Learning Objectives

• Create and use expressions for simple budgets involving income and expenses
• Solve one-step equations connected to saving and spending plans
• Compare saving and spending outcomes using percentages and fractions

Learning Objectives

• Understand the concept of sequences and patterns in mathematics.
• Apply rules and formulas to generate and analyze sequences.
• Use sequences to model real-world situations and introduce basic coding concepts.+ Show more

Learning Objectives

• Understand different types of mathematical models such as linear equations and geometric representations.
• Apply mathematical reasoning to interpret data and predict outcomes in real-world scenarios.
• Evaluate the accuracy and limitations of various modeling techniques.+ Show more

Learning Objectives

• Understand methods for transforming algebraic expressions, including expanding, factoring, and simplifying.
• Evaluate the equivalence of different forms of expressions and their application in solving problems.
• Apply properties of operations to justify algebraic transformations.+ Show more

Learning Objectives

• Calculate and compare costs associated with different payment options including fees and interest.
• Apply percentages to determine transaction fees and interest charges in real-world scenarios.
• Interpret financial data to make responsible payment choices based on cost-benefit analysis.+ Show more

Learning Objectives

• Understand the concept of simple interest and how it is calculated.
• Apply interest formulas to real-world scenarios involving savings and loans.
• Interpret interest rates and assess their impact on financial decisions.+ Show more

Learning Objectives

• Understand the construction of composite trigonometric functions and interpret their graphical properties.
• Apply trigonometric identities and the unit circle to analyze phase shifts and combined functions.
• Solve real-world problems involving periodic phenomena using advanced trigonometric models.+ Show more

Learning Objectives

• Apply trigonometric functions to analyze real-world periodic phenomena.
• Interpret parameters such as amplitude, phase shift, and frequency in modeling scenarios.
• Solve multi-step problems involving modeling cyclic behavior in physics and engineering.+ Show more

Learning Objectives

• Understand the different forms of numerical representations: fractions, decimals, and percents.
• Convert between fractions, decimals, and percents accurately in practical contexts.
• Evaluate the effectiveness of each representation in data interpretation and decision-making.+ Show more

Learning Objectives

• Interpret income sources and expenses to make informed financial decisions.
• Apply percentages and calculations to project future savings or expenditures.
• Analyze how different choices influence personal financial stability.+ Show more

Learning Objectives

• Understand how exponents model exponential growth and decay in real-world contexts.
• Apply the rules of exponents to solve practical problems involving scaling, population growth, and decay.
• Interpret and analyze exponential functions through calculations and reasoning.+ Show more

Learning Objectives

• Apply percentage calculations to real-world financial scenarios.
• Interpret and analyze income and expense data to set realistic financial goals.
• Develop multi-step problem-solving strategies for budgeting and saving.+ Show more