Grade 9 Maths Worksheets

Learning Objectives

• Factor rational expressions to reveal common numerator and denominator factors.
• Simplify rational expressions by canceling matching factors while tracking excluded values.
• Explain why a simplified rational expression is equivalent only for allowed input values.

Learning Objectives

• Understand and apply volume formulas for prisms, cylinders, and other three-dimensional figures.
• Perform unit conversions and estimate volumes in real-world scenarios.
• Assess the reasonableness of calculated volumes and interpret their significance.+ Show more

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

• Understand how to analyze and compare different financial products using unit prices and interest rates.
• Develop problem-solving skills involving calculations of costs, percentages, and interest over time.
• Apply mathematical reasoning to evaluate consumer choices related to savings, loans, and credit options.+ Show more

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 fractional reasoning to interpret ratios and proportions in real-world scenarios.
• Solve practical problems involving division of resources, discounts, and data interpretation using fractions.
• Develop strategies for multi-step calculations involving fractions in everyday contexts.+ Show more

Learning Objectives

• Understand basic mathematical concepts used in financial modeling.
• Apply percentage and ratio calculations to personal finance scenarios.
• Interpret and analyze financial data to make informed budgeting decisions.+ Show more

Learning Objectives

• Rewrite algebraic expressions using exponent rules for products, quotients, and powers-to-a-power
• Create equivalent exponent forms and identify which rule justifies each rewrite
• Solve for variables in equations by first rewriting expressions into simpler exponent forms

Learning Objectives

• Find and interpret median and interquartile range (IQR) from a box plot and explain what they say about center and spread.
• Use mean/median and range/IQR to compare two data sets, especially when one distribution is skewed or has outliers.
• Justify which statistical measure (median vs mean, IQR vs range) is most appropriate for a given distribution shape.

Learning Objectives

• Develop clarity in articulating mathematical ideas using precise language, symbols, and visual tools.
• Apply reasoning and problem-solving skills to interpret and communicate mathematical concepts and solutions.
• Use effective mathematical notation and explanations to enhance collaboration and understanding.

Learning Objectives

• Understand the relationship between decimals and percentages and convert between them.
• Apply conversion skills to interpret data and solve real-world problems involving percentages and decimals.
• Develop problem-solving strategies for multi-step calculations involving percentage and decimal representations.+ Show more

Learning Objectives

• Classify real numbers as rational or irrational
• Use the rule for sums to predict whether a sum is rational or irrational without full evaluation
• Reason about rationality patterns when adding rational and irrational numbers+ Show more

Learning Objectives

• Identify lines of symmetry in geometric figures.
• Calculate angles of rotation required for symmetry.
• Apply symmetry concepts to real-world design and patterns.+ Show more

Learning Objectives

• Understand and calculate measures of variability such as range, interquartile range, and standard deviation.
• Interpret the extent of data variation and its implications for data reliability.
• Apply concepts of variability to real-world data sets for better analysis and decision-making.+ Show more

Learning Objectives

• Identify opposite, adjacent, and hypotenuse sides in right triangles
• Select the correct trigonometric ratio for a given angle
• Calculate missing side lengths using sine, cosine, or tangent+ Show more

Learning Objectives

• Evaluate function notation such as f(x) by substituting an input value and simplifying to find the output.
• Interpret statements like f(a) = b to describe what output b corresponds to for the input a in context.
• Connect the input (the value inside f( )) and the output (the value of f( )) correctly when reading and writing function values.

Learning Objectives

• Apply mathematical reasoning to model and analyze financial scenarios.
• Calculate interest, savings growth, and expense impacts over time.
• Interpret financial data to make informed decisions.+ Show more

Learning Objectives

• Understand how to calculate simple interest using the interest formula.
• Apply interest calculations to real-life financial scenarios involving savings and loans.
• Interpret the effects of principal, rate, and time on the total interest earned or paid.+ Show more

Learning Objectives

• Apply mathematical symbols and language to articulate reasoning clearly.
• Use diagrams and models to justify and verify solutions efficiently.
• Solve multi-step problems involving calculations, data interpretation, and real-world contexts.+ Show more

Learning Objectives

• Understand different sampling methods and their applications
• Calculate biases and interpret data from various samples
• Analyze the impact of sampling variability on data analysis+ Show more

Learning Objectives

• Understand how to calculate experimental probabilities from data gathered through trials.
• Interpret data to compare experimental results with theoretical probabilities.
• Apply probability concepts to real-world scenarios involving randomness and sample size.+ Show more

Learning Objectives

• Interpret a decimal expansion as a location on a number line
• Use truncations of a decimal to form successive approximations and understand what they do to accuracy
• Distinguish rational and irrational numbers by how their decimal expansions behave on the number line

Learning Objectives

• Understand different methods of data collection such as surveys and observational studies.
• Apply sampling techniques to gather representative data.
• Interpret data sets to assess their validity and accuracy.+ Show more

Learning Objectives

• Understand and apply different methods for measuring the length of geometric objects.
• Convert and compare measurement units in real-world contexts.
• Calculate the perimeter of polygons accurately using appropriate formulas.+ Show more

Learning Objectives

• Apply mathematical calculations to interpret personal financial data.
• Analyze income and expenses to assess budgeting effectiveness.
• Use percentages and data interpretation skills in practical financial scenarios.+ Show more

Learning Objectives

• Use the Inscribed Angle Theorem: an inscribed angle equals half the measure of the corresponding central angle that intercepts the same arc.
• Use the same-arc property: inscribed angles that intercept the same arc are congruent.
• Set up and solve simple equations to find unknown angle measures in circle diagrams.

Learning Objectives

• Derive linear equations from real-world problems involving distance, cost, and quantities.
• Solve for variables in linear equations and interpret solutions within practical scenarios.
• Apply understanding of linear equations to analyze data, make predictions, and interpret graphical models.+ Show more

Learning Objectives

• Apply mathematical calculations to analyze different budgeting options.
• Interpret financial data to make informed decisions about expenses and savings.
• Evaluate the effectiveness of various budgeting strategies through logical reasoning.+ Show more

Learning Objectives

• Understand how geometric figures are represented in coordinate planes.
• Apply algebraic methods to analyze properties such as symmetry and congruence.
• Perform calculations involving distance, midpoints, and transformations in coordinate systems.+ Show more

Learning Objectives

• Use the distance formula to find the length of a segment between two points on a coordinate plane
• Compute horizontal and vertical changes (Δx and Δy) and substitute them into the distance formula
• Interpret squared differences to handle negative coordinates correctly

Learning Objectives

• Understand how to construct and interpret mathematical models and visual representations.
• Apply mathematical reasoning to analyze real-world problems involving growth, measurements, and data.
• Evaluate the effectiveness of different models and representations in solving complex problems.+ Show more

Learning Objectives

• Rewrite quadratic equations and expressions in completing-square (vertex) form
• Solve quadratic equations by transforming them into a perfect-square equation
• Use square roots to find all real solutions after completing the square

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

• Evaluate combined functions such as (f+g)(x), (f-g)(x), (fg)(x), and (f/g)(x) at a given x-value.
• Write combined function rules in terms of f(x) and g(x), including simplifying when possible.
• Identify restrictions on x for (f/g)(x) when the denominator function equals 0.

Learning Objectives

• Understand the hierarchy of operations in mathematical expressions used in models.
• Apply order of operations to evaluate complex formulas accurately.
• Interpret real-world scenarios involving calculations with correct operation sequencing.+ 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

• Calculate and interpret the amount of interest accrued over different periods.
• Understand the impact of interest on total debt repayment.
• Evaluate different borrowing options based on interest rates and terms.+ Show more

Learning Objectives

• Recognize difference of squares and perfect square trinomial patterns
• Rewrite polynomials into equivalent factored (product) forms using identities
• Use factored forms to identify when a polynomial equals zero

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

• Identify the x-values that create holes in rational functions when factors cancel.
• Simplify rational expressions by cancelling common factors and describing the domain restrictions.
• Explain why cancelling a common factor produces a hole rather than a vertical asymptote.

Learning Objectives

• Understand how to perform addition, subtraction, multiplication, and division with integers.
• Apply integer operations to solve real-world problems involving financial transactions and temperature changes.
• Develop strategies for accurate computation and reasoning with integers.+ 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

• Reinforce understanding of key geometric concepts, properties, and measurement strategies.
• Apply geometric reasoning and calculations to solve real-world problems.
• Analyze shape properties, transformations, and similarity in practical contexts.+ Show more

Learning Objectives

• Describe what it means for a relationship to be a function (each input maps to exactly one output).
• Use a context to write an explicit function rule that models the relationship between two quantities.
• Evaluate a function and solve for inputs using an equation based on the function rule.+ Show more

Learning Objectives

• Develop strategic mathematical reasoning through collaborative discussion and problem-solving.
• Apply computation and interpretation skills in real-world contexts involving percentages, measurements, and data analysis.
• Enhance understanding of multi-step problem solving by sharing reasoning and debating strategies.+ Show more

Learning Objectives

• Identify and use the fact that a radius perpendicular to a chord bisects the chord
• Use the right angle formed by a perpendicular radius to relate radii, distances to chords, and half-chord lengths
• Solve for unknown chord segment lengths using midpoint and perpendicular constraints

Learning Objectives

• Describe whether a function’s output increases or decreases as the input changes using interval notation.
• Read increasing/decreasing intervals from a graph by using key features such as intercepts/vertices and direction.
• Interpret monotonic trends from a table and translate them into interval notation.

Learning Objectives

• Understand how to create graphs from linear equations and tables.
• Interpret the slope and intercepts of a linear graph in real-world contexts.
• Apply algebraic and graphical methods to solve problems involving linear relations.+ Show more