Grade 9 Maths Worksheets

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

• Interpret what a factor does to the value of an expression (multiplying a whole quantity).
• Use coefficients to explain how scaling changes an output.
• Interpret exponents as repeated multiplication and apply this meaning in expressions.+ Show more

Learning Objectives

• Identify when two figures are similar using equal corresponding angles and proportional corresponding side lengths
• Use the scale factor between similar figures to find unknown side lengths
• Solve similarity problems involving proportional relationships and apply angle equality to find missing angles+ 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

• 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

• 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

• Describe how a dilation scales distances from a fixed center using a scale factor
• Find the image of points under a dilation using coordinates and the scale factor
• Use dilation properties to reason about proportional segments, preserved angles, and parallel lines

Learning Objectives

• Interpret what each variable in a formula represents by using unit reasoning
• Use a formula to calculate an output while checking that units are consistent
• Rewrite formulas and apply unit-based thinking to confirm constants and conversion factors

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

• 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

• 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

• 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

• 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

• Factorise quadratic trinomials using integer factor pairs
• Use the factored form to solve quadratic equations
• Identify the zeros (solution values) from factored products

Learning Objectives

• Use the Remainder Theorem to find the remainder when a polynomial is divided by a linear factor
• Convert remainder information into an equation involving p(a) and solve for unknown coefficients
• Check understanding by distinguishing correct and incorrect statements about remainders

Learning Objectives

• Use the Remainder Theorem to find the remainder when dividing a polynomial by (x − a)
• Evaluate p(a) quickly by substitution, without performing long division
• Use remainders to solve for unknown parameters inside a polynomial

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

• Clear denominators in rational equations to form equivalent polynomial (often quadratic) equations
• Identify excluded values (values that make denominators zero) when solving rational equations
• Solve the resulting quadratic and check candidate solutions against excluded values

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

• 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

• Identify what coefficients, factors, and exponents represent in an algebraic expression.
• Interpret how changing parts of an expression changes the quantity described in a context.
• Translate between worded descriptions and algebraic expressions using correct structure.+ 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

• 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

• 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

• 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

• Identify the input and output variables from a table of reliable data pairs.
• Construct an explicit functional rule that matches the pattern in a table.
• Use the rule to predict output values for new inputs.

Learning Objectives

• Interpret key features of a graph (points, slope/shape, vertex) to determine a function rule.
• Use coordinate pairs on a graph to find an explicit equation and describe how outputs change as inputs change.
• Use the domain shown by the graph when applying the model beyond the plotted points.

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

• Identify x-intercepts and y-intercepts from a coordinate grid by reading where a graph crosses the axes.
• Interpret x-intercepts as input values where the output equals 0 (zeros).
• Interpret the y-intercept as the output value when the input is 0.+ Show more

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

• Use function composition (f∘g)(x)=f(g(x)) to build a new function
• Evaluate composed functions for given inputs while respecting domain constraints
• Solve equations involving composed functions

Learning Objectives

• Identify relative maxima and relative minima (turning points) from a function graph.
• Connect turning points to meaningful peaks and dips in the modeled quantity.
• Describe end behavior using output values as inputs become very large in magnitude or approach domain boundaries.

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

• Read a dot plot (line plot with stacked markers) to determine frequencies for specific values.
• Interpret histogram-style information by using bin boundaries to count how many observations fall in each interval.
• Use bin width correctly when comparing how often values occur (clusters vs gaps).

Learning Objectives

• Identify typical values (centre) such as the median and mode from line plots and box plots.
• Interpret spread (range and IQR) to describe variability and how it affects reliability or risk in real contexts.
• Use shape features (skewness, clustering, and gaps) and outliers to explain differences between data sets.

Learning Objectives

• Use box plots to compare the center (median) and spread (IQR) of two groups.
• Use line plots to compare typical values and variability between groups by describing where most data cluster.
• Make informal comparative inferences about populations using sample summaries, including uncertainty and the effect of outliers.

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

• Read a box plot to identify the five-number summary: minimum, Q1, median, Q3, and maximum.
• Calculate and interpret the interquartile range (IQR) from Q1 and Q3, including what it says about the middle 50% of the data.
• Use the 1.5 × IQR rule to identify outliers on a box plot.+ Show more

Learning Objectives

• Factorise quadratics into the form (x − r)(x − s)
• Use the zero-product property to find solutions of (x − r)(x − s) = 0
• Interpret the number and location of solutions from the factors

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 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

• Interpret income sources and calculate total income.
• Create and analyze a basic personal budget plan.
• Apply percentages to determine expenses and savings.+ 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 data sets to identify patterns and relationships.
• Apply mathematical reasoning to analyze trends in data.
• Use line graphs and scatter plots to interpret data changes.+ 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

• Calculate the mean, median, and mode of various data sets.
• Compare and interpret measures of central tendency in real-world contexts.
• Apply measures of central tendency to analyze data from surveys, test scores, and measurements.+ Show more

Learning Objectives

• Understand and interpret probability concepts in real-world scenarios.
• Calculate probabilities based on data and models.
• Assess the consistency of experimental results with theoretical probabilities.+ Show more