Maths Worksheets

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

• Use the scale factor of a dilation to find image lengths and distances from the center of dilation
• Find coordinates of a point after a dilation using the scale factor
• Explain which geometric properties are preserved by dilations (angles and parallel lines) and which are scaled (lengths)

Learning Objectives

• Use the coordinate distance formula to find the length of a segment between two points
• Use the midpoint formula to find the point halfway along a segment
• Interpret distance and midpoint results in terms of symmetry and geometric relationships

Learning Objectives

• Interpret solutions of quadratic equations within real-world contexts.
• Evaluate the reasonableness and relevance of algebraic solutions in practical scenarios.
• Translate quadratic roots into meaningful interpretations related to problem situations.+ Show more

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

• Add and subtract complex numbers by combining real parts with real parts and imaginary parts with imaginary parts
• Multiply complex numbers using distributive and associative laws before replacing i² with -1
• Rewrite results clearly in the form a + bi by collecting like terms

Learning Objectives

• Develop skills in interpreting community data sets through calculations and analysis.
• Understand and evaluate data distributions, averages, and variability in real-world contexts.
• Apply mathematical reasoning to assess the reliability and limitations of data used for community decisions.+ Show more

Learning Objectives

• Interpret lengths on a scale drawing and identify corresponding drawing and actual lengths
• Find a scale factor as a ratio (actual ÷ drawing) and use it consistently
• Use the scale factor to calculate missing drawing or actual lengths+ 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

• Represent geometric objects using algebraic equations on the coordinate plane (lines, circles, and absolute value graphs).
• Justify coordinate geometry statements by reasoning algebraically about relationships, not by checking only a few cases.
• Use algebraic transformations (expanding, rearranging, substituting) to prove two conditions describe the same set of points.

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

• Use the power of a power rule to simplify expressions with exponents raised to other exponents.
• Use product and quotient rules for powers to combine or divide exponential terms.
• Convert between radicals and rational exponents correctly, including negative exponents.+ Show more

Learning Objectives

• Understand and apply different division algorithms for multi-digit numbers and decimals.
• Develop reasoning skills about remainders and use place value to solve division problems.
• Evaluate the accuracy and appropriateness of various division methods in real-world contexts.+ Show more

Learning Objectives

• Understand how to interpret the slope of a line in real-world contexts.
• Calculate the slope given data points and equations.
• Analyze the implications of positive and negative slopes in practical situations.+ Show more

Learning Objectives

• Translate ratio language (a:b form and words like “for every” and “per”) into consistent comparisons of two quantities
• Identify which two quantities are being compared in a ratio statement
• Use ratio language to match equivalent representations of the same ratio

Learning Objectives

• Develop mathematical reasoning and problem-solving skills related to perseverance.
• Apply self-regulation strategies to overcome challenging tasks.
• Interpret real-world scenarios using calculations involving percentages, measurements, and data.+ 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

• Convert between equivalent polynomial forms (expanded, factored, and vertex form) for quadratics
• Use factoring to identify zeros and x-intercepts of polynomial functions
• Use completing the square to rewrite quadratics in a form that reveals the vertex and maximum/minimum value+ 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

• Understand how exponential functions can model real-world growth and decay scenarios.
• Construct exponential models based on data and interpret their parameters.
• Apply exponential formulas to solve problems involving population growth, radioactive decay, and financial calculations.+ 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

• Recall and apply surface area formulas for cylinders, cones, pyramids, and spheres
• Connect 2D measures on faces (such as radius and slant height) to 3D surface area
• Use scaling ideas to explain how surface area and volume change for similar solids

Learning Objectives

• Interpret linear relationships using tables, graphs, and equations
• Identify the constant rate of change and link it to the slope of a graph
• Use an equation to model a real-world situation and make predictions

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

• Understand how to apply the Law of Sines to solve for missing sides or angles in triangles.
• Interpret real-world problems involving non-right triangles using the Law of Sines.
• Perform multi-step calculations accurately applying the sine law in various contexts.+ Show more

Learning Objectives

• Use two-way tables to find conditional probabilities
• Calculate conditional probabilities from counts using P(A|B) = A∩B / B
• Interpret what conditional probability means in context and compare different conditions

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

• Define residuals as the vertical difference between an observed data value and the predicted value from a line of best fit
• Compute and interpret residuals (including the meaning of positive vs negative residuals) to judge how well a linear model fits
• Use patterns in residuals to decide whether a linear fit is appropriate or if a different model may be needed

Learning Objectives

• Understand the concept of exponential decay and its mathematical representation.
• Apply decay models to real-world situations such as radioactive decay and depreciation.
• Interpret parameters within decay functions to analyze quantities over time.+ Show more

Learning Objectives

• Understand different methods of data collection such as surveys and observations.
• Apply mathematical calculations to interpret data gathered from real-world scenarios.
• Develop reasoning skills related to sampling techniques and ethical considerations in data gathering.+ Show more

Learning Objectives

• Understand the concept of inverse functions and their symmetry across the line y = x.
• Learn how to algebraically find inverse functions for various types of functions.
• Apply inverse functions to solve real-world problems involving data reversal and modeling.+ Show more

Learning Objectives

• Recognise how open and closed endpoints show strict and non-strict inequalities on a number line.
• Read a solution set from an inequality number line and write the matching inequality.
• Represent the solution set of an inequality using interval notation.

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

• 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 apply step-by-step algorithms to solve algebraic problems.
• Develop logical reasoning skills to interpret and evaluate solution sequences.
• Practice translating real-world problems into mathematical procedures.+ Show more

Learning Objectives

• Identify what the parts of an expression (coefficients, exponents, and factors) represent in a real situation
• Translate a word description into an algebraic expression and interpret the result
• Explain how changes to an expression’s structure affect the quantities it models

Learning Objectives

• Understand the characteristics of sinusoidal functions, including amplitude, period, and phase shift.
• Apply mathematical reasoning to interpret real-world data using sine models.
• Calculate parameters of sine functions from given data or scenarios.+ Show more

Learning Objectives

• Understand the basic criteria for triangle congruence, including side-angle-side and angle-side-angle.
• Apply the congruence criteria to determine whether two triangles are congruent in real-world contexts.
• Use logical reasoning and calculations to verify congruence of geometric figures.+ 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

• Understand and interpret the slope and intercepts of a linear relation.
• Apply the algebraic form of a line to solve real-world problems.
• Analyze graphs of lines to identify their properties and equations.+ Show more

Learning Objectives

• Interpret and calculate percentages in various contexts such as discounts, taxes, and markups.
• Translate between fractions, decimals, and percentages accurately.
• Apply proportional reasoning to real-world problems involving price changes.+ Show more

Learning Objectives

• Recognise when two figures are similar using corresponding angles and a constant scale factor.
• Calculate a corresponding length using multiplication (or division) with the scale factor from one figure to the similar figure.
• Interpret scale factor directions (from original to image, and image back to original) correctly.

Learning Objectives

• Understand different techniques of data collection such as surveys, observations, and experiments.
• Apply mathematical reasoning to analyze data collection scenarios and interpret results accurately.
• Evaluate the impact of method choices on data reliability and bias in real-world contexts.+ Show more

Learning Objectives

• Apply interest rate formulas to calculate loan and investment costs.
• Interpret data from financial models to compare options effectively.
• Solve multi-step problems involving budgets, repayment plans, and interest calculations.+ Show more