Maths Worksheets

Learning Objectives

• Understand the process of constructing regression models from data.
• Calculate and interpret the slope and intercept in the context of real-world data.
• Apply regression analysis to predict outcomes based on variable relationships.+ Show more

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

• Determine slope using rise and run from two points on a coordinate grid
• Compare slopes from different pairs of points on the same line to confirm slope is constant
• Use sign (positive/negative/zero) to interpret slope direction from points

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

• Apply vector operations to calculate areas, distances, and angles in geometric figures.
• Model diagonals and sides of polygons using vectors to analyze spatial relationships.
• Utilize scalar and vector products to determine angles and areas in real-world contexts.+ Show more

Learning Objectives

• Understand the concept of vertical and horizontal asymptotes and their role in function behaviour.
• Apply algebraic and graphical techniques to identify asymptotes of rational and exponential functions.
• Analyze the relationship between limits and asymptotic behaviour to interpret function trends.+ Show more

Learning Objectives

• Understand that converting a decimal to a percent means multiplying by 100
• Convert decimals (including decimals greater than 1) into percents
• Relate the size of a decimal to the size of its percent value

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

• Understand the concept of continuity at critical points of functions.
• Apply limit calculations to determine continuity at points where derivatives are zero or undefined.
• Analyze the behavior of functions near critical points to identify potential extrema.+ Show more

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

• 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 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

• Write composed functions using the correct order (f ∘ g)(x) = f(g(x)).
• Evaluate composed function models by substituting one function into another.
• Interpret composed models as multi-step processes where one output becomes the next input.+ Show more

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

• Translate word and graphical constraints into inequalities in one variable.
• Solve one-variable inequalities and describe the solution set correctly.
• Explain how inequality direction changes when multiplying or dividing by a negative number.+ Show more

Learning Objectives

• Identify the role of coefficients and constant terms in algebraic expressions
• Explain how each part of an expression affects the overall value in context
• Use structure (addition and multiplication in particular) to simplify and interpret expressions+ Show more

Learning Objectives

• Use relative frequency (number of successes ÷ number of trials) to estimate a probability.
• Describe how relative frequency tends to stabilize as the number of trials increases.
• Compare experimental estimates to a probability model using closeness (error).+ 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

• Understand the importance of sampling methods and biases in data collection.
• Apply mathematical reasoning to evaluate the trustworthiness of data sets.
• Perform calculations involving percentages, averages, and data interpretation in real-world contexts.+ Show more

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

• Read ratio relationships from tape (strip) diagrams by using the part counts as equal ratio groups.
• Scale a diagram to find equivalent ratios and missing quantities while keeping the same comparison units.
• Use diagram reasoning to determine missing values in totals and part-to-part comparisons.

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

• 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 a line of best fit to model the overall trend in a scatter plot
• Calculate the slope and intercept of a best-fit line and interpret what they mean
• Use a best-fit line to make reasonable predictions within the domain of the data+ Show more

Learning Objectives

• Apply probability concepts to practical scenarios such as finance, sports, and engineering.
• Calculate expected values and interpret probability distributions in real-world contexts.
• Develop problem-solving skills involving multi-step probability calculations and data analysis.+ Show more

Learning Objectives

• Understand the properties of logarithms and how to apply them to solve equations.
• Develop skills to rewrite and manipulate logarithmic and exponential expressions.
• Apply logarithmic methods to solve real-world problems involving growth, decay, and data interpretation.+ Show more

Learning Objectives

• Translate a real-world situation into a one-variable equation using a clear variable definition
• Solve linear one-variable equations using inverse operations
• Interpret the solution by checking that it fits the original situation

Learning Objectives

• Understand different types of discontinuities in functions and their characteristics.
• Apply graphical and analytical methods to identify and classify discontinuities.
• Solve real-world problems involving functions with points of discontinuity.+ Show more

Learning Objectives

• Apply algebraic methods to solve real-world multi-variable problems.
• Interpret graphical data to analyze complex systems.
• Construct models that reflect intricate phenomena in practical contexts.+ Show more

Learning Objectives

• Rearrange algebraic formulas to isolate a chosen variable using inverse operations.
• Maintain algebraic equivalence by performing the same operation to both sides of an equation.
• Substitute into rearranged formulas accurately and interpret results using constraints (e.g., non-zero denominators, non-negative roots).

Learning Objectives

• Use a common nonzero denominator to clear fractions from both sides of an equation.
• Solve the resulting equation with integer coefficients and keep the same solution set.
• Connect clearing denominators to checking solutions in the original fractional equation.

Learning Objectives

• Describe congruence using transformations such as translations, reflections, and rotations.
• Use coordinates to find the image of points after a transformation.
• Verify congruence by comparing corresponding lengths in transformed figures.

Learning Objectives

• Use the unit circle to determine the signs of sine and cosine in each quadrant
• Convert between angle measures and the corresponding sine/cosine values using reference angles
• Model periodic behavior by interpreting amplitude, period, and phase shift in sine and cosine functions

Learning Objectives

• Solve equations of the form x² = a and x³ = a using exact radical solutions
• Express solutions symbolically using square roots and cube roots (not decimals)
• Relate radical solutions to their positions on the number line

Learning Objectives

• Write a polynomial function in factored form from given zeros and multiplicities
• Use multiplicity to determine whether the graph crosses or bounces at each x-intercept
• Determine end behavior from the degree and leading coefficient of a factored polynomial

Learning Objectives

• Solve one-variable equations and interpret the solution in context
• Solve and interpret one-variable inequalities, including checking boundary values
• Translate a real-world scenario into an equation or inequality in one variable+ 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

• Solve quadratic equations in one variable by using factoring, completing the square, or the quadratic formula when appropriate
• Recognize which solving method best matches the structure of a quadratic equation
• Interpret solutions in context (e.g., intersection points or times when a value is 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

• Use the identity i^2 = −1 to expand products and powers involving complex numbers.
• Verify polynomial identities by expanding both sides and simplifying to the same polynomial form.
• Factor and expand expressions with complex factors while keeping results in valid polynomial form.

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

• Apply mathematical reasoning to interpret workplace data such as surveys and reports.
• Calculate and compare percentages, averages, and trends in organizational data.
• Analyze data to support decision-making related to safety, productivity, and morale.+ Show more

Learning Objectives

• Classify numbers as rational or irrational
• Use closure properties to predict whether an expression is rational or irrational
• Apply addition and multiplication rules involving rational and irrational numbers

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

Learning Objectives

• Interpret square root notation as the magnitude whose square equals a nonnegative number
• Solve equations of the form x^2 = p using square roots, including both positive and negative solutions
• Connect algebraic solutions to radical form using ±√p+ Show more

Learning Objectives

• Explain why corresponding angle measures stay the same when making a scale drawing.
• Use angle preservation to find the actual angle from the angle shown on the drawing.
• Justify that scaling changes lengths but not the opening between intersecting rays.

Learning Objectives

• Compare rational numbers by using their positions relative to 0 on the number line.
• Order rational numbers with different signs and with the same sign.
• Use absolute value (distance from 0) to justify comparisons.

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