Maths Worksheets

Learning Objectives

• Identify how exponential growth changes multiplicatively from one step to the next.
• Compare exponential and linear patterns to determine which grows faster and when a crossover occurs.
• Use limits to describe long-term behavior of exponential decay toward a nonzero value.

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

• 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

• 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

• 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 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

• Apply polynomial and rational functions to model real-world phenomena.
• Translate real-world situations into algebraic functions and interpret data.
• Solve problems involving function optimization, analysis, and parameter effects.+ Show more

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

• Understand the concept of expected value as the long-term average outcome of random variables.
• Apply probability and outcomes to calculate expected value in real-world scenarios.
• Interpret expected value as a measure of central tendency in probabilistic models.+ Show more

Learning Objectives

• Use the formula for the area of a triangle, A = (1/2) · b · h, where h is the perpendicular height to the base b.
• Read base and perpendicular height values from a triangle diagram and compute the triangle’s area.
• Find a missing base or height using the triangle area formula by setting up and solving an equation.+ 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

• 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

• Use an equation to model a relationship between two variables and interpret what ordered pairs satisfy the equation.
• Connect the form of a function (including absolute value transformations) to key features on its graph, such as the vertex.
• Interpret and describe linear inequalities in two variables using a coordinate-plane model and test points.

Learning Objectives

• Analyze the end behavior of polynomial functions based on degree and leading coefficient.
• Determine the roots and multiplicities of polynomials through factoring and interpret their effects on graph shape.
• Apply polynomial concepts to model real-world situations involving data trends and patterns.+ Show more

Learning Objectives

• Compare exponential and linear models by evaluating them at multiple input values
• Identify how multiplicative (exponential) growth differs from additive (linear) growth
• Find and interpret the crossover point where an exponential model overtakes a linear model+ Show more

Learning Objectives

• Determine the area scale factor when all lengths in a scale drawing are multiplied by the same scale factor
• Use the rule area scale factor = (length scale factor)² to find missing areas
• Interpret how changing linear dimensions affects surface coverage on a scale drawing

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

• Understand and apply basic trigonometric identities to solve equations.
• Solve trigonometric equations within specified intervals using algebraic and graphical methods.
• Interpret solutions of trigonometric equations in real-world contexts, such as periodic phenomena.+ Show more

Learning Objectives

• Identify proportional relationships on a coordinate grid by checking that the line passes through the origin.
• Use plotted points on a proportional graph to find the constant of proportionality k and the equation y = kx.
• Interpret proportional graphs using rate reasoning: compute and compare y/x values for nonzero points.+ Show more

Learning Objectives

• Choose an appropriate reporting accuracy (decimal places or significant figures) based on the smallest measurement precision.
• Apply rounding rules correctly for addition/subtraction and multiplication/division while keeping precision consistent through calculations.
• Avoid misleading precision by rounding final answers to match what the data can support.

Learning Objectives

• Understand and apply algebraic techniques to evaluate limits analytically.
• Interpret limits graphically and from tables to determine function behavior near points and at infinity.
• Solve multi-step limit problems involving rationalization, factorization, and special limits.+ Show more

Learning Objectives

• Solve equations of the form px + q = r by using equivalent transformations to isolate the variable.
• Handle fractions and negative numbers correctly when subtracting q and dividing by p.
• Check that a proposed value makes the original equation true.

Learning Objectives

• Explain how sampling variability affects sample statistics and uncertainty in conclusions
• Interpret confidence intervals and explain what they mean (and do not mean)
• Use sample size and estimates (e.g., p̂) to compute standard error and confidence intervals

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

• Recognise proportional relationships by checking whether corresponding values form equivalent ratios
• Use constant multiplicative change (a single scale factor) to find missing values in proportional situations
• Identify the constant of proportionality k in models of the form y = kx

Learning Objectives

• Use a scale factor to convert a drawing length to an actual length in a scale drawing.
• Set up and use a consistent correspondence between matching segments to find missing lengths.
• Solve simple equations that model proportional relationships in scale drawings.

Learning Objectives

• Understand and apply the Law of Sines to solve non-right triangles in real-world contexts.
• Use the Law of Cosines to find unknown sides or angles in oblique triangles.
• Develop reasoning skills to interpret given data and justify solutions in geometric problems.+ Show more

Learning Objectives

• Express complex numbers in the form a + bi and identify the real part a and imaginary coefficient b
• Rewrite expressions involving i into standard complex form a + bi
• Interpret and use the values of a and b to understand properties of complex numbers+ Show more

Learning Objectives

• Understand different sampling techniques and their applications in data collection.
• Apply mathematical reasoning to interpret sampling data and estimate populations.
• Calculate sample sizes, probabilities, and margins of error in practical scenarios.+ Show more

Learning Objectives

• Use the triangle area formula A = (1/2)bh to find the area of a geometric component on a scale drawing.
• Apply a uniform scale factor to relate drawing areas to actual areas.
• Use additive area relationships to combine areas of parts to get a total actual area.+ Show more

Learning Objectives

• Understand the differences between discrete and continuous probability distributions.
• Calculate probabilities for discrete events and interpret probability density functions.
• Apply concepts of probability distributions to real-world scenarios involving data and measurements.+ Show more

Learning Objectives

• Use scale factors to fill in missing entries in a proportional ratio table
• Use unit rate reasoning to find the output for any input in a proportional relationship
• Explain why corresponding entries in a proportional table stay in the same ratio

Learning Objectives

• Understand how to formulate algebraic expressions and equations based on real-world data.
• Apply algebraic methods to interpret and analyze models of phenomena such as population growth and resource consumption.
• Evaluate the accuracy and limitations of algebraic models in practical contexts.+ 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 how trigonometric functions can model real-world periodic phenomena.
• Interpret amplitude, period, and phase shift in the context of oscillating patterns.
• Apply formulas for sine and cosine functions to solve practical problems involving periodic motion.+ Show more

Learning Objectives

• Understand the concept of amortization and its application in loan repayment.
• Calculate periodic loan payments using amortization formulas.
• Interpret amortization schedules to analyze principal and interest payments over time.+ 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

• Use volume formulas to find the volume of cylinders, cones, and spheres.
• Substitute values for radius and height into the correct formula and simplify accurately.
• Solve for an unknown radius or height using volume relationships.+ Show more

Learning Objectives

• Understand how derivatives are used to find critical points in optimization problems.
• Apply second derivative tests to determine local maxima and minima of functions.
• Solve real-world optimization problems involving areas, volumes, and economic profits.+ 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

• Define relative frequency as the fraction of times an event occurs in repeated trials
• Calculate relative frequency from a set of observed counts (and simplify the fraction)
• Use relative frequency to estimate probability and interpret it as long-run behavior

Learning Objectives

• Translate real situations into probability models using clear assumptions about the sample space and equally likely outcomes
• Use probability models to compute likelihoods, including complements
• Compare scenarios by using the probability model outcomes rather than intuition+ Show more

Learning Objectives

• Understand how degrees of numerator and denominator affect the end behavior of rational functions.
• Interpret asymptotes and complex features in the graphs of rational functions.
• Apply transformations and composite functions to analyze rational graphs.+ Show more

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

• Translate word statements into linear equations of the form px + q = r
• Identify the variable, coefficient(s), and constant when rewriting a situation as an equation
• Solve linear equations after rewriting from words

Learning Objectives

• Evaluate functions by substituting an input value into a given function rule.
• Use a function graph to find outputs for specific inputs.
• Solve for the input when an output value is given for an absolute value function.+ Show more

Learning Objectives

• Use circle similarity to relate radii, circumferences, arc lengths, and areas through scale factors.
• Apply constant ratios such as \(\frac{C}{r}=2\pi\) and \(\frac{A}{r^2}=\pi\) to solve problems.
• Determine how circumference and area change when the radius is multiplied by a scale factor.

Learning Objectives

• Understand and apply the fundamental principles of counting in real-world scenarios.
• Calculate the total number of outcomes for combined independent events.
• Interpret and solve problems involving permutations and combinations.+ Show more