Maths Worksheets

Learning Objectives

• Calculate the surface area of a right rectangular prism by adding the areas of matching face pairs.
• Use the formula SA = 2(lw + lh + wh) for edge lengths l, w, and h.
• Apply the same multiplication structure when one or more side lengths are fractional.

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

• Understand and identify the symmetry properties of functions, including even and odd functions.
• Analyze the end behavior of rational and exponential functions using algebraic and graphical methods.
• Apply concepts of symmetry and end behavior to interpret function limits, asymptotes, and long-term trends.+ Show more

Learning Objectives

• Solve multi-step rate problems using equations that model a fixed fee plus a unit rate times a quantity.
• Use ratio reasoning to scale quantities while keeping the same rate relationship.
• Interpret results in context and check that answers make sense with units and the story of the problem.

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

• Apply trigonometric ratios to model real-world phenomena such as navigation and engineering.
• Formulate mathematical models involving periodic functions and interpret their results in context.
• Solve multi-step problems involving angles, distances, and wave patterns using trigonometry.+ Show more

Learning Objectives

• Understand that solving x^3 = p gives x = ∛p
• Use cube root notation correctly for positive and negative values of p
• Evaluate cube roots by checking that cubing the result gives p

Learning Objectives

• Identify variability in a data set by describing how spread out the values are (range and IQR).
• Read box plots to find quartiles and interpret the IQR as a measure of variability.
• Use line plots to describe variability by finding the mode, range, clusters, and gaps.+ Show more

Learning Objectives

• Describe how translations, rotations, and reflections move points on a 2D coordinate grid.
• Calculate the image of a point under a specified rigid motion.
• Use properties of rigid motions to verify that distances and angles are preserved.

Learning Objectives

• Understand and perform vector operations in three-dimensional space.
• Calculate angles and distances between vectors in space.
• Apply vector analysis to real-world problems involving navigation and physics.+ Show more

Learning Objectives

• Recognise that proportional relationships form straight lines that pass through the origin.
• Find the unit rate (slope) k from plotted points on a line through the origin.
• Use y = kx to predict y-values for new x-values and check whether a point fits the relationship.

Learning Objectives

• Combine successive rational changes (rises and drops) to find a net change in context
• Use rational multipliers and fractions to scale quantities and interpret the meaning of the result
• Check whether a rational answer makes sense by interpreting its direction and magnitude in the scenario

Learning Objectives

• Understand the concept of confidence intervals for population means and proportions.
• Apply formulas to calculate confidence intervals in real-world scenarios.
• Interpret the results of statistical inference to make informed decisions.+ Show more

Learning Objectives

• Use the inscribed angle theorem to find an inscribed angle from its intercepted arc.
• Use the relationship between an inscribed angle and its intercepted arc to find missing arc measures.
• Justify that inscribed angles subtending the same arc are congruent.+ Show more

Learning Objectives

• Solve linear equations in one variable using the properties of equality while keeping both sides balanced.
• Use inverse operations to isolate the variable, including when the equation has fractions or like terms.
• Check solutions by substituting the value back into the original equation.

Learning Objectives

• Explain how random sampling and sampling variability affect statistical conclusions.
• Distinguish between a population parameter and a sample statistic when making inferences.
• Interpret confidence intervals as estimates that reflect uncertainty, not exact values.+ Show more

Learning Objectives

• Understand the properties and transformations of exponential and logarithmic functions.
• Apply inverse relationships between exponential and logarithmic functions to solve equations.
• Interpret real-world data involving exponential growth and decay using logarithms.+ 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

• 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

• 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

• Explain how integer exponents represent repeated multiplication and repeated division
• Use the exponent rules for integer powers (including zero and negative exponents) to find equivalent expressions
• Rewrite expressions with integer exponents as equivalent numerical values

Learning Objectives

• Use Bayes’ theorem to interpret test results (e.g., PPV and NPV)
• Calculate probabilities of positive/negative test outcomes using sensitivity, specificity, and prevalence
• Distinguish between P(D|+) and P(+|D) and explain why they differ

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

• 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

• Understand how to adjust and improve existing mathematical models based on new data.
• Apply recalibration techniques to enhance model accuracy in real-world scenarios.
• Develop reasoning strategies for justifying modifications to models.+ Show more

Learning Objectives

• Use vertical angles to find unknown angle measures in intersecting lines.
• Use linear pair relationships to solve for unknown angles on a straight line.
• Recognise and apply the idea of supplementary angles formed by adjacent angles.

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

• Distinguish linear change from exponential growth/decay using constant difference versus constant percent change
• Interpret tables to decide whether data are better modeled by a linear trend or exponential behavior
• Use percent change to predict future values in exponential growth/decay situations

Learning Objectives

• Check whether a proposed value makes an equation true by substituting it and comparing both sides
• Solve an equation step-by-step while keeping equality balanced using inverse operations
• Explain why equivalent transformations keep an equation true

Learning Objectives

• Understand methods of data classification and organization.
• Create and interpret frequency tables for large data sets.
• Apply data coding techniques to simplify data analysis.+ Show more

Learning Objectives

• Use the AA triangle similarity criterion to decide when two triangles are similar from angle information.
• Identify corresponding vertices and corresponding sides when triangles are similar.
• Use proportional side relationships from similarity to find missing side lengths.

Learning Objectives

• Understand how to plot functions and data points on coordinate axes.
• Interpret graphical features such as trends, intersections, and turning points.
• Apply graphical methods to analyze real-world data and models.+ Show more

Learning Objectives

• Convert a ratio into a unit rate by dividing so the second quantity is 1
• Interpret unit rates in real-world contexts such as speed and price per item
• Solve problems using unit rates to scale to different quantities

Learning Objectives

• Identify and interpret the median, quartiles (Q1 and Q3), and whiskers on a box plot
• Calculate the interquartile range (IQR) from Q1 and Q3
• Use box plot features to describe the spread (IQR and overall range) of a data set

Learning Objectives

• Interpret confidence levels as evidence from repeated sampling and avoid common misinterpretations.
• Use confidence intervals (and estimated margins of error) to justify conclusions about population parameters.
• Explain how sampling variability can produce different sample statistics while still being consistent with the same population.+ Show more

Learning Objectives

• Use parameters h, k, and a in y=a|x-h|+k to describe horizontal/vertical shifts and vertical stretching/compressing/reflection.
• Read key features (vertex, axis of symmetry, minimum/maximum, and intersections) from transformed absolute value graphs.
• Solve equations of the form a|x-h|+k=c using algebra (and/or the graph) with correct x-values.+ Show more

Learning Objectives

• Identify when a question is statistical and explain how collected data is used to answer it.
• Use line plots to read frequencies and summarize data using features like mode, total frequency, and range.
• Use box plots to interpret median, quartiles (Q1 and Q3), and the interquartile range (IQR) to describe spread.+ Show more

Learning Objectives

• Understand that equivalent ratios represent the same relationship by multiplying or dividing both terms by the same nonzero number
• Use tape diagrams and ratio tables to find missing values in equivalent ratio situations
• Decide whether two ratio statements are equivalent by comparing their scaled quantities

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

• Apply derivatives to analyze velocity and acceleration in physical systems.
• Interpret the rate of change of quantities in real-world contexts.
• Solve related rates problems involving motion and measurements.+ Show more

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

• Identify amplitude, period, phase shift, and vertical shift from a given sine or cosine model
• Use unit-circle angle reasoning to determine when a periodic trig model reaches maximum or minimum values
• Solve for the timing of repeated values using the period and the model’s parameter B

Learning Objectives

• Read dot plots, histograms, and box plots to identify key features such as shape, center, and spread
• Interpret one-to-one scales by connecting visual features (median, quartiles, bar heights) to quantitative meaning
• Distinguish typical values from extreme values (outliers) using graphical information and the 1.5×IQR rule

Learning Objectives

• Add and subtract integers and rational numbers using sign-sensitive calculations.
• Solve linear equations involving rational coefficients by performing balanced inverse operations.
• Use equivalent forms (like factoring/distributing) to simplify rational-number expressions.

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

• 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

• Identify the degree and leading coefficient of a polynomial and use them to describe end behavior
• Use factored form to find x-intercepts (zeros) and determine whether the graph crosses or touches the x-axis from factor multiplicity
• Determine key turning-point information using derivatives (critical points) for polynomial functions+ Show more

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