Maths Worksheets

Learning Objectives

• Translate real situations into inequalities that describe feasible (allowed) variable values.
• Interpret the meaning of solutions by checking whether candidate points satisfy all constraints at once.
• Use boundary cases (where equality holds) correctly for both strict and inclusive inequalities.+ Show more

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

• 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

• 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

• Convert numbers between standard form and scientific notation
• Use exponent rules to multiply and divide numbers written in scientific notation
• Compare numbers in scientific notation using their powers of 10

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

• 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

• 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

• 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

• Represent constraints using inequalities and boundary lines
• Interpret how the inequality direction determines the shaded solution region
• Use inequality substitution to test whether points satisfy a constraint+ Show more

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

• 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

• 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

• Translate a real-world situation into an equation by defining variables and writing equivalent modeled expressions
• Solve equations to find the variable value that satisfies the modeled relationship
• Interpret the solution in context and check that it makes sense

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

• Summarize a distribution of relative frequency estimates using its center (typical value).
• Describe variability using measures such as the interquartile range (IQR) or range.
• Compare distributions from different chance processes by comparing their center and spread.

Learning Objectives

• Understand proportional relationships can be written in the form y = kx.
• Identify and interpret the constant of proportionality k as the unit rate.
• Solve simple equations of the form kx = y to find x or k.+ 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

• Use tape diagrams to interpret ratios and ratios that stay equivalent when quantities are scaled.
• Solve multi-step ratio scaling problems by applying proportional scale factors consistently across steps.
• Check that intermediate and final quantities keep the same ratio.

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

• Interpret the constant of proportionality k in y = kx as the ratio y/x for any nonzero pair (x, y)
• Use k to find missing values in proportional relationships (solve for y or x)
• Connect proportional tables, graphs, and tape diagrams to the same constant k+ Show more

Learning Objectives

• Use rational approximations to locate the value of an irrational number (like √2) between nearby decimals on a number line
• Compare irrational numbers by comparing their rational decimal approximations
• Translate number-line order information into inequality statements

Learning Objectives

• Factor quadratics with no real roots into linear factors over the complex numbers using conjugate pairs
• Use completing the square to find complex roots and write the corresponding conjugate linear factors
• Expand and simplify products of conjugate linear factors to recover the original quadratic

Learning Objectives

• Expand products of complex numbers of the form (a + bi)(c + di) using distributive multiplication.
• Simplify expressions using i^2 = −1 and collect like terms to write answers in the form x + yi.
• Identify real and imaginary parts after complex multiplication.+ Show more

Learning Objectives

• Explain why dividing by a nonzero rational number q is the same as multiplying by its reciprocal 1/q.
• Rewrite quotients of rational numbers as multiplication problems using multiplicative inverses.
• Evaluate and simplify rational-number divisions and interpret the reciprocal/cancellation patterns.

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

• 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 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

• Use the distributive property with rational coefficients (fractions and negatives) to expand expressions with parentheses
• Rewrite equivalent expressions by distributing the same rational factor to every term inside parentheses
• Combine like terms after distribution to simplify correctly+ Show more

Learning Objectives

• Interpret |x| as the distance of a rational number x from 0
• Compare rational numbers using their absolute values (distances from 0)
• Solve simple absolute value equations+ Show more

Learning Objectives

• Translate real-world situations into rational-number expressions using addition, subtraction, multiplication, and division.
• Interpret the meaning of positive and negative values (gain vs. loss, up vs. down) in the context of the situation.
• Simplify and evaluate rational expressions to find interpretable results.

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

• Interpret what an input–output statement like f(a)=b means in a real context
• Connect the same function meaning across equations, tables, and graphs
• Distinguish between the input value (a) and the output value (b) when reading function notation

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 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 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

• 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

• 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

• 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

• Add and subtract radicals by combining only like radicals (same radicand).
• Simplify radical expressions using perfect squares and exponent/root rules.
• Simplify products and quotients of radicals by combining factors under one radical when appropriate.

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

• Use the distributive property to rewrite equivalent expressions with multiplication over addition and subtraction
• Simplify equivalent expressions by distributing and combining like terms
• Determine whether two expressions are equivalent by comparing distributive rewrites

Learning Objectives

• Convert fractions to terminating decimals and relate them to equivalent decimals on a number line.
• Convert between fractions, decimals, and percents for the same rational value.
• Recognise when a fraction will have a terminating decimal and connect repeating decimals to fraction form.

Learning Objectives

• Interpret a quotient involving a fraction divided by a whole number using equal-size grouping.
• Interpret a quotient involving a whole number divided by a fraction as how many fractional-sized groups fit.
• Use multiplication to check division answers (divisor × quotient = dividend).+ Show more

Learning Objectives

• Use commutative and associative properties to rewrite expressions as equivalent expressions.
• Use identity properties (0 and 1) and inverse operations to replace parts of an expression without changing its value.
• Check that two expressions are equivalent by showing the operation changes preserve the overall value.

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

• Explain why opposite rational numbers are the same distance from 0 using absolute value
• Find absolute values for positive and negative rational numbers shown on a number line
• Use opposite relationships to compare absolute values and distances on a number line