Maths Worksheets

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

• 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

• 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

• 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

• 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

• Translate real situations into equations/inequalities using two variables.
• Interpret how changing one variable affects the other in a two-variable model.
• Graph linear inequalities in two variables by describing which side of the boundary line to shade.+ 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

• 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

• 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 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

• 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

• 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

• Represent probability using numbers between 0 and 1 and interpret 0 and 1
• Match probability statements to inequalities and interval notation
• Convert probability values between decimal and fraction forms when outcomes are equally likely

Learning Objectives

• Identify the slope and y-intercept from points on a line in a coordinate grid.
• Write a linear function equation y = mx + b from two points.
• Use linear models to make predictions from the graph (including slope meaning).+ Show more

Learning Objectives

• Solve quadratic equations in one variable by factoring or using algebraic methods
• Connect the zeros of a quadratic to the x-intercepts of its graph
• Use the discriminant to predict the number of real solutions and x-intersections

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

• Use coordinate differences to find the base and perpendicular height of a triangle on a coordinate plane
• Compute the area of a triangle using A = 1/2 × base × height
• Explain why horizontal and vertical coordinate changes give the measurements for base and height

Learning Objectives

• Use the proportional function rule y = kx to find unknown inputs or outputs
• Determine the constant of proportionality k from given values and apply it to new values
• Solve proportional relationships in context, interpreting the results as meaningful

Learning Objectives

• Combine like terms to simplify algebraic expressions
• Use the distributive property to simplify expressions
• Factor out a common factor to rewrite expressions in simpler equivalent forms+ Show more

Learning Objectives

• Identify the rule that generates terms in a numeric pattern
• Use algebraic expressions to describe linear and geometric pattern rules
• Translate between a pattern rule and a condition using inequalities+ 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

• Interpret solution sets for equations and inequalities in the context of a problem statement
• Use equivalent algebraic forms to keep the same meaning when modelling and interpreting results
• Match inequality solution direction to words like “at least” and “no more than”

Learning Objectives

• Interpret the meaning of a logarithm as an exponent required to reach a target output.
• Use parameters (shifts and base) in logarithmic models to solve for unknown inputs.
• Relate changes in the base to changes in sensitivity (how quickly the output increases).

Learning Objectives

• Identify the parameters a and b in an exponential function f(x)=a·b^x
• Construct an exponential model from initial value and growth/decay factor
• Use the model to make predictions by evaluating f(x) for given x

Learning Objectives

• Use the unit circle to match an angle θ with its point (cosθ, sinθ).
• Evaluate sine and cosine for special angles using x- and y-coordinates.
• Apply quadrant sign rules to determine the signs of sinθ and cosθ.

Learning Objectives

• Solve rational equations by clearing denominators and using domain restrictions
• Identify and reject extraneous solutions by checking answers in the original equation
• Write the set of values excluded by denominators and explain why they must be excluded

Learning Objectives

• Find the conjugate of a complex number and use it to rationalise denominators in division
• Simplify complex-number quotients into standard form a+bi by eliminating the imaginary part of the denominator
• Identify the real and imaginary parts of a quotient after conjugate multiplication

Learning Objectives

• Identify when two figures are similar using equal corresponding angles and proportional corresponding side lengths
• Use the scale factor between similar figures to find unknown side lengths
• Solve similarity problems involving proportional relationships and apply angle equality to find missing angles+ Show more

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

• Interpret what each variable in a formula represents by using unit reasoning
• Use a formula to calculate an output while checking that units are consistent
• Rewrite formulas and apply unit-based thinking to confirm constants and conversion factors

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

• 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

• 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

• Add complex numbers by combining like terms (real parts with real parts, imaginary parts with imaginary parts).
• Use the associative and distributive ideas to regroup complex numbers without changing the sum.
• Write sums in the standard form a+bi and interpret the real and imaginary components.

Learning Objectives

• Rearrange algebraic formulas to make a chosen variable the subject using equivalent transformations.
• Use the rearranged form to interpret how changing one quantity affects another.
• Check that two formula forms are equivalent by substituting values.

Learning Objectives

• Interpret the parameters a and b in an exponential model y=a·b^x
• Determine whether an exponential function represents growth or decay from the value of b
• Use a and b to predict values of a function at different time steps

Learning Objectives

• Create and interpret graphs that model real-world situations using ordered pairs and linear patterns.
• Use graphs to find key features such as the rate of change (slope) and starting value (y-intercept).
• Solve linear equations and relate the algebraic solution back to a model.+ Show more

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

• Compute conditional probabilities using P(A|B) = P(A ∩ B) / P(B).
• Translate situations into conditional-probability calculations from counts and tables.
• Interpret what conditional probability means and how it differs from P(B|A).

Learning Objectives

• Use addition or subtraction to eliminate a variable when solving a system of two linear equations
• Solve the resulting one-variable linear equation after elimination
• Substitute back into an original equation to find the second variable and the ordered pair

Learning Objectives

• Use the Pythagorean theorem a^2 + b^2 = c^2 to find missing side lengths in right triangles.
• Identify which side is the hypotenuse and match its value correctly to the right-angle vertex.
• Apply Pythagorean thinking to real-world contexts such as diagonals and ladder reach.

Learning Objectives

• Use the form y = kx to describe proportional relationships that pass through the origin.
• Interpret the unit rate k as the slope of a proportional graph.
• Use proportional graphs to find missing y-values for given x-values and to compare rates of change.

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 surface area formulas to calculate total outside area of 3D shapes.
• Combine base area and lateral area to find the total surface area for composite shapes.
• Solve equations that come from surface area formulas involving π.+ Show more

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

• 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

• Interpret discounts, sales, and per-unit prices to compare value between options.
• Calculate savings and sale prices using proportional reasoning.
• Use ratios and tables to decide which purchase is the better buy.