Maths Worksheets

Learning Objectives

• Find and interpret median and interquartile range (IQR) from a box plot and explain what they say about center and spread.
• Use mean/median and range/IQR to compare two data sets, especially when one distribution is skewed or has outliers.
• Justify which statistical measure (median vs mean, IQR vs range) is most appropriate for a given distribution shape.

Learning Objectives

• Use the distributive property to expand expressions of the form p(x+q)
• Convert factored/parenthetical equations into equivalent linear equations
• Combine like terms correctly after expanding, then solve for the variable

Learning Objectives

• Understand how to assess income and expenses for personal budgeting.
• Apply mathematical calculations to determine savings and financial goals.
• Interpret data related to income sources and expenditure patterns.+ Show more

Learning Objectives

• Read and interpret rational numbers as points on a number line, relative to 0.
• Use the number line to compare rational numbers and describe their positions (left/right of 0).
• Find distances between points and from 0 using absolute value ideas.

Learning Objectives

• Understand the concept of composing functions and its effects on graphs and algebraic expressions.
• Apply function composition to solve real-world problems involving measurements, budgeting, and data interpretation.
• Analyze how composition relates to inverse functions and interpret the behavior of composed functions.+ Show more

Learning Objectives

• Use substitution to evaluate expressions when a variable is given a value
• Apply the order of operations correctly, including with fractions and negative numbers
• Interpret the evaluated value as a quantity from a real-life context

Learning Objectives

• Multiply rational numbers and apply predictable sign rules for products and quotients.
• Divide rational numbers by rewriting division as multiplication by the reciprocal.
• Simplify products and quotients of fractions and check reasonableness using magnitude.+ Show more

Learning Objectives

• Find the volume of a right rectangular prism by multiplying the three perpendicular edge lengths
• Express prism volume as a product when edge lengths are fractional
• Use scaling to reason how changing one edge length affects the volume

Learning Objectives

• Identify whether a data display shows a positive, negative, or no association between two variables
• Explain why correlation (association) does not prove causation
• Use numerical features of graphs (center/spread/outliers) to describe relationships without making causal claims

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

• Interpret key features of graphs of functions, including where they increase or decrease and where maxima or minima occur
• Use intercepts to describe how a function behaves at specific input values
• Sketch or describe a graph using features (not just isolated points)+ Show more

Learning Objectives

• Solve systems of two linear equations using substitution and elimination.
• Interpret a system’s solution as the intersection point that satisfies both equations at the same time.
• Check whether an ordered pair satisfies both equations in a system.+ Show more

Learning Objectives

• Use substitution to rewrite one equation to express one variable in terms of the other
• Substitute that expression into the second equation to form and solve a one-variable equation
• Determine the corresponding value of the second variable and write the ordered pair solution

Learning Objectives

• Identify and use the fact that a radius perpendicular to a chord bisects the chord
• Use the right angle formed by a perpendicular radius to relate radii, distances to chords, and half-chord lengths
• Solve for unknown chord segment lengths using midpoint and perpendicular constraints

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

Learning Objectives

• Translate a situation with constraints into an equation in one variable
• Solve equations by using algebraic steps and by interpreting solutions
• Use absolute value graphs to solve absolute value equations

Learning Objectives

• Use two-way tables to find conditional probabilities
• Calculate conditional probabilities from counts using P(A|B) = A∩B / B
• Interpret what conditional probability means in context and compare different conditions

Learning Objectives

• Apply the distributive property to expand expressions with parentheses.
• Combine like terms after expansion to write an equivalent linear expression in simplest form.
• Handle negative and fractional coefficients correctly during distributive expansion.

Learning Objectives

• Describe what it means for a relationship to be a function (each input maps to exactly one output).
• Use a context to write an explicit function rule that models the relationship between two quantities.
• Evaluate a function and solve for inputs using an equation based on the function rule.+ Show more

Learning Objectives

• Translate “at least” and “no more than” situations into linear inequalities
• Solve linear inequalities and interpret the solution as a range of allowed values
• Match inequality signs to open/closed boundaries when representing solution sets on number lines

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

• Interpret unit rates as ratios divided to a per-1 quantity, even when amounts are fractions
• Compute unit rates by dividing by a fractional quantity (using equivalent fractions or reciprocals)
• Use tape diagrams and ratio reasoning to support unit rate calculations with fractional parts+ Show more

Learning Objectives

• Apply trigonometric identities to simplify complex expressions.
• Solve equations involving periodic and oscillatory functions.
• Interpret solutions geometrically and algebraically in real-world contexts.+ Show more

Learning Objectives

• Evaluate exact trigonometric values for common radian angles using the unit circle.
• Determine the signs of sine, cosine, and tangent based on the quadrant.
• Use radian angle relationships and periodicity to find equivalent trig values.

Learning Objectives

• Understand the concept of implicit differentiation and when it is applied
• Apply implicit differentiation to find derivatives of implicitly defined functions
• Interpret derivatives at points on curves defined by relations involving both variables+ Show more

Learning Objectives

• Use unit conversion factors written as ratios to cancel unwanted units
• Convert quantities that include derived units (e.g., speed, density, area, volume per time)
• Apply a multi-step conversion chain while keeping units consistent throughout

Learning Objectives

• Solve multi-step ratio problems by finding an intermediate unit rate or quantity and then scaling to the final amount
• Keep the same proportional multiplier within each proportional relationship while applying it across steps
• Translate ratio situations into equations and use algebra to find missing values

Learning Objectives

• Classify numbers as rational or irrational based on their decimal expansions
• Convert between fractions and terminating or repeating decimals to identify rational numbers
• Recognize common irrational numbers such as √2 and π and justify why they are irrational

Learning Objectives

• Interpret absolute value |x| as the distance of x from 0 on a number line.
• Explain why absolute values are always nonnegative and why opposite signs can give the same absolute value.
• Compute absolute values using distance from 0 and absolute value properties.

Learning Objectives

• Rewrite quadratic equations and expressions in completing-square (vertex) form
• Solve quadratic equations by transforming them into a perfect-square equation
• Use square roots to find all real solutions after completing the square

Learning Objectives

• Write and use formulas while tracking units so that numerators and denominators match correctly across steps
• Compute values from formulas and check that the resulting units make sense for the context
• Rearrange formulas and interpret what each term represents in terms of units

Learning Objectives

• Identify the gradient (rate of change) and y-intercept (starting value) from points on a line
• Write a linear equation in the form y = mx + b that matches a graph
• Use y = mx + b to predict y-values for given x-values

Learning Objectives

• Apply geometric principles to analyze complex figures involving polygons and circles.
• Use trigonometry to determine angles and side lengths in geometric configurations.
• Justify relationships and properties of geometric figures through reasoning and calculations.+ Show more

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

• Interpret complex statistical models such as multiple regression and non-linear models in real-world contexts.
• Evaluate the assumptions and limitations of advanced statistical models.
• Apply mathematical reasoning to analyze data and draw informed conclusions.+ Show more

Learning Objectives

• Recall and apply surface area formulas for cylinders, cones, pyramids, and spheres
• Connect 2D measures on faces (such as radius and slant height) to 3D surface area
• Use scaling ideas to explain how surface area and volume change for similar solids

Learning Objectives

• Interpret the coefficient in an expression written with a variable as the change per 1 unit of the variable.
• Interpret the constant term in an expression as the fixed amount that does not change.
• Use the coefficient and constant term to compute values of expressions and describe how outputs change.

Learning Objectives

• Use ratio tables to identify the constant multiplier in a proportional relationship.
• Solve equations of the form kx = y to find the missing value in a proportional relationship.
• Connect the constant of proportionality k to unit rate (how much y changes when x increases by 1).+ Show more

Learning Objectives

• Classify real numbers as rational or irrational
• Use the rule for sums to predict whether a sum is rational or irrational without full evaluation
• Reason about rationality patterns when adding rational and irrational numbers+ Show more

Learning Objectives

• Represent a percent increase or decrease as a multiplicative factor (e.g., +15% → ×1.15, −25% → ×0.75).
• Use proportional reasoning to find a new amount from a base amount after a percent change.
• Interpret percent models and conversion tables to move between fraction, decimal, and percent forms.

Learning Objectives

• Understand the basic form of exponential growth functions and their applications.
• Apply exponential formulas to solve real-world problems involving growth and decay.
• Interpret growth rates and initial values in exponential models.+ Show more

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

• Understand and recall fundamental trigonometric identities including Pythagorean, angle sum, and double-angle identities.
• Apply identities to simplify complex trigonometric expressions and solve equations involving various angles.
• Interpret identities both geometrically and algebraically to enhance reasoning about function symmetries and transformations.+ Show more

Learning Objectives

• Write and interpret algebraic expressions using numbers, variables, and operation symbols.
• Use parentheses and order of operations to determine what an expression means.
• Evaluate expressions by substituting values for variables.

Learning Objectives

• Use the Remainder Theorem to connect dividing by x-a to the value p(a).
• Use p(a)=0 to decide when x-a is a factor of p(x).
• Use non-zero remainders to rule out incorrect factors/roots.

Learning Objectives

• Link proportional situations across ratio tables, equations, and contextual descriptions by keeping the same multiplier.
• Use a constant of proportionality to complete missing values in a ratio table.
• Translate between an equation (y = kx) and the scaling described in other representations.

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

• Apply the distributive property to expand expressions with parentheses to form an equivalent equation.
• Combine like terms on each side to simplify to a linear equation in one variable.
• Solve the resulting linear equation by isolating the variable while keeping both sides balanced.+ Show more