Maths Worksheets

Learning Objectives

• Rewrite expressions using the power of a power rule: (a^m)^n = a^(mn).
• Use the product of powers rule: a^m · a^n = a^(m+n) and the quotient rule: a^m ÷ a^n = a^(m−n).
• Solve exponent equations by rewriting both sides with the same base and equating exponents.

Learning Objectives

• Convert between radical notation and rational exponent notation using a^(1/n)=ⁿ√(a)
• Rewrite expressions like √(a^m) and ∛(a^m) as a^(m/n) (and vice versa) using exponent rules
• Simplify expressions by applying rational exponent laws after conversion+ Show more

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

• Understand and evaluate functions using function notation for specific inputs.
• Apply algebraic manipulation to compose functions and interpret their transformations.
• Develop problem-solving skills involving functions in real-world contexts such as budgeting and measurements.+ Show more

Learning Objectives

• Translate real-world rate statements into numerical ratios and simple equations.
• Use unit rates to predict outcomes for new quantities in a situation.
• Check that a rate statement matches the quantities given and interpret what is changing over time or quantity.

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

• Understand the algebraic computation of the vector (cross) product in three dimensions.
• Interpret the geometric significance of the cross product as a vector orthogonal to the plane.
• Apply the cross product to solve real-world problems involving torque, forces, and area calculations.+ Show more

Learning Objectives

• Translate contextual statements about input and output into correct function notation (e.g., f(a)=b).
• Interpret given function values to explain what the model says about inputs and outputs.
• Evaluate function expressions at specified inputs to find outputs.

Learning Objectives

• Use complementary angle relationships in a right triangle to convert between sine and cosine values.
• Use complementary angle cofunction relationships to convert between tangent and cotangent values.
• Apply cofunction identities to solve for missing trigonometric ratios of acute angles.

Learning Objectives

• Standardize a normal random variable using z = (x − μ)/σ
• Approximate probabilities for normal intervals using standard normal CDF values
• Use continuity correction when approximating binomial probabilities with a normal model

Learning Objectives

• Understand the concept of correlation and how to interpret the correlation coefficient.
• Apply scatter plot analysis to identify relationships between two variables.
• Calculate and interpret the regression line in real-world data scenarios.+ Show more

Learning Objectives

• Convert rational numbers between fractions, decimals, and percents.
• Use converted forms to decide which of two numbers is greater or less.
• Order numbers by interpreting their positions on a number line after converting.+ Show more

Learning Objectives

• Understand the concept of independent and dependent events in probability.
• Apply the multiplication rule to calculate the probability of compound events.
• Use tree diagrams to visualize and compute probabilities of sequential outcomes.+ Show more

Learning Objectives

• Explain that absolute value gives the distance from 0, so it is always nonnegative
• Use the number line to compute absolute values from points to 0
• Interpret real-life situations (like elevation or temperature) using absolute value as distance+ Show more

Learning Objectives

• Understand the formal definition of limits and how they describe the behaviour of functions near specific points or infinity.
• Apply algebraic and graphical methods to evaluate limits and determine points of continuity.
• Analyze functions for continuity or discontinuity at given points, including cusps and jumps.+ Show more

Learning Objectives

• Understand basic probability concepts and how to calculate simple probabilities in real-world scenarios.
• Apply probabilistic reasoning to evaluate risks and support informed decision-making.
• Interpret likelihood and compare different probabilistic outcomes in everyday contexts.+ Show more

Learning Objectives

• Identify proportional relationships of the form y = kx and the meaning of the constant of proportionality k
• Use plotted points on a coordinate grid to find k and write the rule y = kx
• Complete a ratio table for a proportional relationship and determine missing values+ Show more

Learning Objectives

• Identify when two algebraic expressions are equivalent by rewriting them using distributive property and combining like terms
• Expand expressions with brackets (e.g., a(b+c)) to show equivalent forms clearly
• Explain how the structure of an expression shows what each coefficient contributes+ Show more

Learning Objectives

• Interpret a percent as a part out of 100 and connect it to equivalent decimals.
• Convert between percent form and decimal form for rational numbers.
• Use number lines and bar (tape) models to locate equivalent percent/decimal values.

Learning Objectives

• Understand the concept of derivatives as measures of instantaneous rates of change.
• Apply derivative rules to compute rates in real-world contexts.
• Interpret the geometric meaning of derivatives as slopes of tangent lines.+ Show more

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

• Explain what a unit rate is and how it relates to ratios.
• Complete and interpret ratio tables by finding missing values.
• Convert between equivalent rates using consistent scaling to get values for a denominator of 1.+ Show more

Learning Objectives

• Choose the correct trigonometric ratio (sin, cos, or tan) based on which sides are given relative to an acute angle in a right triangle
• Use trigonometric ratios to calculate missing side lengths and acute angle measures in right triangles
• Justify computations by relating the chosen ratio to opposite, adjacent, and hypotenuse sides

Learning Objectives

• Understand the relationship between zeros of polynomial functions and their multiplicities.
• Apply factoring techniques to identify zeros and their multiplicities in polynomials.
• Analyze how multiplicity affects the graph behavior at zeros, including touching or crossing the x-axis.+ Show more

Learning Objectives

• Recognize that similarity transformations keep angle measures the same while changing side lengths by a common scale factor.
• Use transformation sequences (dilations, rotations, reflections, translations) to map one figure to a similar figure on a coordinate grid.
• Find scale factors and corresponding lengths using ratios and proportional reasoning.

Learning Objectives

• Calculate sine, cosine, and tangent of an acute angle in a right triangle using side ratios.
• Use the Pythagorean theorem to find missing sides before applying trigonometric ratios.
• Explain why trigonometric ratios depend only on the acute angle for similar right triangles.

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

• Use values from a table to find a unit rate (the amount for 1 unit).
• Fill in missing table entries using a constant rate or consistent conversion.
• Interpret table rows as equivalent rate comparisons and explain the method.

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

• Understand and apply the definitions of sine, cosine, and tangent in right-angled triangles.
• Calculate unknown side lengths and angles using trigonometric ratios.
• Interpret real-world problems involving measurements and distances using trigonometry.+ Show more

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 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

• Factor rational expressions to reveal common numerator and denominator factors.
• Simplify rational expressions by canceling matching factors while tracking excluded values.
• Explain why a simplified rational expression is equivalent only for allowed input values.

Learning Objectives

• Understand the definition and notation of vectors in two and three dimensions.
• Calculate the magnitude and direction of vectors in real-world contexts.
• Interpret vectors as directed line segments and analyze their properties.+ Show more

Learning Objectives

• Describe how a dilation scales distances from a fixed center using a scale factor
• Find the image of points under a dilation using coordinates and the scale factor
• Use dilation properties to reason about proportional segments, preserved angles, and parallel lines

Learning Objectives

• Compare two numerical distributions using measures of center and spread (especially median and interquartile range).
• Use box plots to read quartiles (Q1, median, Q3), compute the IQR, and interpret variability.
• Describe how distributions differ by being shifted left or right and by having greater or smaller spread.

Learning Objectives

• Evaluate combined functions such as (f+g)(x), (f-g)(x), (fg)(x), and (f/g)(x) at a given x-value.
• Write combined function rules in terms of f(x) and g(x), including simplifying when possible.
• Identify restrictions on x for (f/g)(x) when the denominator function equals 0.

Learning Objectives

• Use the definition i² = −1 to simplify expressions involving i
• Calculate powers of i (e.g., i³, i⁴, i⁵, i⁶) using patterns from i² = −1
• Simplify products and squares of expressions containing i (including (a+b)(a−b) forms)+ Show more

Learning Objectives

• Add and subtract rational expressions by finding a common denominator and combining numerators
• Simplify rational expressions by cancelling common factors while keeping expressions equivalent
• State excluded values (values that make any original denominator equal to zero)

Learning Objectives

• Understand and apply advanced polynomial factorization methods such as synthetic division and the Rational Root Theorem.
• Solve polynomial equations by identifying zeros and their multiplicities.
• Analyze polynomial behavior and graph shapes based on factorization.+ Show more

Learning Objectives

• Understand and calculate the mean, median, and mode of data sets.
• Interpret measures of central tendency in real-world contexts.
• Compare the usefulness and limitations of different measures considering data skewness and outliers.+ Show more

Learning Objectives

• Understand and apply the power, product, quotient, and chain rules for derivatives.
• Interpret derivatives in terms of increasing/decreasing intervals and real-world applications.
• Develop problem-solving skills through multi-step differentiation exercises.+ Show more

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

• Apply unit conversions to real-world measurement problems.
• Estimate quantities and resources needed in workplace scenarios.
• Interpret measurements visually and numerically for resource management.+ Show more

Learning Objectives

• Describe the direction of association in a scatter plot (positive, negative, or none).
• Judge the strength of association by how tightly points cluster around a general trend.
• Read coordinates from a scatter plot and use them to support conclusions about the pattern.

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

• 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

• Rewrite algebraic expressions using exponent rules for products, quotients, and powers-to-a-power
• Create equivalent exponent forms and identify which rule justifies each rewrite
• Solve for variables in equations by first rewriting expressions into simpler exponent forms