Grade 11 Maths Worksheets

Learning Objectives

• Rewrite rational expressions into equivalent simplified forms by using factoring and canceling common factors.
• Identify excluded values by tracking when original denominators would be zero, even after cancellation.
• Explain why two algebraically similar rational forms may differ in domain and solution validity.

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 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

• 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

• Convert between equivalent polynomial forms (expanded, factored, and vertex form) for quadratics
• Use factoring to identify zeros and x-intercepts of polynomial functions
• Use completing the square to rewrite quadratics in a form that reveals the vertex and maximum/minimum value+ Show more

Learning Objectives

• Solve one-variable equations and interpret the solution in context
• Solve and interpret one-variable inequalities, including checking boundary values
• Translate a real-world scenario into an equation or inequality in one variable+ Show more

Learning Objectives

• Rearrange algebraic formulas to isolate a chosen variable using inverse operations.
• Maintain algebraic equivalence by performing the same operation to both sides of an equation.
• Substitute into rearranged formulas accurately and interpret results using constraints (e.g., non-zero denominators, non-negative roots).

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 addition rule to find probabilities of unions of events (including mutually exclusive and overlapping events).
• Use the multiplication rule, including conditional probability: P(A ∩ B) = P(A|B)P(B).
• Use complements to simplify probability calculations.+ 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

• 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

• 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

• Compare two data distributions using their center, spread, and shape.
• Interpret how differences in mean/median and measures of spread (range/IQR) affect conclusions.
• Use skewness and outliers to explain why summary statistics may differ between two data sets.

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

• Use the power of a power rule to simplify expressions with exponents raised to other exponents.
• Use product and quotient rules for powers to combine or divide exponential terms.
• Convert between radicals and rational exponents correctly, including negative exponents.+ Show more

Learning Objectives

• State what a rational exponent m/n means in terms of roots and powers
• Rewrite a^(m/n) using radical notation: (n√a)^m
• Evaluate expressions with rational exponents by taking the n-th root first (for a>0)+ Show more

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

• 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 an equation to model a relationship between two variables and interpret what ordered pairs satisfy the equation.
• Connect the form of a function (including absolute value transformations) to key features on its graph, such as the vertex.
• Interpret and describe linear inequalities in two variables using a coordinate-plane model and test points.

Learning Objectives

• Add and subtract complex numbers by combining real parts with real parts and imaginary parts with imaginary parts
• Multiply complex numbers using distributive and associative laws before replacing i² with -1
• Rewrite results clearly in the form a + bi by collecting like terms

Learning Objectives

• Write complex numbers in standard form a + bi and identify the real part a and imaginary part b
• Simplify expressions involving i using i^2 = -1
• Add and multiply complex numbers by combining real and imaginary parts correctly

Learning Objectives

• Identify the role of coefficients and constant terms in algebraic expressions
• Explain how each part of an expression affects the overall value in context
• Use structure (addition and multiplication in particular) to simplify and interpret expressions+ Show more

Learning Objectives

• Choose an appropriate reporting accuracy (decimal places or significant figures) based on the smallest measurement precision.
• Apply rounding rules correctly for addition/subtraction and multiplication/division while keeping precision consistent through calculations.
• Avoid misleading precision by rounding final answers to match what the data can support.

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

• Identify domain restrictions, including excluded x-values, from rational functions
• Determine vertical asymptotes and holes by factoring and checking canceled factors
• Find x- and y-intercepts by using zeros of the numerator with nonzero denominators+ Show more

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

• 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

• 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

• 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

• Write a polynomial function in factored form from given zeros and multiplicities
• Use multiplicity to determine whether the graph crosses or bounces at each x-intercept
• Determine end behavior from the degree and leading coefficient of a factored polynomial

Learning Objectives

• Identify how exponential growth changes multiplicatively from one step to the next.
• Compare exponential and linear patterns to determine which grows faster and when a crossover occurs.
• Use limits to describe long-term behavior of exponential decay toward a nonzero value.

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

• Apply volume formulas for prisms and related solids using correct base area and dimensions
• Solve measurement problems by finding missing dimensions or comparing volumes
• Use consistent units and interpret calculated volumes in context

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

• 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

• 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

• Use circle similarity to relate radii, circumferences, arc lengths, and areas through scale factors.
• Apply constant ratios such as \(\frac{C}{r}=2\pi\) and \(\frac{A}{r^2}=\pi\) to solve problems.
• Determine how circumference and area change when the radius is multiplied by a scale factor.

Learning Objectives

• Represent geometric objects using algebraic equations on the coordinate plane (lines, circles, and absolute value graphs).
• Justify coordinate geometry statements by reasoning algebraically about relationships, not by checking only a few cases.
• Use algebraic transformations (expanding, rearranging, substituting) to prove two conditions describe the same set of points.

Learning Objectives

• Choose appropriate quantities and definitions so that a model’s calculated values represent the intended measurements.
• Read and interpret values accurately from absolute value graphs and linear inequality graphs used in quantity modeling.
• Justify whether a given point or computed value is consistent with a model (including strict vs inclusive conditions).

Learning Objectives

• Apply proportional reasoning to adjust ingredient quantities in recipes.
• Interpret ratios and proportions to maintain recipe consistency during scaling.
• Solve multi-step problems involving ratios, percentages, and measurements in practical contexts.+ Show more

Learning Objectives

• Understand and interpret proportional relationships in real-world problems.
• Apply indirect measurement techniques to estimate distances, heights, or lengths.
• Develop mathematical reasoning skills through multi-step problem-solving scenarios.+ Show more

Learning Objectives

• Understand the relationship between angle measures and trigonometric values on the unit circle.
• Apply geometric interpretations of sine, cosine, and tangent in various quadrants.
• Analyze symmetry properties and periodicity of trigonometric functions.+ Show more

Learning Objectives

• Interpret and evaluate function notation in various representations.
• Apply function composition and inverse functions to analyze real-world data.
• Solve multi-step problems involving function calculations and interpretations.+ Show more

Learning Objectives

• Understand the concept of inverse functions, particularly between exponential and logarithmic functions.
• Apply algebraic techniques to find inverse functions and solve exponential and logarithmic equations.
• Interpret graphs of inverse functions and relate their properties.+ Show more

Learning Objectives

• Understand the concept of scaling and proportional relationships.
• Apply ratios to interpret scaled measurements in real-world contexts.
• Perform multi-step calculations involving scaling factors and measurements.+ Show more

Learning Objectives

• Understand the concept of complex roots in quadratic and polynomial functions.
• Apply formulas to find complex roots of quadratic equations.
• Analyze how complex roots influence the graph and behavior of polynomial functions.+ Show more

Learning Objectives

• Understand how shifts, stretches, and reflections affect the basic trigonometric graphs.
• Apply transformations to equations of sine, cosine, and tangent functions to model real-world periodic phenomena.
• Interpret the graphical effects of algebraic modifications on trigonometric functions and relate these to practical contexts.+ Show more