Grade 10 Maths Worksheets

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

• Compare exponential and linear models by evaluating them at multiple input values
• Identify how multiplicative (exponential) growth differs from additive (linear) growth
• Find and interpret the crossover point where an exponential model overtakes a linear model+ 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

• 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

• Rewrite expressions to reveal structure, such as common factors and repeated terms, without changing the value.
• Use exponent and absolute value structure to produce equivalent forms that are easier to simplify or interpret.
• Connect different representations (graph form, vertex form, piecewise form) by rewriting expressions carefully.

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

• 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

• Add and subtract polynomials by combining like terms to form an equivalent expression
• Multiply polynomials using distributive property and expand to standard form
• Divide polynomials by a monomial and simplify to an equivalent polynomial expression+ 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

• 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

• Multiply rational expressions by factoring and cancelling common factors efficiently
• Simplify products of rational expressions into equivalent rational expressions
• Identify restrictions on variables from denominator factors that cannot be zero

Learning Objectives

• Recognize and create equivalent polynomial forms by expanding and factoring.
• Simplify equivalent rational expressions while correctly identifying excluded values.
• Use alternative forms (like vertex/standard forms or graph features) to reveal key properties without changing the represented values.

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

• 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

• 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

• 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

• Interpret confidence levels as evidence from repeated sampling and avoid common misinterpretations.
• Use confidence intervals (and estimated margins of error) to justify conclusions about population parameters.
• Explain how sampling variability can produce different sample statistics while still being consistent with the same population.+ 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

• 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

• 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

• 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

• 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

• Identify what the parts of an expression (coefficients, exponents, and factors) represent in a real situation
• Translate a word description into an algebraic expression and interpret the result
• Explain how changes to an expression’s structure affect the quantities it models

Learning Objectives

• Evaluate functions by substituting an input value into a given function rule.
• Use a function graph to find outputs for specific inputs.
• Solve for the input when an output value is given for an absolute value function.+ 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

• 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

• Use the identity i^2 = −1 to expand products and powers involving complex numbers.
• Verify polynomial identities by expanding both sides and simplifying to the same polynomial form.
• Factor and expand expressions with complex factors while keeping results in valid polynomial form.

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

• Solve polynomial equations that have no real solutions by using complex numbers
• Use the facts i² = −1 and complex arithmetic to find and verify complex solutions
• Interpret solutions as roots of factored forms of polynomials involving i

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

• 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

• 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

• 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

• 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

• Recognise when two figures are similar using corresponding angles and a constant scale factor.
• Calculate a corresponding length using multiplication (or division) with the scale factor from one figure to the similar figure.
• Interpret scale factor directions (from original to image, and image back to original) correctly.

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

• Use the scale factor of a dilation to find image lengths and distances from the center of dilation
• Find coordinates of a point after a dilation using the scale factor
• Explain which geometric properties are preserved by dilations (angles and parallel lines) and which are scaled (lengths)

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

• Use the AA triangle similarity criterion to decide when two triangles are similar from angle information.
• Identify corresponding vertices and corresponding sides when triangles are similar.
• Use proportional side relationships from similarity to find missing side lengths.

Learning Objectives

• Use parameters h, k, and a in y=a|x-h|+k to describe horizontal/vertical shifts and vertical stretching/compressing/reflection.
• Read key features (vertex, axis of symmetry, minimum/maximum, and intersections) from transformed absolute value graphs.
• Solve equations of the form a|x-h|+k=c using algebra (and/or the graph) with correct x-values.+ Show more

Learning Objectives

• Calculate the distance between two points using the distance formula.
• Interpret distance calculations in real-world contexts like navigation and resource placement.
• Understand and apply the midpoint formula to determine optimal locations.+ Show more

Learning Objectives

• Calculate and compare interest earned from different savings accounts and investment vehicles.
• Analyze loan terms and interest rates to determine the most cost-effective option.
• Apply percentage calculations to real-world financial scenarios.+ Show more

Learning Objectives

• Identify the vertex and axis of symmetry from quadratic equations and graphs.
• Analyze how changes in the quadratic equation affect the parabola's position and shape.
• Apply algebraic and graphical methods to interpret quadratic functions in real-world contexts.+ Show more

Learning Objectives

• Understand the characteristics of sinusoidal functions, including amplitude, period, and phase shift.
• Apply mathematical reasoning to interpret real-world data using sine models.
• Calculate parameters of sine functions from given data or scenarios.+ Show more

Learning Objectives

• Understand the properties of sine and cosine functions, including amplitude, period, phase shift, and vertical displacement.
• Apply mathematical reasoning to interpret and compare sinusoidal models in real-world contexts.
• Calculate and analyze parameters of periodic functions to solve practical problems involving cycles and oscillations.+ Show more

Learning Objectives

• Understand the concept of compound interest and how it differs from simple interest.
• Calculate future value of investments using compound interest formulas.
• Analyze the effect of compounding frequency on investment growth.+ Show more

Learning Objectives

• Develop problem-solving skills involving oblique triangles using trigonometry.
• Interpret and analyze real-world measurement problems involving multiple angles and sides.
• Apply the Law of Cosines and Law of Sines accurately in complex scenarios.+ Show more

Learning Objectives

• Apply right-triangle ratios to solve measurement problems in real-world contexts.
• Use the sine law and cosine law to interpret and analyze complex measurement scenarios.
• Evaluate and justify the most appropriate trigonometric tools for solving practical problems.+ Show more