Grade 9 math practice
The full de-streamed MTH1W course: number, algebra, linear relations, data, geometry and financial literacy — unlimited practice questions with tutor-style worked solutions.
Development of Numbers and Number Sets
3 question sets · 10 questions each, easiest to hardest
Investigate and describe the development and use of numeration systems, including contributions from diverse cultures
Development and Use of Numbers · 30 questions, easiest to hardest
Identify and describe different number sets, and classify numbers within these sets
Number Sets · 30 questions, easiest to hardest
Describe the relationships between different subsets of the real number system
Number Sets · 30 questions, easiest to hardest
Powers
2 question sets · 10 questions each, easiest to hardest
Number Sense and Operations
5 question sets · 10 questions each, easiest to hardest
Compare, order, and perform operations with rational numbers, in various forms
Rational Numbers · 30 questions, easiest to hardest
Solve problems involving ratios and rates using proportional reasoning
Rational Numbers · 30 questions, easiest to hardest
Solve problems involving percentages and proportional relationships, using various tools
Rational Numbers · 30 questions, easiest to hardest
Solve financial problems involving compound interest, currency exchange, and financial decision-making
Applications · 30 questions, easiest to hardest
Solve problems requiring various operations with rational numbers and percentages, in applications from other subjects and everyday life
Applications · 30 questions, easiest to hardest
Algebraic Expressions and Equations
5 question sets · 10 questions each, easiest to hardest
Describe the historical development of algebraic thinking and notation, and connect algebraic representations to real-world contexts
Development and Use of Algebra · 30 questions, easiest to hardest
Add, subtract, and multiply polynomials, and simplify algebraic expressions involving exponents
Algebraic Expressions and Equations · 30 questions, easiest to hardest
Solve linear equations with integer and rational coefficients, including equations with variables on both sides
Algebraic Expressions and Equations · 30 questions, easiest to hardest
Solve algebraic equations that model real-world problems
Algebraic Expressions and Equations · 30 questions, easiest to hardest
Rearrange formulas involving multiple variables, and use the rearranged formula to solve related problems
Algebraic Expressions and Equations · 30 questions, easiest to hardest
Coding
3 question sets · 10 questions each, easiest to hardest
Solve problems and create computational representations of mathematical situations using coding, for linear relations
Coding · 30 questions, easiest to hardest
Read, alter, and debug existing code (including code involving loops and conditionals) to represent mathematical situations
Coding · 30 questions, easiest to hardest
Use coding to demonstrate an understanding of linear relations, including graphing/representing linear relations and making and testing conjectures
Coding · 30 questions, easiest to hardest
Application of Relations
3 question sets · 10 questions each, easiest to hardest
Construct tables of values, graphs, and equations to represent linear relations derived from real-life situations
Application of Linear and Non-Linear Relations · 30 questions, easiest to hardest
Compare, using tables of values, graphs, and equations, the situations represented by linear and non-linear relations
Application of Linear and Non-Linear Relations · 30 questions, easiest to hardest
Solve problems by interpreting graphs of linear and non-linear relations, including problems involving direct and partial variation
Application of Linear and Non-Linear Relations · 30 questions, easiest to hardest
Characteristics of Relations
4 question sets · 10 questions each, easiest to hardest
Identify and describe the characteristics (rate of change, initial value) of linear relations from various representations
Characteristics of Linear and Non-Linear Relations · 30 questions, easiest to hardest
Determine, through investigation, the properties of the slope of a line, and connect the slope to rate of change
Characteristics of Linear and Non-Linear Relations · 30 questions, easiest to hardest
Identify and describe the significance of the x-intercept and y-intercept of linear relations in various contexts, and determine the intercepts of a linear relation
Characteristics of Linear and Non-Linear Relations · 30 questions, easiest to hardest
Compare, using a variety of tools and strategies, the graphical representations of linear and non-linear relations, and identify the key differences between them
Characteristics of Linear and Non-Linear Relations · 30 questions, easiest to hardest
Collection, Representation, and Analysis of Data
3 question sets · 10 questions each, easiest to hardest
Describe applications of data management, and explain why data collection and analysis are important
Application of Data · 30 questions, easiest to hardest
Collect data through primary or secondary sources, and represent the data using appropriate data management tools and graphs
Representation and Analysis of Data · 30 questions, easiest to hardest
Analyse and interpret data to identify patterns and trends, make and justify conclusions, and communicate findings using appropriate statistical vocabulary
Representation and Analysis of Data · 30 questions, easiest to hardest
Mathematical Modelling
5 question sets · 10 questions each, easiest to hardest
Identify and describe real-world applications of mathematical modelling
Application of Mathematical Modelling · 30 questions, easiest to hardest
Step 1: understand the problem — identify the questions inherent in a problem, and identify the information needed to answer the question
Process of Mathematical Modelling · 30 questions, easiest to hardest
Step 2: analyse the situation — identify variables and assumptions, gather data, and select appropriate mathematical representations and tools
Process of Mathematical Modelling · 30 questions, easiest to hardest
Step 3: create a mathematical model — create the mathematical model, and use it to analyse and solve the problem
Process of Mathematical Modelling · 30 questions, easiest to hardest
Step 4: analyse and assess the model — analyse the model, verify and interpret original results, and communicate a conclusion or refine the model as needed
Process of Mathematical Modelling · 30 questions, easiest to hardest
Geometric and Measurement Relationships
6 question sets · 10 questions each, easiest to hardest
Describe the development of geometric and measurement relationships, and connect them to real-world applications
Geometric and Measurement Relationships · 30 questions, easiest to hardest
Solve problems involving the areas and perimeters of composite two-dimensional shapes
Geometric and Measurement Relationships · 30 questions, easiest to hardest
Solve problems involving the surface areas and volumes of composite three-dimensional objects
Geometric and Measurement Relationships · 30 questions, easiest to hardest
Solve problems involving similar triangles in real-life contexts
Geometric and Measurement Relationships · 30 questions, easiest to hardest
Solve problems involving the metric and imperial systems, using conversions within and between systems
Geometric and Measurement Relationships · 30 questions, easiest to hardest
Solve optimization problems requiring maximization or minimization of perimeter, area, surface area, or volume, given various constraints
Geometric and Measurement Relationships · 30 questions, easiest to hardest
Endless practice
Generated fresh every time — adaptive difficulty, never runs out
Evaluate powers
Evaluate powers with integer bases and whole-number exponents.
Product and quotient laws of exponents
Simplify expressions like x^5 · x^3 or x^8 ÷ x^2 using exponent laws.
Add and subtract fractions
Add or subtract fractions with unlike denominators; answer in lowest terms.
Order of operations with integers
Evaluate expressions with brackets, powers, and the four operations on integers.
Percent of a number and percent change
Find a percent of an amount, including tax and discount problems.
Unit rates
Compute unit rates and use them to compare or scale real-world quantities.
Collect like terms
Simplify an algebraic expression by collecting like terms.
Distribute and simplify
Expand an expression using the distributive property, then collect like terms.
Exponent laws on monomials
Simplify a product, quotient, or power of a power of monomials using the exponent laws.
Solve one- and two-step equations
Solve one- and two-step linear equations for x.
Solve multi-step equations with brackets
Solve linear equations with the variable on both sides, including equations with brackets.
Translate word problems into equations
Translate a word problem into a linear equation and solve it.
Direct variation
Use direct variation (y = kx) to find a total or a constant of variation in context.
Partial variation word problems
Use partial variation (y = mx + b) to model a fixed fee plus a rate, and solve in either direction.
Identify the equation of a relation from a table
Given a table of values, decide whether a relation is direct or partial variation and identify its equation.
Calculate slope from two points
Calculate the slope of a line given two points on it.
Rewrite in slope-intercept form
Rewrite a linear equation from standard form into slope-intercept form y = mx + b.
Write the equation of a line from slope and a point
Write the equation of a line in the form y = mx + b, given its slope and one point on it.
Rate of change from a table; linear or not
Use first differences in a table of values to find the rate of change, or to recognize a non-linear relation.
Mean, median, and mode
Calculate the mean, median, or mode of a small data set from a real-world context.
Range of a data set
Find the range of a data set as a simple measure of spread.
Correlation from a scatter plot
Classify the correlation shown by a set of paired data as strong positive, strong negative, or no correlation.
Predicting with a line of best fit
Use the equation of a line of best fit to predict a value, and classify the prediction as interpolation or extrapolation.
Angles formed by parallel lines and a transversal
Use angle relationships (corresponding, alternate, co-interior) formed when a transversal crosses parallel lines to find a missing angle.
Interior angles of a polygon
Use the polygon interior-angle-sum formula (n - 2) * 180 to find a regular polygon's interior angle or a missing angle in an irregular polygon.
Area of composite 2D shapes
Find the area of a composite two-dimensional shape by decomposing it into rectangles, triangles, and semicircles.
Surface area of prisms and cylinders
Find the surface area of a rectangular prism, a cylinder, or an open-top prism.
Volume of prisms, cylinders, and composite solids
Find the volume of a rectangular prism, cylinder, triangular prism, or a composite solid made from two prisms.
Simple interest
Use the simple interest formula I = Prt to find interest earned, the total amount, or the principal needed.
Compound interest
Use A = P(1 + r)^n to find the future value or interest earned on a compound-interest investment.
Personal budgets
Build and analyze a simple monthly budget: total expenses, money left over, percent spent on a category, or how much to cut to break even.
Currency exchange
Convert between Canadian dollars and a foreign currency using a given exchange rate.
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