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Grade 10 Math
CONTENTS

As students’ progress to Grade 10, they familiarize themselves further with mathematical concepts while also initiating the process of their college applications, shortlisting career options.

Numbers

The study of whole numbers and their properties is called Number theory. Number theory is a large and interesting area in mathematics, including studying Prime numbers, rational numbers and so on. Number theory is important because it helps you to understand and master how the numbers function which helps with logical reasoning skills.
Factors
Prime factorization
Greatest common factor
Least common multiple
GCF and LCM: word problems
Square roots
Cube roots
Classify rational and irrational numbers
Classify numbers
Compare and order rational numbers
Absolute value and opposites
Number lines
Convert between decimals and fractions
Exponents

The exponent of a number tells us how many times to multiply that number with itself. It is written as a small number to the right and above the base number.
Exponents with integer bases
Exponents with decimal and fractional bases
Negative exponents
Multiplication with exponents
Division with exponents
Multiplication and division with exponents
Power rule
Evaluate expressions using properties of exponents
Identify equivalent expressions involving exponents
Scientific notation

Scientific notation is a way of representing a number where that number is written in two parts: just the digits with the decimal point placed after the first digit, followed by power of 10.
Convert between standard and scientific notation
Compare numbers written in scientific notation
Multiply numbers written in scientific notation
Divide numbers written in scientific notation
Radical expressions

The symbol √ is called radical in mathematics. Radical expression is any expression containing this symbol. The √ symbol is used to indicate square root or nth root of a number. Understanding radical expressions are important for future math works and also for real lives problems such as calculating inflation and interest.
Simplify radical expressions
Simplify radical expressions by rationalizing the denominator
Multiply radical expressions
Add and subtract radical expressions
Simplify radical expressions using the distributive property
Simplify radical expressions: mixed review
Rational exponents

Using rational numbers as exponents. A rational exponent represents both an integer exponent and an nth root. The root is found in the denominator and the integer exponent is found in the numerator. In other words, a rational exponent is an exponent that is a fraction.
Evaluate rational exponents
Multiplication with rational exponents
Division with rational exponents
Power rule with rational exponents
Simplify expressions involving rational exponents I
Simplify expressions involving rational exponents II
Coordinate plane

The plane containing X axis and Y axis is called coordinate plane. Cartesian coordinated can be used to pinpoint where we are on a map or graph. We can mark a point on a graph by how far along and how far up it is, the point (10,6) is 10 units along and 6 units up. Coordinate plane is exciting and important for learning math and it has important use in real life like mapping an area or arranging furniture in your room.
Coordinate plane review
Midpoints
Distance between two points
Solve equations

Solving an equation is the process of finding a value (or values) that we can put in place of a variable which makes the equation true. Solving an equation is like solving a puzzle which means there are things we can (an cannot) do.
Model and solve equations using algebra tiles
Write and solve equations that represent diagrams
Solve one-step linear equations
Solve two-step linear equations
Solve advanced linear equations
Solve equations with variables on both sides
Solve equations: complete the solution
Find the number of solutions
Create equations with no solutions or infinitely many solutions
Solve linear equations: word problems
Solve linear equations: mixed review
Single-variable inequalities

In mathematics sometimes we only know that something is greater or smaller than. Inequality tells us about the relative size of two values. A single-variable inequality is a mathematical statement that relates a linear expression as either less than or greater than another. Learning equations and inequalities helping to get ready for more advanced math problems.
Graph inequalities
Write inequalities from graphs
Identify solutions to inequalities
Solve one-step linear inequalities: addition and subtraction
Solve one-step linear inequalities: multiplication and division
Solve one-step linear inequalities
Graph solutions to one-step linear inequalities
Solve two-step linear inequalities
Graph solutions to two-step linear inequalities
Solve advanced linear inequalities
Graph solutions to advanced linear inequalities
Graph compound inequalities
Write compound inequalities from graphs
Solve compound inequalities
Graph solutions to compound inequalities
Data and graphs

A collection of facts, such as numbers, measurements or observations is called data. We can create a table with the data. A diagram of values, usually shown as lines is called graph. Understanding data and the appropriate graph related to it can help interpreting data.
Interpret bar graphs, line graphs and histograms
Create bar graphs, line graphs and histograms
Interpret circle graphs
Interpret stem-and-leaf plots
Interpret box-and-whisker plots
Interpret a scatter plot
Scatter plots: line of best fit
Relations and functions

A relation is a set of inputs and outputs, while a function is a relation with one output for each input. It works like a machine that takes something in (input) and at the end gives us something back (output). F(x) is the traditional way of expressing functions. Each function has three parts the Input, the Relationship and the Output.
Relations: convert between tables, graphs, mappings and lists of points
Domain and range of relations
Identify independent and dependent variables
Identify functions
Identify functions: vertical line test
Find values using function graphs
Evaluate a function
Evaluate a function: plug in an expression
Complete a function table from a graph
Complete a function table from an equation
Interpret the graph of a function: word problems
Direct and inverse variation

A relationship between two variables in which one is a constant multiple of the other is called direct variation. The statement “Y varies directly as X” means that when X increases, Y increases by the same factor.
Identify proportional relationships
Find the constant of variation
Graph a proportional relationship
Write direct variation equations
Write and solve direct variation equations
Identify direct variation and inverse variation
Write inverse variation equations
Write and solve inverse variation equations
Linear functions

A function related an input to an output. It works like a machine that takes something in (input) and at the end gives us something back (output). F(x) is the traditional way of expressing functions. Each function has three parts the Input, the Relationship and the Output. Linear equations are equations that make a straight line when graphed.
Identify linear functions
Find the slope of a graph
Find the slope from two points
Find a missing coordinate using slope
Slope-intercept form: find the slope and y-intercept
Slope-intercept form: graph an equation
Slope-intercept form: write an equation from a graph
Slope-intercept form: write an equation
Slope-intercept form: write an equation from a table
Slope-intercept form: write an equation from a word problem
Write linear functions to solve word problems
Complete a table and graph a linear function
Compare linear functions: graphs, tables and equations
Write equations in standard form
Standard form: find x- and y-intercepts
Standard form: graph an equation
Equations of horizontal and vertical lines
Graph a horizontal or vertical line
Point-slope form: graph an equation
Point-slope form: write an equation
Point-slope form: write an equation from a graph
Slopes of parallel and perpendicular lines
Write an equation for a parallel or perpendicular line
Find the distance between a point and a line
Find the distance between two parallel lines
Transformations of linear functions
Systems of linear equations

Two or more equations containing common variables is called the system of equations. A system of equations in which every equation is linear is called system of linear equations. For any linear system, there are three possible outcomes: there is only one solution, there are infinitely solutions or there are no solutions at all. If the number of equations is more than the variables the system is called overdetermined, while if the variables are more than the equations the system is called underdetermined.
Is (x, y) a solution to the system of equations?
Solve a system of equations by graphing
Solve a system of equations by graphing: word problems
Find the number of solutions to a system of equations by graphing
Find the number of solutions to a system of equations
Classify a system of equations by graphing
Classify a system of equations
Solve a system of equations using substitution
Solve a system of equations using substitution: word problems
Solve a system of equations using elimination
Solve a system of equations using elimination: word problems
Solve a system of equations using any method
Solve a system of equations using any method: word problems
Monomials

A polynomial with just one term is called a Monomial.
Identify monomials
Multiply monomials
Divide monomials
Multiply and divide monomials
Powers of monomials
Polynomials

The sum or difference of terms which have variables raised to positive integer powers and which have coefficients. A polynomial can have constants, variables and exponents, but never division by variable. Even though the poly- means many the polynomials terms should be finite.
Polynomial vocabulary
Model polynomials with algebra tiles
Add and subtract polynomials using algebra tiles
Add and subtract polynomials
Add polynomials to find perimeter
Multiply a polynomial by a monomial
Multiply two polynomials using algebra tiles
Multiply two binomials
Multiply two binomials: special cases
Multiply polynomials
Factoring

Finding what to multiply to get an expression is called factoring or factorizing. Factoring is like splitting an expression into a multiplication of simpler expressions. Factoring is important because it helps us to simplify expressions.
GCF of monomials
Factor out a monomial
Factor quadratics with leading coefficient 1
Factor quadratics with other leading coefficients
Factor quadratics using algebra tiles
Factor quadratics: special cases
Factor by grouping
Factor polynomials
Quadratic equations

An equation where the highest exponent of the variable is two is called quadratic equation. In other words, an equation includes only second-degree polynomials. The quadratic equation is used to find the curve on a Cartesian plane.
Characteristics of quadratic functions
Complete a function table: quadratic functions
Solve a quadratic equation using square roots
Solve a quadratic equation using the zero product property
Solve a quadratic equation by factoring
Complete the square
Solve a quadratic equation by completing the square
Solve a quadratic equation using the quadratic formula
Using the discriminant
Parabolas

Parabola is a special curve, shaped like an arch. Any point of a parabola is at an equal distance from a fixed point (the focus), and a fixed straight line (the directrix). For formal definition we say: for a given point, called focus, and a given line not through the focus, called directrix, a parabola is the locus of points such that the distance of the focus equals the distance to the directrix. Not all U-shaped curves are parabola, a parabola should satisfy the conditions listed above. Parabola has many important applications in real life, such as designing automobiles headlights to calculating the path of a ballistic missile.
Identify the direction a parabola opens
Find the vertex of a parabola
Find the axis of symmetry of a parabola
Write equations of parabolas in vertex form from graphs
Write equations of parabolas in vertex form using properties
Graph parabolas
Functions: linear, quadratic, exponential

A function related an input to an output. It works like a machine that takes something in (input) and at the end gives us something back (output). F(x) is the traditional way of expressing functions. Each function has three parts the Input, the Relationship and the Output. Linear equations are equations that make a straight line when graphed.
Identify linear, quadratic and exponential functions from graphs
Identify linear, quadratic and exponential functions from tables
Write linear, quadratic and exponential functions
Linear functions over unit intervals
Exponential functions over unit intervals
Describe linear and exponential growth and decay
Rational functions and expressions

A function that be written as a polynomial divided by a polynomial is a rational function. It is rational because one is divided by the other, like a ratio.
Rational functions: asymptotes and excluded values
Simplify complex fractions
Simplify rational expressions
Multiply and divide rational expressions
Divide polynomials
Add and subtract rational expressions
Solve rational equations
Circles in the coordinate plane

A circle is a two-dimensional shape made by drawing a curve that is always the same distance from a center. In other words, a circle is the locus of all points that are a fixed distance from a given point.
Find the centre of a circle
Find the radius or diameter of a circle
Write equations of circles in standard form from graphs
Write equations of circles in standard form using properties
Graph circles
Logic

One area of mathematics that has its roots deep in philosophy is the study of logic. Mathematical log helps to detect whether a statement is valid or invalid.
Identify hypotheses and conclusions
Counterexamples
Truth tables
Truth values
Conditionals
Negations
Converses, inverses and contrapositives
Biconditionals
Measurement

Measurement is the process of assigning a number to a physical property, like length, area, mass, etc.
Estimate metric measurements
Convert rates and measurements: metric units
Estimate imperial measurements of length
Convert rates and measurements: imperial units of length
Unit rates
Unit prices with imperial length conversions
Imperial mixed units of length
Convert between metric and imperial units of length
Scale drawings: word problems
Constructions

Construction in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge and a pencil. Construction is important in geometry because it allows you to draw lines, angles, and polygons with the simplest tools at you hand.
Construct an angle bisector
Construct a congruent angle
Two-dimensional figures

Two-dimensional geometry or plane geometry is about flat shapes like triangles and circles. Two-dimensional figures have only two dimensions such as width and height but no thickness. It also known as “2D”.
Polygon vocabulary
Interior angles of polygons
Perimeter
Area of triangles and quadrilaterals
Area and perimeter in the coordinate plane I
Area and perimeter in the coordinate plane II
Area and circumference of circles
Area of compound figures
Area between two shapes
Area and perimeter of similar figures
Identify trapezoids
Classify quadrilaterals
Graph quadrilaterals
Properties of parallelograms
Properties of rhombuses
Three-dimensional figures

Having three dimensions such as Height, Width and Depth, like any real-world object is a three-dimensional figure. Three-dimensional geometry is about solid shapes like spheres or cubes. It is also known as “3D”.
Three-dimensional figure vocabulary
Parts of three-dimensional figures
Nets and drawings of three-dimensional figures
Introduction to surface area and volume
Surface area of prisms and cylinders
Surface area of pyramids and cones
Volume of prisms and cylinders
Volume of pyramids and cones
Surface area and volume of spheres
Introduction to similar solids
Surface area and volume of similar solids
Surface area and volume review
Cross-sections of three-dimensional figures
Solids of revolution
Congruent figures

When we change a shape by using Turn, flip, slide or resize it is called transformation. If one shape can become another using Turn, Flip or Slide then shapes are congruent. Congruence keeps the size, area, angles and line lengths of the shape.
Congruent line segments
Congruence statements and corresponding parts
Solve problems involving corresponding parts
Identify congruent figures
SSS and SAS Theorems
ASA and AAS Theorems
SSS, SAS, ASA and AAS Theorems
SSS Theorem in the coordinate plane
Congruency in isosceles and equilateral triangles
Hypotenuse-Leg Theorem
Triangles

Triangle is a polygon with 3 sides.
Classify triangles
Triangle Angle-Sum Theorem
Midsegments of triangles
Triangles and bisectors
Identify medians, altitudes, angle bisectors and perpendicular bisectors
Angle-side relationships in triangles
Triangle Inequality Theorem
Similarity

When we change a shape by using Turn, flip, slide or resize it is called transformation. Two shapes are similar when one can become the other after a resize, flip, slide or turn. When two shapes are similar then the corresponding angles are equal, and the lines are in proportion. This can make life a lot easier when solving geometry problems.
Identify similar figures
Similarity ratios
Similarity statements
Side lengths and angle measures in similar figures
Similar triangles and indirect measurement
Perimeters of similar figures
Similarity rules for triangles
Similar triangles and similarity transformations
Similarity of circles
Triangle Proportionality Theorem
Areas of similar figures
Right triangles

Right triangles are important in geometry due to their properties and the use of Pythagoras theorem.
Pythagorean Theorem
Converse of the Pythagorean theorem
Pythagorean Inequality Theorems
Special right triangles
Trigonometry

Trigonometry is the study of triangles with emphasis on calculations involving the lengths of sides and the angles. Trigonometry is based on six functions, namely Sine, Cosine, Tangent, Cotangent, Secant, and Cosecant. Trigonometry also includes study of the properties of these functions and their graphs. Trigonometry is an important field in mathematics with a lot of applications in real life problems, like calculating the waves and tides in oceans, creating maps, satellite systems and a lot more.
Trigonometric ratios: sin, cos and tan
Trigonometric ratios: csc, sec and cot
Find trigonometric functions of special angles
Find trigonometric functions using a calculator
Inverses of trigonometric functions
Trigonometric ratios: find a side length
Trigonometric ratios: find an angle measure
Solve a right triangle
Transformations

When we change a shape by using Turn, flip, slide or resize it is called transformation. Transformation is an operation or operations that alter the form of a figure. Transformations are important in geometry and advanced math works.
Translations: graph the image
Translations: find the coordinates
Translations: write the rule
Reflections: graph the image
Reflections: find the coordinates
Rotate polygons about a point
Rotations: graph the image
Rotations: find the coordinates
Classify congruence transformations
Compositions of congruence transformations: graph the image
Transformations that carry a polygon onto itself
Congruence transformations: mixed review
Dilations: graph the image
Dilations: find the coordinates
Dilations: scale factor and classification
Dilations and parallel lines
Probability

Probability is the chance of something happening or how likely it is that some event will happen. Probability is a number between 0 (not happening) to 1 (certainly happening).
Theoretical and experimental probability
Compound events: find the number of outcomes
Independent and dependent events
Factorials
Permutations
Counting principle
Permutation and combination notation
Geometric probability
Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of data. Statistics is a strong tool in everyday life to get answers about data and make concrete decisions.
Mean, median, mode and range
Quartiles
Identify biased samples
Mean absolute deviation
Variance and standard deviation