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Year 10 Maths Topics

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Number System and Radicals
Understanding the number systems
Prime factorisation
Greatest Common Factors (GCF)
Least Common Multiple (LCM)
Rational vs. Irrational numbers
Converting repeating decimals to fractions
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Rational Numbers
Comparing and ordering rational numbers
Solving problems with rational numbers in decimal form
Solving problems with rational numbers in fraction form
Determine square roots of rational numbers
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Ratios, Rates, and Proportions
Ratios
Rates
Proportions
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Percents
Representing percents
Percents, fractions, and decimals
Percent of a number
Adding and multiplying percents
Taxes, discounts, tips and more
Simple interest
Finance: Compound interest
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Pythagorean Theorem
Squares and square roots
Pythagorean theorem
Estimating square roots
Using the pythagorean relationship
Applications of pythagorean theorem
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Volume
Introduction to volume
Volume of prisms
Volume of cylinders
Word problems relating volume of prisms and cylinders
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Scale Factors and Similarity
Enlargements and reductions with scale factors
Scale diagrams
Similar triangles
Similar polygons
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Solving Linear Equations
Solving linear equations using multiplication and division
Solving two-step linear equations: ax + b = c, x/a + b = c
Solving linear equations using distributive property: a(x + b) = c
Solving linear equations with variables on both sides
Solving literal equations
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Data and Graphs
Reading and drawing bar graphs
Reading and drawing histograms
Reading and drawing line graphs
Box-and-whisker plots and scatter plots
Stem-and-leaf plots
Pie charts
Reading and drawing Venn diagrams
Frequency tables and dot plots
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Direct Variation
Identifying proportional relationships
Understanding graphs of proportional relationships
Understanding tables of values of proportional relationships
Applications of linear relationships
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Introduction to Relations and Functions
Relationship between two variables
Understand relations between x- and y-intercepts
Domain and range of a function
Identifying functions
Function notation
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Linear Functions
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)M=(2x1​+x2​​,2y1​+y2​​)
Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}m=x2​−x1​y2​−y1​​
Gradient intercept form: y = mx + b
General form: Ax + By + C = 0
Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)y−y1​=m(x−x1​)
Rate of change
Graphing linear functions using table of values
Graphing linear functions using x- and y-intercepts
Graphing from gradient-intercept form y=mx+b
Graphing linear functions using a single point and gradient
Word problems of graphing linear functions
Parallel and perpendicular lines in linear functions
Applications of linear relations
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Linear Inequalities
Express linear inequalities graphically and algebraically
Solving one-step linear inequalities
Solving multi-step linear inequalities
Compound inequalities
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Solving Simultaneous Equations
Determining number of solutions to linear equations
Solving simultaneous equations by graphing
Solving simultaneous equations by elimination
Solving simultaneous equations by substitution
Money related questions in linear equations
Unknown number related questions in linear equations
Distance and time related questions in linear equations
Rectangular shape related questions in linear equations
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Exponents
Product rule of exponents
Quotient rule of exponents
Power of a product rule
Power of a quotient rule
Power of a power rule
Negative exponent rule
Combining the exponent rules
Scientific notation
Convert between radicals and rational exponents
Solving for exponents
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Introduction to Polynomials
Characteristics of polynomials
Equivalent expressions of polynomials
Adding and subtracting polynomials
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Operations of Polynomials
What is a polynomial?
Polynomial components
Multiplying monomial by monomial
Multiplying monomial by binomial
Multiplying binomial by binomial
Multiplying polynomial by polynomial
Applications of polynomials
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Factorising Polynomial Expressions
Common factors of polynomials
Factorising polynomials by grouping
Solving polynomials with the unknown "b" from x^2 + bx + c
Solving polynomials with the unknown "c" from x^2 + bx + c
Factorising polynomials: x^2 + bx + c
Applications of polynomials: x^2 + bx + c
Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + cax2+bx+c
Factorising polynomials: ax2+bx+cax^2 + bx + cax2+bx+c
Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
Evaluating polynomials
Using algebra tiles to factorise polynomials
Solving polynomial equations
Word problems of polynomials
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Radicals
Square and square roots
Cubic and cube roots
Evaluating and simplifying radicals
Converting radicals to mixed radicals
Converting radicals to entire radicals
Adding and subtracting radicals
Multiplying and dividing radicals
Rationalize the denominator
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Algebraic Fractions
Simplifying algebraic fractions and restrictions
Adding and subtracting algebraic fractions
Multiplying algebraic fractions
Dividing algebraic fractions
Solving equations with algebraic fractions
Applications of equations with algebraic fractions
Simplifying complex fractions
Partial fraction decomposition
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Reciprocal Functions
Graphing reciprocals of linear functions
Graphing reciprocals of quadratic functions
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Statistics
Median and mode
Mean
Range and outliers
Application of averages
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Probability
Determining probabilities using tree diagrams and tables
Probability of independent events
Probability with Venn diagrams

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