Year 10 Maths Help & Practice

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1Number System and Radicals
2Patterns and Solving Equations
3Linear Equations (Basic)
- 3.1Model and solve one-step linear equations: ax = b, x/a = b
- 3.2Solving two-step linear equations using addition and subtraction: ax + b = c
- 3.3Solving two-step linear equations using multiplication and division: x/a + b = c
- 3.4Solving two-step linear equations using distributive property: a(x + b) = c
- 3.1Model and solve one-step linear equations: ax = b, x/a = b
4Solving Linear Equations
5Solving Linear Inequalities
6Introduction to Relations and Functions
7Linear Relations
8Linear Functions
- 8.1Distance formula:
- 8.2Midpoint formula:
- 8.3Gradient equation:
- 8.4Gradient intercept form: y = mx + b
- 8.5General form: Ax + By + C = 0
- 8.6Gradient-point form:
- 8.7Rate of change
- 8.8Graphing linear functions using table of values
- 8.9Graphing linear functions using x- and y-intercepts
- 8.10Graphing from gradient-intercept form y=mx+b
- 8.11Graphing linear functions using a single point and gradient
- 8.12Word problems of graphing linear functions
- 8.13Parallel and perpendicular lines in linear functions
- 8.14Applications of linear relations
- 8.1Distance formula:
9Solving Simultaneous Equations
- 9.1Determining number of solutions to linear equations
- 9.2Solving simultaneous equations by graphing
- 9.3Solving simultaneous equations by elimination
- 9.4Solving simultaneous equations by substitution
- 9.5Money related questions in linear equations
- 9.6Unknown number related questions in linear equations
- 9.7Distance and time related questions in linear equations
- 9.8Rectangular shape related questions in linear equations
- 9.1Determining number of solutions to linear equations
10Transformations of Functions
- 10.1Transformations of functions: Horizontal translations
- 10.2Transformations of functions: Vertical translations
- 10.3Reflection across the y-axis: y = f(-x)
- 10.4Reflection across the x-axis: y = -f(x)
- 10.5Transformations of functions: Horizontal stretches
- 10.6Transformations of functions: Vertical stretches
- 10.7Combining transformations of functions
- 10.8Even and odd functions
- 10.1Transformations of functions: Horizontal translations
11Exponents
- 11.1Product rule of exponents
- 11.2Quotient rule of exponents
- 11.3Power of a product rule
- 11.4Power of a quotient rule
- 11.5Power of a power rule
- 11.6Negative exponent rule
- 11.7Combining the exponent rules
- 11.8Scientific notation
- 11.9Convert between radicals and rational exponents
- 11.10Solving for exponents
- 11.1Product rule of exponents
12Exponential Functions
- 12.1Exponents: Product rule (a^x)(a^y) = a^(x+y)
- 12.2Exponents: Division rule (a^x / a^y) = a^(x-y)
- 12.3Exponents: Power rule (a^x)^y = a^(x * y)
- 12.4Exponents: Negative exponents
- 12.5Exponents: Zero exponent: a^0 = 1
- 12.6Exponents: Rational exponents
- 12.7Graphing exponential functions
- 12.8Graphing transformations of exponential functions
- 12.9Finding an exponential function given its graph
- 12.10Finance: Compound interest
- 12.1Exponents: Product rule (a^x)(a^y) = a^(x+y)
13Logarithmic Functions
- 13.1What is a logarithm?
- 13.2Converting from logarithmic form to exponential form
- 13.3Evaluating logarithms without a calculator
- 13.4Common logarithms
- 13.5Natural log: ln
- 13.6Evaluating logarithms using change-of-base formula
- 13.7Converting from exponential form to logarithmic form
- 13.8Solving exponential equations with logarithms
- 13.9Product rule of logarithms
- 13.10Quotient rule of logarithms
- 13.11Combining product rule and quotient rule in logarithms
- 13.12Evaluating logarithms using logarithm rules
- 13.13Solving logarithmic equations
- 13.14Graphing logarithmic functions
- 13.15Finding a logarithmic function given its graph
- 13.1What is a logarithm?
14Introduction to Polynomials
15Multiplying and Dividing Polynomials
16Operations of Polynomials
17Factorising Polynomial Expressions
- 17.1Common factors of polynomials
- 17.2Factorising polynomials by grouping
- 17.3Solving polynomials with the unknown "b" from x^2 + bx + c
- 17.4Solving polynomials with the unknown "c" from x^2 + bx + c
- 17.5Factorising polynomials: x^2 + bx + c
- 17.6Applications of polynomials: x^2 + bx + c
- 17.7Solving polynomials with the unknown "b" from
- 17.8Factorising polynomials:
- 17.9Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
- 17.10Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
- 17.11Evaluating polynomials
- 17.12Using algebra tiles to factorise polynomials
- 17.13Solving polynomial equations
- 17.14Word problems of polynomials
- 17.1Common factors of polynomials
18Factorising Polynomial (Advanced)
19Quadratic Functions
- 19.1Characteristics of quadratic functions
- 19.2Transformations of quadratic functions
- 19.3Quadratic function in general form: y = ax^2 + bx + c
- 19.4Quadratic function in vertex form: y = a(x-p)^2 + q
- 19.5Completing the square
- 19.6Converting from general to vertex form by completing the square
- 19.7Shortcut: Vertex formula
- 19.8Graphing parabolas for given quadratic functions
- 19.9Finding the quadratic functions for given parabolas
- 19.10Applications of quadratic functions
- 19.1Characteristics of quadratic functions
20Conics
21Radicals
22Algebraic Fractions
- 22.1Simplifying algebraic fractions and restrictions
- 22.2Adding and subtracting algebraic fractions
- 22.3Multiplying algebraic fractions
- 22.4Dividing algebraic fractions
- 22.5Solving equations with algebraic fractions
- 22.6Applications of equations with algebraic fractions
- 22.7Simplifying complex fractions
- 22.8Partial fraction decomposition
- 22.1Simplifying algebraic fractions and restrictions
23Reciprocal Functions
24Scale Factors and Similarity
25Properties of Triangles
26Congruent Triangles
27Pythagorean Theorem
28Introduction to Surface Area of 3D Shapes
29Introduction to Volume
30Surface Area and Volume
31Circles
32Introduction to Trigonometry
- 32.1Use sine ratio to calculate angles and sides (Sin = )
- 32.2Use cosine ratio to calculate angles and sides (Cos = )
- 32.3Use tangent ratio to calculate angles and sides (Tan = )
- 32.4Combination of SohCahToa questions
- 32.5Solving expressions using 45-45-90 special right triangles
- 32.6Solving expressions using 30-60-90 special right triangles
- 32.7Word problems relating ladder in trigonometry
- 32.8Word problems relating guy wire in trigonometry
- 32.9Other word problems relating angles in trigonometry
- 32.1Use sine ratio to calculate angles and sides (Sin = )
33Trigonometric Ratios and Angle Measure
34Bearings
35Graphing Trigonometric Functions
36Introduction to Probability
37Statistics
38Data and Graphs
39Introduction to Matrices
40Determinants and Inverses of Matrices
- 40.1The determinant of a 2 x 2 matrix
- 40.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
- 40.3The inverse of a 2 x 2 matrix
- 40.4The inverse of 3 x 3 matrices with matrix row operations
- 40.5The inverse of 3 x 3 matrix with determinants and adjugate
- 40.62 x 2 invertible matrix
- 40.7Solving linear systems using Cramer's Rule
- 40.8Solving linear systems using 2 x 2 inverse matrices
- 40.1The determinant of a 2 x 2 matrix
