# 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:
##### 4Solving Linear Equations

##### 5Solving Linear Inequalities

##### 6Introduction to Relations and Functions

##### 7Linear Relations

##### 8Linear Functions

- 8.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 8.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 8.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 8.4Gradient intercept form: y = mx + b
- 8.5General form: Ax + By + C = 0
- 8.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 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: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 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
##### 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 $ax^2 + bx + c$
- 17.8Factorising polynomials: $ax^2 + bx + c$
- 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 = $\frac{o}{h}$ )
- 32.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )
- 32.3Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )
- 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 = $\frac{o}{h}$ )
##### 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