# Year 10 Maths Help & Practice

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##### 1Number System and Radicals

##### 2Rational Numbers

##### 3Ratios, Rates, and Proportions

##### 4Percents

##### 5Pythagorean Theorem

##### 6Volume

##### 7Scale Factors and Similarity

##### 8Solving Linear Equations

##### 9Data and Graphs

##### 10Direct Variation

##### 11Introduction to Relations and Functions

##### 12Linear Functions

- 12.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 12.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 12.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 12.4Gradient intercept form: y = mx + b
- 12.5General form: Ax + By + C = 0
- 12.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 12.7Rate of change
- 12.8Graphing linear functions using table of values
- 12.9Graphing linear functions using x- and y-intercepts
- 12.10Graphing from gradient-intercept form y=mx+b
- 12.11Graphing linear functions using a single point and gradient
- 12.12Word problems of graphing linear functions
- 12.13Parallel and perpendicular lines in linear functions
- 12.14Applications of linear relations

- 12.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 13Linear Inequalities

##### 14Solving Simultaneous Equations

- 14.1Determining number of solutions to linear equations
- 14.2Solving simultaneous equations by graphing
- 14.3Solving simultaneous equations by elimination
- 14.4Solving simultaneous equations by substitution
- 14.5Money related questions in linear equations
- 14.6Unknown number related questions in linear equations
- 14.7Distance and time related questions in linear equations
- 14.8Rectangular shape related questions in linear equations

- 14.1Determining number of solutions to linear equations
##### 15Exponents

- 15.1Product rule of exponents
- 15.2Quotient rule of exponents
- 15.3Power of a product rule
- 15.4Power of a quotient rule
- 15.5Power of a power rule
- 15.6Negative exponent rule
- 15.7Combining the exponent rules
- 15.8Scientific notation
- 15.9Convert between radicals and rational exponents
- 15.10Solving for exponents

- 15.1Product rule of exponents
##### 16Introduction to Polynomials

##### 17Operations of Polynomials

##### 18Factorising Polynomial Expressions

- 18.1Common factors of polynomials
- 18.2Factorising polynomials by grouping
- 18.3Solving polynomials with the unknown "b" from
*x^2 + bx + c* - 18.4Solving polynomials with the unknown "c" from
*x^2 + bx + c* - 18.5Factorising polynomials:
*x^2 + bx + c* - 18.6Applications of polynomials:
*x^2 + bx + c* - 18.7Solving polynomials with the unknown "b" from $ax^2 + bx + c$
- 18.8Factorising polynomials: $ax^2 + bx + c$
- 18.9Factorising perfect square trinomials:
*(a + b)^2 = a^2 + 2ab + b^2*or*(a - b)^2 = a^2 - 2ab + b^2* - 18.10Find the difference of squares:
*(a - b)(a + b) = (a^2 - b^2)* - 18.11Evaluating polynomials
- 18.12Using algebra tiles to factorise polynomials
- 18.13Solving polynomial equations
- 18.14Word problems of polynomials

- 18.1Common factors of polynomials
##### 19Radicals

##### 20Algebraic Fractions

- 20.1Simplifying algebraic fractions and restrictions
- 20.2Adding and subtracting algebraic fractions
- 20.3Multiplying algebraic fractions
- 20.4Dividing algebraic fractions
- 20.5Solving equations with algebraic fractions
- 20.6Applications of equations with algebraic fractions
- 20.7Simplifying complex fractions
- 20.8Partial fraction decomposition

- 20.1Simplifying algebraic fractions and restrictions
##### 21Reciprocal Functions

##### 22Statistics

##### 23Probability