# Third Year Maths Help & Practice

## All in One PlaceEverything you need for JC, LC, and college level maths and science classes. | ## Learn with EaseWe’ve mastered the national curriculum so that you can revise with confidence. | ## Instant Help24/7 access to the best tips, walkthroughs, and practice exercises available. |

#### Make math click 💡 and get better grades! Join for Free

##### 1Number System and Radicals

##### 2Ratios, Rates, and Proportions

##### 3Percents

##### 4Measuring Systems

##### 5Coordinates, Quadrants, and Transformations

##### 6Angles, Lines, and Transversals

##### 7Properties of Triangles

##### 8Circles

##### 9Congruent Triangles

##### 10Symmetry and Surface Area

##### 11Scale Factors and Similarity

##### 12Pythagorean Theorem

##### 13Introduction to 3-Dimensional Figures

##### 14Volume

##### 15Introduction to Trigonometry

- 15.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
- 15.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )
- 15.3Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )
- 15.4Combination of SohCahToa questions
- 15.5Solving expressions using 45-45-90 special right triangles
- 15.6Solving expressions using 30-60-90 special right triangles
- 15.7Word problems relating ladder in trigonometry
- 15.8Word problems relating guy wire in trigonometry
- 15.9Other word problems relating angles in trigonometry

- 15.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
##### 16Patterns and Solving Equations

##### 17Introduction to Linear Relations

##### 18Linear Inequalities

##### 19Introduction to Relations and Functions

##### 20Data and Graphs

##### 21Linear Functions

- 21.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 21.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 21.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 21.4Gradient intercept form: y = mx + b
- 21.5General form: Ax + By + C = 0
- 21.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 21.7Rate of change
- 21.8Graphing linear functions using table of values
- 21.9Graphing linear functions using x- and y-intercepts
- 21.10Graphing from gradient-intercept form y=mx+b
- 21.11Graphing linear functions using a single point and gradient
- 21.12Word problems of graphing linear functions
- 21.13Parallel and perpendicular lines in linear functions
- 21.14Applications of linear relations

- 21.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 22Linear Equations

- 22.1Introduction to linear equations
- 22.2Introduction to nonlinear equations
- 22.3Special case of linear equations: Horizontal lines
- 22.4Special case of linear equations: Vertical lines
- 22.5Parallel line equation
- 22.6Perpendicular line equation
- 22.7Combination of both parallel and perpendicular line equations
- 22.8Applications of linear equations

- 22.1Introduction to linear equations
##### 23Solving Simultaneous Equations

- 23.1Determining number of solutions to linear equations
- 23.2Solving simultaneous equations by graphing
- 23.3Solving simultaneous equations by elimination
- 23.4Solving simultaneous equations by substitution
- 23.5Money related questions in linear equations
- 23.6Unknown number related questions in linear equations
- 23.7Distance and time related questions in linear equations
- 23.8Rectangular shape related questions in linear equations

- 23.1Determining number of solutions to linear equations
##### 24Exponents

- 24.1Product rule of exponents
- 24.2Quotient rule of exponents
- 24.3Power of a product rule
- 24.4Power of a quotient rule
- 24.5Power of a power rule
- 24.6Negative exponent rule
- 24.7Combining the exponent rules
- 24.8Scientific notation
- 24.9Convert between radicals and rational exponents
- 24.10Solving for exponents

- 24.1Product rule of exponents
##### 25Quadratic Functions

- 25.1Characteristics of quadratic functions
- 25.2Transformations of quadratic functions
- 25.3Quadratic function in general form:
*y = ax^2 + bx + c* - 25.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 25.5Completing the square
- 25.6Converting from general to vertex form by completing the square
- 25.7Shortcut: Vertex formula
- 25.8Graphing parabolas for given quadratic functions
- 25.9Finding the quadratic functions for given parabolas
- 25.10Applications of quadratic functions

- 25.1Characteristics of quadratic functions
##### 26Polynomials

##### 27Operations of Polynomials

##### 28Factorising Polynomial expressions

- 28.1Common factors of polynomials
- 28.2Factorising polynomials by grouping
- 28.3Solving polynomials with the unknown "b" from
*x^2 + bx + c* - 28.4Solving polynomials with the unknown "c" from
*x^2 + bx + c* - 28.5Factorising polynomials:
*x^2 + bx + c* - 28.6Applications of polynomials:
*x^2 + bx + c* - 28.7Solving polynomials with the unknown "b" from $ax^2 + bx + c$
- 28.8Factorising polynomials: $ax^2 + bx + c$
- 28.9Factorising perfect square trinomials:
*(a + b)^2 = a^2 + 2ab + b^2*or*(a - b)^2 = a^2 - 2ab + b^2* - 28.10Find the difference of squares:
*(a - b)(a + b) = (a^2 - b^2)* - 28.11Evaluating polynomials
- 28.12Solving polynomial equations
- 28.13Word problems of polynomials

- 28.1Common factors of polynomials
##### 29Radicals

##### 30Rational Expressions

- 30.1Simplifying rational expressions and restrictions
- 30.2Adding and subtracting rational expressions
- 30.3Multiplying rational expressions
- 30.4Dividing rational expressions
- 30.5Solving rational equations
- 30.6Applications of rational equations
- 30.7Simplifying complex fractions
- 30.8Partial fraction decomposition

- 30.1Simplifying rational expressions and restrictions
##### 31Reciprocal Functions

##### 32Probability