# NZ Year 11 Maths Help & Practice!

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##### 1Rational Numbers

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

##### 3Direct variation

##### 4Introduction to Relations and Functions

##### 5Linear Functions

- 5.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 5.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 5.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 5.4Gradient intercept form: y = mx + b
- 5.5General form: Ax + By + C = 0
- 5.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 5.7Rate of change
- 5.8Graphing linear functions using table of values
- 5.9Graphing linear functions using x- and y-intercepts
- 5.10Graphing from gradient-intercept form y=mx+b
- 5.11Graphing linear functions using a single point and gradient
- 5.12Word problems of graphing linear functions
- 5.13Parallel and perpendicular lines in linear functions
- 5.14Applications of linear relations

- 5.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 6Linear Inequalities

##### 7Solving Simultaneous Equations

- 7.1Determining number of solutions to linear equations
- 7.2Solving simultaneous equations by graphing
- 7.3Solving simultaneous equations by elimination
- 7.4Solving simultaneous equations by substitution
- 7.5Money related questions in linear equations
- 7.6Unknown number related questions in linear equations
- 7.7Distance and time related questions in linear equations
- 7.8Rectangular shape related questions in linear equations

- 7.1Determining number of solutions to linear equations
##### 8Exponents

##### 9Exponential Functions

- 9.1Exponents: Product rule
*(a^x)(a^y) = a^(x+y)* - 9.2Exponents: Division rule (a^x / a^y) = a^(x-y)
- 9.3Exponents: Power rule
*(a^x)^y = a^(x * y)* - 9.4Exponents: Negative exponents
- 9.5Exponents: Zero exponent:
*a^0 = 1* - 9.6Exponents: Rational exponents
- 9.7Graphing exponential functions
- 9.8Graphing transformations of exponential functions
- 9.9Finding an exponential function given its graph

- 9.1Exponents: Product rule
##### 10Logarithmic Functions

- 10.1What is a logarithm?
- 10.2Converting from logarithmic form to exponential form
- 10.3Evaluating logarithms without a calculator
- 10.4Common logarithms
- 10.5Natural log: ln
- 10.6Evaluating logarithms using change-of-base formula
- 10.7Converting from exponential form to logarithmic form
- 10.8Solving exponential equations with logarithms
- 10.9Product rule of logarithms
- 10.10Quotient rule of logarithms
- 10.11Combining product rule and quotient rule in logarithms
- 10.12Evaluating logarithms using logarithm rules
- 10.13Solving logarithmic equations
- 10.14Graphing logarithmic functions
- 10.15Finding a logarithmic function given its graph

- 10.1What is a logarithm?
##### 11Introduction to Polynomials

##### 12Operations of Polynomials

##### 13Factorising Polynomial Expressions

- 13.1Common factors of polynomials
- 13.2Factorising polynomials by grouping
- 13.3Solving polynomials with the unknown "b" from
*x^2 + bx + c* - 13.4Solving polynomials with the unknown "c" from
*x^2 + bx + c* - 13.5Factorising polynomials:
*x^2 + bx + c* - 13.6Applications of polynomials:
*x^2 + bx + c* - 13.7Solving polynomials with the unknown "b" from $ax^2 + bx + c$
- 13.8Factorising polynomials: $ax^2 + bx + c$
- 13.9Factorising perfect square trinomials:
*(a + b)^2 = a^2 + 2ab + b^2*or*(a - b)^2 = a^2 - 2ab + b^2* - 13.10Find the difference of squares:
*(a - b)(a + b) = (a^2 - b^2)* - 13.11Evaluating polynomials
- 13.12Using algebra tiles to factorise polynomials
- 13.13Solving polynomial equations
- 13.14Word problems of polynomials

- 13.1Common factors of polynomials
##### 14Quadratic Functions

- 14.1Characteristics of quadratic functions
- 14.2Transformations of quadratic functions
- 14.3Quadratic function in general form:
*y = ax^2 + bx + c* - 14.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 14.5Completing the square
- 14.6Converting from general to vertex form by completing the square
- 14.7Shortcut: Vertex formula
- 14.8Graphing parabolas for given quadratic functions
- 14.9Finding the quadratic functions for given parabolas
- 14.10Applications of quadratic functions

- 14.1Characteristics of quadratic functions
##### 15Conics

##### 16Radicals

##### 17Algebraic Fractions

- 17.1Simplifying algebraic fractions and restrictions
- 17.2Adding and subtracting algebraic fractions
- 17.3Multiplying algebraic fractions
- 17.4Dividing algebraic fractions
- 17.5Solving equations with algebraic fractions
- 17.6Applications of equations with algebraic fractions
- 17.7Simplifying complex fractions
- 17.8Partial fraction decomposition

- 17.1Simplifying algebraic fractions and restrictions
##### 18Reciprocal Functions

##### 19Rational Functions

##### 20Sequences and Series

##### 21Angles, Lines and Transversals

##### 22Symmetry and Surface Area

##### 23Properties of triangles

##### 24Pythagorean Theorem

##### 25Circle Geometry

##### 26Scale Factors and Similarity

##### 27Congruent Triangles

##### 28Introduction to volume

##### 29Surface Area and Volume

##### 30Introduction to Trigonometry

- 30.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
- 30.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )
- 30.3Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )
- 30.4Combination of SohCahToa questions
- 30.5Solving expressions using 45-45-90 special right triangles
- 30.6Solving expressions using 30-60-90 special right triangles
- 30.7Word problems relating ladder in trigonometry
- 30.8Word problems relating guy wire in trigonometry
- 30.9Other word problems relating angles in trigonometry

- 30.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
##### 31Trigonometric Ratios and Angle Measure

##### 32Bearings

##### 33Statistics

##### 34Probability

##### 35Data and Graphs