NZ Year 11 Maths Tutor, Help and Practice Online

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1Rational Numbers
1. 1.1Comparing and ordering rational numbers
2. 1.2Solving problems with rational numbers in decimal form
3. 1.3Solving problems with rational numbers in fraction form
4. 1.4Determine square roots of rational numbers
2Ratios, Rates, and Proportions
1. 2.1Ratios
2. 2.2Rates
3. 2.3Proportions
3Direct variation
1. 3.1Identifying proportional relationships
2. 3.2Understanding graphs of proportional relationships
3. 3.3Graphing and writing equations of proportional relationships
4. 3.4Applications of proportional relationships
4Introduction to Relations and Functions
1. 4.1Relationship between two variables
2. 4.2Understand relations between x- and y-intercepts
3. 4.3Domain and range of a function
4. 4.4Identifying functions
5. 4.5Function notation
5Linear Functions
1. 5.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ $d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}$
2. 5.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$ $M = (\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})$
3. 5.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$ $m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}$
4. 5.4Gradient intercept form: y = mx + b
5. 5.5General form: Ax + By + C = 0
6. 5.6Gradient-point form: $y - y_1 = m (x - x_1)$ $y - y_{1} = m (x - x_{1})$
7. 5.7Rate of change
8. 5.8Graphing linear functions using table of values
9. 5.9Graphing linear functions using x- and y-intercepts
10. 5.10Graphing from gradient-intercept form y=mx+b
11. 5.11Graphing linear functions using a single point and gradient
12. 5.12Word problems of graphing linear functions
13. 5.13Parallel and perpendicular lines in linear functions
14. 5.14Applications of linear relations
6Linear Inequalities
1. 6.1Express linear inequalities graphically and algebraically
2. 6.2Solving one-step linear inequalities
3. 6.3Solving multi-step linear inequalities
4. 6.4Compound inequalities
7Solving Simultaneous Equations
1. 7.1Determining number of solutions to linear equations
2. 7.2Solving simultaneous equations by graphing
3. 7.3Solving simultaneous equations by elimination
4. 7.4Solving simultaneous equations by substitution
5. 7.5Money related questions in linear equations
6. 7.6Unknown number related questions in linear equations
7. 7.7Distance and time related questions in linear equations
8. 7.8Rectangular shape related questions in linear equations
8Exponents
1. 8.1Product rule of exponents
2. 8.2Quotient rule of exponents
3. 8.3Power of a product rule
4. 8.4Power of a quotient rule
5. 8.5Power of a power rule
6. 8.6Negative exponent rule
7. 8.7Combining the exponent rules
8. 8.8Scientific notation
9. 8.9Convert between radicals and rational exponents
10. 8.10Solving for exponents
9Exponential Functions
1. 9.1Exponents: Product rule $(a^x)(a^y)=a^{(x+y)}$ $(a^{x}) (a^{y}) = a^{(x + y)}$
2. 9.2Exponents: Division rule ${a^x \over a^y}=a^{(x-y)}$ $\frac{a ^{x}}{a ^{y}} = a^{(x - y)}$
3. 9.3Exponents: Power rule $(a^x)^y = a^{(x\cdot y)}$ $(a^{x})^{y} = a^{(x \cdot y)}$
4. 9.4Exponents: Negative exponents
5. 9.5Exponents: Zero exponent: $a^0 = 1$ $a^{0} = 1$
6. 9.6Exponents: Rational exponents
7. 9.7Graphing exponential functions
8. 9.8Graphing transformations of exponential functions
9. 9.9Finding an exponential function given its graph
10Logarithmic Functions
1. 10.1What is a logarithm?
2. 10.2Converting from logarithmic form to exponential form
3. 10.3Evaluating logarithms without a calculator
4. 10.4Common logarithms
5. 10.5Natural log: ln
6. 10.6Evaluating logarithms using change-of-base formula
7. 10.7Converting from exponential form to logarithmic form
8. 10.8Solving exponential equations with logarithms
9. 10.9Product rule of logarithms
10. 10.10Quotient rule of logarithms
11. 10.11Combining product rule and quotient rule in logarithms
12. 10.12Evaluating logarithms using logarithm rules
13. 10.13Solving logarithmic equations
14. 10.14Graphing logarithmic functions
15. 10.15Finding a logarithmic function given its graph
11Introduction to Polynomials
1. 11.1Characteristics of polynomials
2. 11.2Equivalent expressions of polynomials
3. 11.3Adding and subtracting polynomials
12Operations of Polynomials
1. 12.1What is a polynomial?
2. 12.2Polynomial components
3. 12.3Multiplying monomial by monomial
4. 12.4Multiplying monomial by binomial
5. 12.5Multiplying binomial by binomial
6. 12.6Multiplying polynomial by polynomial
7. 12.7Applications of polynomials
13Factorising Polynomial Expressions
1. 13.1Common factors of polynomials
2. 13.2Factorising polynomials by grouping
3. 13.3Solving polynomials with the unknown "b" from $x^2 + bx + c$ $x^{2} + b x + c$
4. 13.4Solving polynomials with the unknown "c" from $x^2 + bx + c$ $x^{2} + b x + c$
5. 13.5Factorising polynomials: $x^2 + bx + c$ $x^{2} + b x + c$
6. 13.6Applications of polynomials: $x^2 + bx + c$ $x^{2} + b x + c$
7. 13.7Solving polynomials with the unknown "b" from $ax^2 + bx + c$ $a x^{2} + b x + c$
8. 13.8Factorising polynomials: $ax^2 + bx + c$ $a x^{2} + b x + c$
9. 13.9Factorising perfect square trinomials: $(a + b)^2 = a^2 + 2ab + b^2$ $(a + b)^{2} = a^{2} + 2 ab + b^{2}$ or $(a - b)^2 = a^2 - 2ab + b^2$ $(a - b)^{2} = a^{2} - 2 ab + b^{2}$
10. 13.10Find the difference of squares: $(a - b)(a + b) = (a^2 - b^2)$ $(a - b) (a + b) = (a^{2} - b^{2})$
11. 13.11Evaluating polynomials
12. 13.12Using algebra tiles to factorise polynomials
13. 13.13Solving polynomial equations
14. 13.14Word problems of polynomials
14Quadratic Functions
1. 14.1Characteristics of quadratic functions
2. 14.2Transformations of quadratic functions
3. 14.3Quadratic function in general form: $y = ax^2 + bx+c$ $y = a x^{2} + b x + c$
4. 14.4Quadratic function in vertex form: y = $a(x-p)^2 + q$ $a (x - p)^{2} + q$
5. 14.5Completing the square
6. 14.6Converting from general to vertex form by completing the square
7. 14.7Shortcut: Vertex formula
8. 14.8Graphing parabolas for given quadratic functions
9. 14.9Finding the quadratic functions for given parabolas
10. 14.10Applications of quadratic functions
15Conics
1. 15.1Conics - Parabola
2. 15.2Conics - Ellipse
3. 15.3Conics - Circle
4. 15.4Conics - Hyperbola
16Radicals
1. 16.1Operations with radicals
2. 16.2Conversion between entire radicals and mixed radicals
3. 16.3Adding and subtracting radicals
4. 16.4Multiplying radicals
5. 16.5Solving radical equations
17Algebraic Fractions
1. 17.1Simplifying algebraic fractions and restrictions
2. 17.2Adding and subtracting algebraic fractions
3. 17.3Multiplying algebraic fractions
4. 17.4Dividing algebraic fractions
5. 17.5Solving equations with algebraic fractions
6. 17.6Applications of equations with algebraic fractions
7. 17.7Simplifying complex fractions
8. 17.8Partial fraction decomposition
18Reciprocal Functions
1. 18.1Graphing reciprocals of linear functions
2. 18.2Graphing reciprocals of quadratic functions
19Rational Functions
1. 19.1What is a rational function?
2. 19.2Point of discontinuity
3. 19.3Vertical asymptote
4. 19.4Horizontal asymptote
5. 19.5Slant asymptote
6. 19.6Graphs of rational functions
7. 19.7Solving rational inequalities
20Sequences and Series
1. 20.1Arithmetic sequences
2. 20.2Arithmetic series
3. 20.3Geometric sequences
4. 20.4Geometric series
5. 20.5Infinite geometric series
6. 20.6Sigma notation
7. 20.7Arithmetic mean vs. Geometric mean
21Angles, Lines and Transversals
1. 21.1Pairs of lines and angles
2. 21.2Parallel lines and transversals
3. 21.3Parallel line proofs
4. 21.4Perpendicular line proofs
22Symmetry and Surface Area
1. 22.1Line symmetry
2. 22.2Rotational symmetry and transformations
3. 22.3Surface area of 3-dimensional shapes
23Properties of triangles
1. 23.1Classifying Triangles
2. 23.2Isosceles and Equilateral Triangles
24Pythagorean Theorem
1. 24.1Squares and square roots
2. 24.2Pythagorean theorem
3. 24.3Estimating square roots
4. 24.4Using the pythagorean relationship
5. 24.5Applications of pythagorean theorem
25Circle Geometry
1. 25.1Angles in a circle
2. 25.2Chord properties
3. 25.3Tangent properties
4. 25.4Circles and circumference
5. 25.5Arcs of a circle
6. 25.6Areas and sectors of circles
26Scale Factors and Similarity
1. 26.1Enlargements and reductions with scale factors
2. 26.2Scale diagrams
3. 26.3Similar triangles
4. 26.4Similar polygons
27Congruent Triangles
1. 27.1Congruence and Congruent Triangles
2. 27.2Triangles Congruent by SSS Proofs
3. 27.3Triangles Congruent by SAS and HL Proofs
4. 27.4Triangles Congruent by ASA and AAS Proofs
28Introduction to volume
1. 28.1Introduction to volume
2. 28.2Volume of prisms
3. 28.3Volume of cylinders
4. 28.4Word problems relating volume of prisms and cylinders
29Surface Area and Volume
1. 29.1Surface area and volume of prisms
2. 29.2Surface area and volume of pyramids
3. 29.3Surface area and volume of cylinders
4. 29.4Surface area and volume of cones
5. 29.5Surface area and volume of spheres
30Introduction to Trigonometry
1. 30.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ $\frac{o}{h}$ )
2. 30.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ $\frac{a}{h}$ )
3. 30.3Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ $\frac{o}{a}$ )
4. 30.4Combination of SohCahToa questions
5. 30.5Solving expressions using 45-45-90 special right triangles
6. 30.6Solving expressions using 30-60-90 special right triangles
7. 30.7Word problems relating ladder in trigonometry
8. 30.8Word problems relating guy wire in trigonometry
9. 30.9Other word problems relating angles in trigonometry
31Trigonometric Ratios and Angle Measure
1. 31.1Standard angle
2. 31.2Coterminal angles
3. 31.3Reference angles
4. 31.4Find the exact value of trigonometric ratios
5. 31.5ASTC rule in trigonometry (All Students Take Calculus)
6. 31.6Unit circle
7. 31.7Law of sines
8. 31.8Law of cosines
9. 31.9Applications of the sine law and cosine law
32Bearings
1. 32.1Introduction to bearings
2. 32.2Bearings and direction word problems
3. 32.3Angle of elevation and depression
33Statistics
1. 33.1Median and mode
2. 33.2Mean
3. 33.3Range and outliers
4. 33.4Application of averages
34Probability
1. 34.1Determining probabilities using tree diagrams and tables
2. 34.2Probability of independent events
3. 34.3Probability with Venn diagrams
35Data and Graphs
1. 35.1Reading and drawing bar graphs
2. 35.2Reading and drawing histograms
3. 35.3Reading and drawing line graphs
4. 35.4Box-and-whisker plots and scatter plots
5. 35.5Stem-and-leaf plots
6. 35.6Reading and drawing Venn diagrams
7. 35.7Frequency tables and dot plots

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NZ Year 11 Maths made completely easy!

1Rational Numbers

2Ratios, Rates, and Proportions

3Direct variation

4Introduction to Relations and Functions

5Linear Functions

6Linear Inequalities

7Solving Simultaneous Equations

8Exponents

9Exponential Functions

10Logarithmic Functions

11Introduction to Polynomials

12Operations of Polynomials

13Factorising Polynomial Expressions

14Quadratic Functions

15Conics

16Radicals

17Algebraic Fractions

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

31Trigonometric Ratios and Angle Measure

32Bearings

33Statistics

34Probability

35Data and Graphs

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