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NZ Year 11 Maths Topics

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1.Rational Numbers

1.1Comparing and ordering rational numbers (free lessons)

1.2Solving problems with rational numbers in decimal form

1.3Solving problems with rational numbers in fraction form

1.4Determine square roots of rational numbers

2.Ratios, Rates, and Proportions

2.1Ratios (free lessons)

3.Direct variation

3.1Writing and solving for proportions

3.2Understanding graphs of proportional relationships (free lessons)

3.3Graphing and writing equations of proportional relationships

3.4Applications of proportional relationships (free lessons)

4.Introduction to Relations and Functions

4.1Relationship between two variables (free lessons)

4.2Understand relations between x- and y-intercepts

4.3Domain and range of a function

4.4Identifying functions

4.5Function notation (free lessons)

5.Linear Functions

5.1Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

(free lessons)

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 (free lessons)

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 (free lessons)

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 (free lessons)

5.14Applications of linear relations

6.Linear Inequalities

6.1Express linear inequalities graphically and algebraically (free lessons)

6.2Solving one-step linear inequalities

6.3Solving multi-step linear inequalities

7.Solving Simultaneous Equations

7.1Determining number of solutions to linear equations (free lessons)

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 (free lessons)

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

8.Exponents

8.1Product rule of exponents (free lessons)

8.2Quotient rule of exponents

8.3Power of a product rule

8.4Power of a quotient rule

8.5Power of a power rule (free lessons)

8.6Negative exponent rule

8.7Combining the exponent rules

8.8Scientific notation

8.9Convert between radicals and rational exponents (free lessons)

8.10Solving for exponents

9.Exponential Functions

9.1Exponents: Product rule

(a^x)(a^y)=a^{(x+y)}

(free lessons)

9.2Exponents: Division rule

{a^x \over a^y}=a^{(x-y)}

9.3Exponents: Power rule

(a^x)^y = a^{(x\cdot y)}

(free lessons)

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

10.Logarithmic Functions

10.1What is a logarithm?

10.2Converting from logarithmic form to exponential form (free lessons)

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 (free lessons)

10.8Solving exponential equations with logarithms

10.9Product rule of logarithms (free lessons)

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

11.Introduction to Polynomials

11.1Characteristics of polynomials (free lessons)

11.2Equivalent expressions of polynomials

11.3Adding and subtracting polynomials

12.Operations of Polynomials

12.1What is a polynomial? (free lessons)

12.2Polynomial components

12.3Multiplying monomial by monomial

12.4Multiplying monomial by binomial

12.5Multiplying binomial by binomial (free lessons)

12.6Multiplying polynomial by polynomial

12.7Applications of polynomials

13.Factorising Polynomial Expressions

13.1Common factors of polynomials (free lessons)

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

(free lessons)

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

(a - b)^2 = a^2 - 2ab + b^2

(free lessons)

13.10Find the difference of squares:

(a - b)(a + b) = (a^2 - b^2)

13.11Evaluating polynomials

13.12Using algebra tiles to solve polynomials

13.13Solving polynomial equations (free lessons)

13.14Word problems of polynomials

14.Quadratic Functions

14.1Characteristics of quadratic functions (free lessons)

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 (free lessons)

14.8Finding the quadratic functions for given parabolas (free lessons)

14.9Applications of quadratic functions

15.Conics

15.1Conics - Parabola

15.2Conics - Ellipse

15.3Conics - Circle

15.4Conics - Hyperbola

16.Radicals

16.1Operations with radicals (free lessons)

16.2Conversion between entire radicals and mixed radicals

16.3Adding and subtracting radicals (free lessons)

16.4Multiplying radicals

16.5Solving radical equations

17.Rational Expressions

17.1Simplifying rational expressions and restrictions

17.2Adding and subtracting rational expressions (free lessons)

17.3Multiplying rational expressions

17.4Dividing rational expressions

17.5Solving rational equations

17.6Applications of rational equations

18.Rational Functions

18.1What is a rational function? (free lessons)

18.2Point of discontinuity

18.3Vertical asymptote

18.4Horizontal asymptote

18.5Graphs of rational functions

18.6Solving rational equations

19.Sequences and Series

19.1Arithmetic sequences (free lessons)

19.2Arithmetic series (free lessons)

19.3Geometric sequences

19.4Geometric series

19.5Infinite geometric series

19.6Sigma notation

19.7Arithmetic mean vs. Geometric mean

20.Angles, Lines and Transversals

20.1Pairs of lines and angles

20.2Parallel lines and transversals

20.3Parallel line proofs

20.4Perpendicular line proofs

21.Symmetry and Surface Area

21.1Line symmetry (free lessons)

21.2Rotational symmetry and transformations

21.3Surface area of 3-dimensional shapes

22.Properties of triangles

22.1Classifying Triangles

22.2Isosceles and Equilateral Triangles

23.Pythagorean Theorem

23.1Squares and square roots (free lessons)

23.2Pythagorean theorem

23.3Estimating square roots (free lessons)

23.4Using the pythagorean relationship

23.5Applications of pythagorean theorem

24.Circle Geometry

24.1Angles in a circle (free lessons)

24.2Chord properties

24.3Tangent properties

24.4Circles and circumference

24.5Arcs of a circle

24.6Areas and sectors of circles

25.Scale Factors and Similarity

25.1Enlargements and reductions with scale factors (free lessons)

25.2Scale diagrams

25.3Similar triangles

25.4Similar polygons

26.Congruent Triangles

26.1Congruence and Congruent Triangles

26.2Triangles Congruent by SSS Proofs

26.3Triangles Congruent by SAS and HL Proofs

26.4Triangles Congruent by ASA and AAS Proofs

27.Introduction to volume

27.1Introduction to volume

27.2Volume of prisms

27.3Volume of cylinders

27.4Word problems relating volume of prisms and cylinders

28.Surface Area and Volume

28.1Surface area and volume of prisms (free lessons)

28.2Surface area and volume of pyramids

28.3Surface area and volume of cylinders

28.4Surface area and volume of cones (free lessons)

28.5Surface area and volume of spheres

29.Introduction to Trigonometry

29.1Use sine ratio to calculate angles and side (Sin =

\frac{o}{h}

) (free lessons)

29.2Use cosine ratio to calculate angles and side (Cos =

\frac{a}{h}

29.3Use tangent ratio to calculate angles and side (Tan =

\frac{o}{a}

29.4Combination of SohCahToa questions

29.5Solving expressions using 45-45-90 special right triangles (free lessons)

29.6Solving expressions using 30-60-90 special right triangles

29.7Word problems relating ladder in trigonometry

29.8Word problems relating guy wire in trigonometry

29.9Other word problems relating angles in trigonometry

30.Trigonometric Ratios and Angle Measure

30.1Standard angle

30.2Coterminal angles (free lessons)

30.3Reference angles

30.4Find the exact value of trigonometric ratios

30.5ASTC rule in trigonometry (All Students Take Calculus)

30.6Unit circle (free lessons)

30.7Law of sines

30.8Law of cosines

30.9Applications of the sine law and cosine law

31.Statistics

31.1Median and mode

31.3Range and outliers

31.4Application of averages

32.Probability

32.1Determining probabilities using tree diagrams and tables (free lessons)

32.2Probability of independent events

33.Data and Graphs

33.1Reading and drawing histograms

33.2Reading and drawing line graphs

33.3Box-and-whisker plots and scatter plots

1.Rational Numbers

1.1Comparing and ordering rational numbers (free lessons)

1.2Solving problems with rational numbers in decimal form

1.3Solving problems with rational numbers in fraction form

1.4Determine square roots of rational numbers

2.Ratios, Rates, and Proportions

2.1Ratios (free lessons)

3.Direct variation

3.1Writing and solving for proportions

3.2Understanding graphs of proportional relationships (free lessons)

3.3Graphing and writing equations of proportional relationships

3.4Applications of proportional relationships (free lessons)

4.Introduction to Relations and Functions

4.1Relationship between two variables (free lessons)

4.2Understand relations between x- and y-intercepts

4.3Domain and range of a function

4.4Identifying functions

4.5Function notation (free lessons)

5.Linear Functions

5.1Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

(free lessons)

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 (free lessons)

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 (free lessons)

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 (free lessons)

5.14Applications of linear relations

6.Linear Inequalities

6.1Express linear inequalities graphically and algebraically (free lessons)

6.2Solving one-step linear inequalities

6.3Solving multi-step linear inequalities

7.Solving Simultaneous Equations

7.1Determining number of solutions to linear equations (free lessons)

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 (free lessons)

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

8.Exponents

8.1Product rule of exponents (free lessons)

8.2Quotient rule of exponents

8.3Power of a product rule

8.4Power of a quotient rule

8.5Power of a power rule (free lessons)

8.6Negative exponent rule

8.7Combining the exponent rules

8.8Scientific notation

8.9Convert between radicals and rational exponents (free lessons)

8.10Solving for exponents

9.Exponential Functions

9.1Exponents: Product rule

(a^x)(a^y)=a^{(x+y)}

(free lessons)

9.2Exponents: Division rule

{a^x \over a^y}=a^{(x-y)}

9.3Exponents: Power rule

(a^x)^y = a^{(x\cdot y)}

(free lessons)

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

10.Logarithmic Functions

10.1What is a logarithm?

10.2Converting from logarithmic form to exponential form (free lessons)

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 (free lessons)

10.8Solving exponential equations with logarithms

10.9Product rule of logarithms (free lessons)

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

11.Introduction to Polynomials

11.1Characteristics of polynomials (free lessons)

11.2Equivalent expressions of polynomials

11.3Adding and subtracting polynomials

12.Operations of Polynomials

12.1What is a polynomial? (free lessons)

12.2Polynomial components

12.3Multiplying monomial by monomial

12.4Multiplying monomial by binomial

12.5Multiplying binomial by binomial (free lessons)

12.6Multiplying polynomial by polynomial

12.7Applications of polynomials

13.Factorising Polynomial Expressions

13.1Common factors of polynomials (free lessons)

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

(free lessons)

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

(a - b)^2 = a^2 - 2ab + b^2

(free lessons)

13.10Find the difference of squares:

(a - b)(a + b) = (a^2 - b^2)

13.11Evaluating polynomials

13.12Using algebra tiles to solve polynomials

13.13Solving polynomial equations (free lessons)

13.14Word problems of polynomials

14.Quadratic Functions

14.1Characteristics of quadratic functions (free lessons)

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 (free lessons)

14.8Finding the quadratic functions for given parabolas (free lessons)

14.9Applications of quadratic functions

15.Conics

15.1Conics - Parabola

15.2Conics - Ellipse

15.3Conics - Circle

15.4Conics - Hyperbola

16.Radicals

16.1Operations with radicals (free lessons)

16.2Conversion between entire radicals and mixed radicals

16.3Adding and subtracting radicals (free lessons)

16.4Multiplying radicals

16.5Solving radical equations

17.Rational Expressions

17.1Simplifying rational expressions and restrictions

17.2Adding and subtracting rational expressions (free lessons)

17.3Multiplying rational expressions

17.4Dividing rational expressions

17.5Solving rational equations

17.6Applications of rational equations

18.Rational Functions

18.1What is a rational function? (free lessons)

18.2Point of discontinuity

18.3Vertical asymptote

18.4Horizontal asymptote

18.5Graphs of rational functions

18.6Solving rational equations

19.Sequences and Series

19.1Arithmetic sequences (free lessons)

19.2Arithmetic series (free lessons)

19.3Geometric sequences

19.4Geometric series

19.5Infinite geometric series

19.6Sigma notation

19.7Arithmetic mean vs. Geometric mean

20.Angles, Lines and Transversals

20.1Pairs of lines and angles

20.2Parallel lines and transversals

20.3Parallel line proofs

20.4Perpendicular line proofs

21.Symmetry and Surface Area

21.1Line symmetry (free lessons)

21.2Rotational symmetry and transformations

21.3Surface area of 3-dimensional shapes

22.Properties of triangles

22.1Classifying Triangles

22.2Isosceles and Equilateral Triangles

23.Pythagorean Theorem

23.1Squares and square roots (free lessons)

23.2Pythagorean theorem

23.3Estimating square roots (free lessons)

23.4Using the pythagorean relationship

23.5Applications of pythagorean theorem

24.Circle Geometry

24.1Angles in a circle (free lessons)

24.2Chord properties

24.3Tangent properties

24.4Circles and circumference

24.5Arcs of a circle

24.6Areas and sectors of circles

25.Scale Factors and Similarity

25.1Enlargements and reductions with scale factors (free lessons)

25.2Scale diagrams

25.3Similar triangles

25.4Similar polygons

26.Congruent Triangles

26.1Congruence and Congruent Triangles

26.2Triangles Congruent by SSS Proofs

26.3Triangles Congruent by SAS and HL Proofs

26.4Triangles Congruent by ASA and AAS Proofs

27.Introduction to volume

27.1Introduction to volume

27.2Volume of prisms

27.3Volume of cylinders

27.4Word problems relating volume of prisms and cylinders

28.Surface Area and Volume

28.1Surface area and volume of prisms (free lessons)

28.2Surface area and volume of pyramids

28.3Surface area and volume of cylinders

28.4Surface area and volume of cones (free lessons)

28.5Surface area and volume of spheres

29.Introduction to Trigonometry

29.1Use sine ratio to calculate angles and side (Sin =

\frac{o}{h}

) (free lessons)

29.2Use cosine ratio to calculate angles and side (Cos =

\frac{a}{h}

29.3Use tangent ratio to calculate angles and side (Tan =

\frac{o}{a}

29.4Combination of SohCahToa questions

29.5Solving expressions using 45-45-90 special right triangles (free lessons)

29.6Solving expressions using 30-60-90 special right triangles

29.7Word problems relating ladder in trigonometry

29.8Word problems relating guy wire in trigonometry

29.9Other word problems relating angles in trigonometry

30.Trigonometric Ratios and Angle Measure

30.1Standard angle

30.2Coterminal angles (free lessons)

30.3Reference angles

30.4Find the exact value of trigonometric ratios

30.5ASTC rule in trigonometry (All Students Take Calculus)

30.6Unit circle (free lessons)

30.7Law of sines

30.8Law of cosines

30.9Applications of the sine law and cosine law

31.Statistics

31.1Median and mode

31.3Range and outliers

31.4Application of averages

32.Probability

32.1Determining probabilities using tree diagrams and tables (free lessons)

32.2Probability of independent events

33.Data and Graphs

33.1Reading and drawing histograms

33.2Reading and drawing line graphs

33.3Box-and-whisker plots and scatter plots

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