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NZ Year 11 Maths topics

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1Rational 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

2Ratios, Rates, and Proportions

2.1Ratios (free lessons)
2.2Rates
2.3Proportions

3Direct variation

3.1Identifying proportional relationships
3.2Understanding graphs of proportional relationships (free lessons)
3.3Graphing and writing equations of proportional relationships
3.4Applications of proportional relationships (free lessons)

4Introduction 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 (free lessons)
4.4Identifying functions
4.5Function notation (free lessons)

5Linear Functions

5.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
5.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
5.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
5.4Gradient intercept form: y = mx + b (free lessons)
5.5General form: Ax + By + C = 0 (free lessons)
5.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
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

6Linear Inequalities

6.1Express linear inequalities graphically and algebraically (free lessons)
6.2Solving one-step linear inequalities (free lessons)
6.3Solving multi-step linear inequalities (free lessons)
6.4Compound inequalities

7Solving 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

8Exponents

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

9Exponential Functions

9.1Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
9.2Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
9.3Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
9.4Exponents: Negative exponents
9.5Exponents: Zero exponent: a0=1 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

10Logarithmic 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 (free lessons)
10.14Graphing logarithmic functions
10.15Finding a logarithmic function given its graph

11Introduction to Polynomials

11.1Characteristics of polynomials (free lessons)
11.2Equivalent expressions of polynomials
11.3Adding and subtracting polynomials

12Operations 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

13Factorising Polynomial Expressions

13.1Common factors of polynomials (free lessons)
13.2Factorising polynomials by grouping
13.3Solving polynomials with the unknown "b" from x2+bx+cx^2 + bx + c
13.4Solving polynomials with the unknown "c" from x2+bx+cx^2 + bx + c
13.5Factorising polynomials: x2+bx+cx^2 + bx + c (free lessons)
13.6Applications of polynomials: x2+bx+cx^2 + bx + c
13.7Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + c
13.8Factorising polynomials: ax2+bx+cax^2 + bx + c
13.9Factorising perfect square trinomials: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 or (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2 (free lessons)
13.10Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)
13.11Evaluating polynomials
13.12Using algebra tiles to factorise polynomials
13.13Solving polynomial equations (free lessons)
13.14Word problems of polynomials

14Quadratic Functions

14.1Characteristics of quadratic functions (free lessons)
14.2Transformations of quadratic functions
14.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
14.4Quadratic function in vertex form: y = a(x−p)2+qa(x-p)^2 + q
14.5Completing the square (free lessons)
14.6Converting from general to vertex form by completing the square
14.7Shortcut: Vertex formula (free lessons)
14.8Graphing parabolas for given quadratic functions
14.9Finding the quadratic functions for given parabolas (free lessons)
14.10Applications of quadratic functions

15Conics

15.1Conics - Parabola
15.2Conics - Ellipse
15.3Conics - Circle
15.4Conics - Hyperbola

16Radicals

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

17Algebraic Fractions

17.1Simplifying algebraic fractions and restrictions
17.2Adding and subtracting algebraic fractions (free lessons)
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

18Reciprocal Functions

18.1Graphing reciprocals of linear functions
18.2Graphing reciprocals of quadratic functions

19Rational Functions

19.1What is a rational function? (free lessons)
19.2Point of discontinuity
19.3Vertical asymptote
19.4Horizontal asymptote
19.5Slant asymptote
19.6Graphs of rational functions
19.7Solving rational inequalities

20Sequences and Series

20.1Arithmetic sequences (free lessons)
20.2Arithmetic series (free lessons)
20.3Geometric sequences
20.4Geometric series
20.5Infinite geometric series
20.6Sigma notation
20.7Arithmetic mean vs. Geometric mean

21Angles, Lines and Transversals

21.1Pairs of lines and angles
21.2Parallel lines and transversals
21.3Parallel line proofs
21.4Perpendicular line proofs (free lessons)

22Symmetry and Surface Area

22.1Line symmetry (free lessons)
22.2Rotational symmetry and transformations
22.3Surface area of 3-dimensional shapes (free lessons)

23Properties of triangles

23.1Classifying Triangles
23.2Isosceles and Equilateral Triangles

24Pythagorean Theorem

24.1Squares and square roots (free lessons)
24.2Pythagorean theorem (free lessons)
24.3Estimating square roots (free lessons)
24.4Using the pythagorean relationship
24.5Applications of pythagorean theorem

25Circle Geometry

25.1Angles in a circle (free lessons)
25.2Chord properties
25.3Tangent properties
25.4Circles and circumference
25.5Arcs of a circle
25.6Areas and sectors of circles

26Scale Factors and Similarity

26.1Enlargements and reductions with scale factors (free lessons)
26.2Scale diagrams
26.3Similar triangles
26.4Similar polygons

27Congruent Triangles

27.1Congruence and Congruent Triangles
27.2Triangles Congruent by SSS Proofs
27.3Triangles Congruent by SAS and HL Proofs
27.4Triangles Congruent by ASA and AAS Proofs

28Introduction to volume

28.1Introduction to volume
28.2Volume of prisms
28.3Volume of cylinders
28.4Word problems relating volume of prisms and cylinders

29Surface Area and Volume

29.1Surface area and volume of prisms (free lessons)
29.2Surface area and volume of pyramids
29.3Surface area and volume of cylinders
29.4Surface area and volume of cones (free lessons)
29.5Surface area and volume of spheres

30Introduction to Trigonometry

30.1Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} ) (free lessons)
30.2Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
30.3Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
30.4Combination of SohCahToa questions (free lessons)
30.5Solving expressions using 45-45-90 special right triangles (free lessons)
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

31Trigonometric Ratios and Angle Measure

31.1Standard angle
31.2Coterminal angles (free lessons)
31.3Reference angles
31.4Find the exact value of trigonometric ratios
31.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)
31.6Unit circle (free lessons)
31.7Law of sines
31.8Law of cosines
31.9Applications of the sine law and cosine law

32Bearings

32.1Introduction to bearings
32.2Bearings and direction word problems
32.3Angle of elevation and depression

33Statistics

33.1Median and mode
33.2Mean
33.3Range and outliers
33.4Application of averages

34Probability

34.1Determining probabilities using tree diagrams and tables (free lessons)
34.2Probability of independent events
34.3Probability with Venn diagrams

35Data and Graphs

35.1Reading and drawing bar graphs
35.2Reading and drawing histograms
35.3Reading and drawing line graphs
35.4Box-and-whisker plots and scatter plots
35.5Stem-and-leaf plots
35.6Reading and drawing Venn diagrams
35.7Frequency tables and dot plots
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