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NZ Year 9 Maths topics

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1Number Theory

1.1Divisibility Rules
1.2Prime factors
1.3Determining Common Factors
1.4Determining Common Multiples
1.5Introduction to exponents

2Adding and Subtracting Integers

2.1Introduction to integer addition
2.2Adding integers
2.3Introduction to integer subtraction
2.4Subtracting integers
2.5Application of integer operations

3Multiplying and Dividing Integers

3.1Understanding integer multiplication
3.2Multiplying integers
3.3Understanding integer division
3.4Dividing integers
3.5Applications of integer operations

4Rational Numbers

4.1Comparing and ordering rational numbers (free lessons)
4.2Solving problems with rational numbers in decimal form
4.3Solving problems with rational numbers in fraction form
4.4Determine square roots of rational numbers

5Powers and Exponents

5.1Using exponents to describe numbers (free lessons)
5.2Exponent rules
5.3Order of operations with exponents
5.4Using exponents to solve problems

6Ratios, Rates, and Proportions

6.1Ratios (free lessons)
6.2Rates
6.3Proportions

7Proportional Relationships

7.1Identifying proportional relationships
7.2Understanding graphs of proportional relationships (free lessons)
7.3Understanding tables of values of proportional relationships
7.4Applications of linear relationships (free lessons)

8Percents

8.1Representing percents (free lessons)
8.2Percents, fractions, and decimals
8.3Percent of a number
8.4Adding and multiplying percents
8.5Taxes, discounts, tips and more
8.6Simple interest

9Radicals

9.1Square and square roots (free lessons)
9.2Cubic and cube roots
9.3Evaluating and simplifying radicals
9.4Converting radicals to mixed radicals
9.5Converting radicals to entire radicals (free lessons)
9.6Adding and subtracting radicals
9.7Multiplying and dividing radicals
9.8Rationalize the denominator

10Measuring Systems

10.1Metric systems (free lessons)
10.2Imperial systems
10.3Conversions between metric and imperial systems
10.4Conversions involve squares and cubic

11Coordinates, Quadrants, and Transformations

11.1Cartesian plane
11.2Draw on coordinate planes
11.3Introduction to transformations
11.4Horizontal and vertical distances

12Angles, Lines, and Transversals

12.1Pairs of lines and angles
12.2Parallel lines and transversals
12.3Parallel line proofs
12.4Perpendicular line proofs (free lessons)

13Symmetry and Surface Area

13.1Line symmetry (free lessons)
13.2Rotational symmetry and transformations
13.3Surface area of 3-dimensional shapes (free lessons)

14Properties of triangles

14.1Classifying triangles
14.2Isosceles and equilateral triangles

15Circles

15.1Circles and circumference
15.2Angles in a circle (free lessons)
15.3Arcs of a circle
15.4Areas and sectors of circles

16Scale Factors and Similarity

16.1Enlargements and reductions with scale factors (free lessons)
16.2Scale diagrams
16.3Similar triangles
16.4Similar polygons

17Pythagorean Theorem

17.1Squares and square roots (free lessons)
17.2Pythagorean theorem (free lessons)
17.3Estimating square roots (free lessons)
17.4Using the pythagorean relationship
17.5Applications of pythagorean theorem

18Introduction to 3-Dimensional Figures

18.1Introduction to surface area of 3-dimensional shapes (free lessons)
18.2Nets of 3-dimensional shapes
18.3Surface area of prisms
18.4Surface area of cylinders

19Volume

19.1Introduction to volume
19.2Volume of prisms
19.3Volume of cylinders
19.4Word problems relating volume of prisms and cylinders

20Linear Equations (Basic)

20.1Model and solve one-step linear equations: ax=bax = b, xa=b\frac{x}{a} = b (free lessons)
20.2Solving two-step linear equations using addition and subtraction: ax+b=cax + b = c
20.3Solving two-step linear equations using multiplication and division: xa+b=c\frac{x}{a} + b = c
20.4Solving two-step linear equations using distributive property:   a(x+b)=c\;a\left( {x + b} \right) = c

21Solving Linear Equations

21.1Solving linear equations using multiplication and division (free lessons)
21.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
21.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)
21.4Solving linear equations with variables on both sides
21.5Solving literal equations

22Linear Inequalities

22.1Express linear inequalities graphically and algebraically (free lessons)
22.2Solving one-step linear inequalities (free lessons)
22.3Solving multi-step linear inequalities (free lessons)
22.4Compound inequalities

23Introduction to Relations and Functions

23.1Relationship between two variables (free lessons)
23.2Understand relations between x- and y-intercepts
23.3Domain and range of a function (free lessons)
23.4Identifying functions
23.5Function notation (free lessons)

24Linear Functions

24.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
24.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
24.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
24.4Gradient intercept form: y = mx + b (free lessons)
24.5General form: Ax + By + C = 0 (free lessons)
24.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
24.7Rate of change
24.8Graphing linear functions using table of values
24.9Graphing linear functions using x- and y-intercepts (free lessons)
24.10Graphing from gradient-intercept form y=mx+b
24.11Graphing linear functions using a single point and gradient
24.12Word problems of graphing linear functions
24.13Parallel and perpendicular lines in linear functions (free lessons)
24.14Applications of linear relations

25Multiplication and Division of Polynomials

25.1Common factors of polynomials (free lessons)
25.2Factorising polynomials by grouping
25.3Solving polynomials with the unknown "b" from x2+bx+cx^2 + bx + c
25.4Solving polynomials with the unknown "c" from x2+bx+cx^2 + bx + c
25.5Factorising polynomials: x2+bx+cx^2 + bx + c (free lessons)
25.6Applications of polynomials: x2+bx+cx^2 + bx + c
25.7Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + c
25.8Factorising polynomials: ax2+bx+cax^2 + bx + c
25.9Factorising 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)
25.10Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)
25.11Evaluating polynomials
25.12Using algebra tiles to factorise polynomials
25.13Solving polynomial equations (free lessons)
25.14Word problems of polynomials

26Data and Graphs

26.1Reading and drawing bar graphs
26.2Reading and drawing histograms
26.3Reading and drawing line graphs
26.4Box-and-whisker plots and scatter plots
26.5Stem-and-leaf plots
26.6Pie charts
26.7Reading and drawing Venn diagrams
26.8Frequency tables and dot plots

27Statistics

27.1Median and mode
27.2Mean
27.3Range and outliers
27.4Application of averages

28Probability

28.1Determining probabilities using tree diagrams and tables (free lessons)
28.2Probability of independent events
28.3Probability with Venn diagrams
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