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NZ Year 10 Maths topics

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1Number System and Radicals

1.1Understanding the number systems (free lessons)
1.2Prime factorisation
1.3Greatest Common Factors (GCF)
1.4Least Common Multiple (LCM) (free lessons)
1.5Rational vs. Irrational numbers
1.6Converting repeating decimals to fractions

2Rational Numbers

2.1Comparing and ordering rational numbers (free lessons)
2.2Solving problems with rational numbers in decimal form
2.3Solving problems with rational numbers in fraction form
2.4Determine square roots of rational numbers

3Ratios, Rates, and Proportions

3.1Ratios (free lessons)
3.2Rates
3.3Proportions

4Percents

4.1Representing percents (free lessons)
4.2Percents, fractions, and decimals
4.3Percent of a number
4.4Adding and multiplying percents
4.5Taxes, discounts, tips and more
4.6Simple interest
4.7Finance: Compound interest

5Pythagorean Theorem

5.1Squares and square roots (free lessons)
5.2Pythagorean theorem (free lessons)
5.3Estimating square roots (free lessons)
5.4Using the pythagorean relationship
5.5Applications of pythagorean theorem

6Volume

6.1Introduction to volume
6.2Volume of prisms
6.3Volume of cylinders
6.4Word problems relating volume of prisms and cylinders

7Scale Factors and Similarity

7.1Enlargements and reductions with scale factors (free lessons)
7.2Scale diagrams
7.3Similar triangles
7.4Similar polygons

8Solving Linear Equations

8.1Solving linear equations using multiplication and division (free lessons)
8.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
8.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)
8.4Solving linear equations with variables on both sides
8.5Solving literal equations

9Data and Graphs

9.1Reading and drawing bar graphs
9.2Reading and drawing histograms
9.3Reading and drawing line graphs
9.4Box-and-whisker plots and scatter plots
9.5Stem-and-leaf plots
9.6Pie charts
9.7Reading and drawing Venn diagrams
9.8Frequency tables and dot plots

10Direct Variation

10.1Identifying proportional relationships
10.2Understanding graphs of proportional relationships (free lessons)
10.3Understanding tables of values of proportional relationships
10.4Applications of linear relationships (free lessons)

11Introduction to Relations and Functions

11.1Relationship between two variables (free lessons)
11.2Understand relations between x- and y-intercepts
11.3Domain and range of a function (free lessons)
11.4Identifying functions
11.5Function notation (free lessons)

12Linear Functions

12.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
12.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
12.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
12.4Gradient intercept form: y = mx + b (free lessons)
12.5General form: Ax + By + C = 0 (free lessons)
12.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
12.7Rate of change
12.8Graphing linear functions using table of values
12.9Graphing linear functions using x- and y-intercepts (free lessons)
12.10Graphing from gradient-intercept form y=mx+b
12.11Graphing linear functions using a single point and gradient
12.12Word problems of graphing linear functions
12.13Parallel and perpendicular lines in linear functions (free lessons)
12.14Applications of linear relations

13Linear Inequalities

13.1Express linear inequalities graphically and algebraically (free lessons)
13.2Solving one-step linear inequalities (free lessons)
13.3Solving multi-step linear inequalities (free lessons)
13.4Compound inequalities

14Solving Simultaneous Equations

14.1Determining number of solutions to linear equations (free lessons)
14.2Solving simultaneous equations by graphing
14.3Solving simultaneous equations by elimination
14.4Solving simultaneous equations by substitution
14.5Money related questions in linear equations (free lessons)
14.6Unknown number related questions in linear equations
14.7Distance and time related questions in linear equations
14.8Rectangular shape related questions in linear equations

15Exponents

15.1Product rule of exponents (free lessons)
15.2Quotient rule of exponents
15.3Power of a product rule
15.4Power of a quotient rule
15.5Power of a power rule (free lessons)
15.6Negative exponent rule
15.7Combining the exponent rules
15.8Scientific notation
15.9Convert between radicals and rational exponents (free lessons)
15.10Solving for exponents

16Introduction to Polynomials

16.1Characteristics of polynomials (free lessons)
16.2Equivalent expressions of polynomials
16.3Adding and subtracting polynomials

17Operations of Polynomials

17.1What is a polynomial? (free lessons)
17.2Polynomial components
17.3Multiplying monomial by monomial
17.4Multiplying monomial by binomial
17.5Multiplying binomial by binomial (free lessons)
17.6Multiplying polynomial by polynomial
17.7Applications of polynomials

18Factorising Polynomial Expressions

18.1Common factors of polynomials (free lessons)
18.2Factorising polynomials by grouping
18.3Solving polynomials with the unknown "b" from x2+bx+cx^2 + bx + c
18.4Solving polynomials with the unknown "c" from x2+bx+cx^2 + bx + c
18.5Factorising polynomials: x2+bx+cx^2 + bx + c (free lessons)
18.6Applications of polynomials: x2+bx+cx^2 + bx + c
18.7Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + c
18.8Factorising polynomials: ax2+bx+cax^2 + bx + c
18.9Factorising 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)
18.10Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)
18.11Evaluating polynomials
18.12Using algebra tiles to factorise polynomials
18.13Solving polynomial equations (free lessons)
18.14Word problems of polynomials

19Radicals

19.1Square and square roots (free lessons)
19.2Cubic and cube roots
19.3Evaluating and simplifying radicals
19.4Converting radicals to mixed radicals
19.5Converting radicals to entire radicals (free lessons)
19.6Adding and subtracting radicals
19.7Multiplying and dividing radicals
19.8Rationalize the denominator

20Algebraic Fractions

20.1Simplifying algebraic fractions and restrictions
20.2Adding and subtracting algebraic fractions (free lessons)
20.3Multiplying algebraic fractions
20.4Dividing algebraic fractions
20.5Solving equations with algebraic fractions
20.6Applications of equations with algebraic fractions
20.7Simplifying complex fractions
20.8Partial fraction decomposition

21Reciprocal Functions

21.1Graphing reciprocals of linear functions
21.2Graphing reciprocals of quadratic functions

22Statistics

22.1Median and mode
22.2Mean
22.3Range and outliers
22.4Application of averages

23Probability

23.1Determining probabilities using tree diagrams and tables (free lessons)
23.2Probability of independent events
23.3Probability with Venn diagrams
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