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First Year Maths Topics

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1Number Theory

1.1Divisibility Rules
1.2Determining Common Factors
1.3Determining Common Multiples
1.4Introduction 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

4Operations with Decimals

4.1Adding and subtracting decimals
4.2Multiplying decimals
4.3Dividing decimals
4.4Order of operations (BIDMAS)

5Adding and Subtracting Fractions

5.1Using models to add and subtract fractions
5.2Adding fractions with like denominators
5.3Subtracting fractions with like denominators
5.4Adding and subtracting fractions with unlike denominators
5.5Adding and subtracting mixed numbers

6Multiplying and Dividing Fractions

6.1Multiplying fractions and whole numbers (free lessons)
6.2Dividing fractions with whole numbers
6.3Multiplying proper fractions
6.4Multiplying improper fractions and mixed numbers
6.5Dividing fractions and mixed numbers
6.6Applications of fraction operations

7Rational Numbers

7.1Comparing and ordering rational numbers (free lessons)
7.2Solving problems with rational numbers in decimal form
7.3Solving problems with rational numbers in fraction form
7.4Determine square roots of rational numbers

8Powers, and Exponents

8.1Using exponents to describe numbers (free lessons)
8.2Exponent rules
8.3Order of operations with exponents
8.4Using exponents to solve problems

9Number System and Radicals

9.1Understanding the number systems (free lessons)
9.2Prime factorization
9.3Greatest Common Factors (GCF)
9.4Least Common Multiple (LCM) (free lessons)
9.5Rational vs. Irrational numbers
9.6Converting repeating decimals to fractions

10Ratios, Rates, and Proportions

10.1Ratios (free lessons)
10.2Rates
10.3Proportions

11Pythagorean Theorem

11.1Squares and square roots (free lessons)
11.2Pythagorean theorem (free lessons)
11.3Estimating square roots (free lessons)
11.4Using the pythagorean relationship
11.5Applications of pythagorean theorem

12Proportional Relationships

12.1Understanding graphs of proportional relationships (free lessons)
12.2Graphing and writing equations of proportional relationships
12.3Applications of proportional relationships (free lessons)

13Fractions, Decimals, and Percents

13.1Percent of a number
13.2Taxes, discounts, tips and more
13.3Simple interest

14Measuring Systems

14.1Metric systems (free lessons)
14.2Imperial systems
14.3Conversions between metric and imperial systems
14.4Conversions involve squares and cubic

15Coordinates, Quadrants, and Transformations

15.1Cartesian plane
15.2Draw on coordinate planes
15.3Introduction to transformations
15.4Horizontal and vertical distances

16Linear Equations

16.1Model and solve one-step linear equations: ax=bax = b, xa=b\frac{x}{a} = b (free lessons)
16.2Solving two-step linear equations using addition and subtraction: ax+b=cax + b = c
16.3Solving two-step linear equations using multiplication and division: xa+b=c\frac{x}{a} + b = c
16.4Solving two-step linear equations using distributive property: a(x+b)=c\;a\left( {x + b} \right) = c

17Linear Inequalities

17.1Express linear inequalities graphically and algebraically (free lessons)
17.2Solving one-step linear inequalities (free lessons)
17.3Solving multi-step linear inequalities (free lessons)

18Linear Functions

18.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
18.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
18.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
18.4Gradient intercept form: y = mx + b (free lessons)
18.5General form: Ax + By + C = 0 (free lessons)
18.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
18.7Rate of change
18.8Graphing linear functions using table of values
18.9Graphing linear functions using x- and y-intercepts (free lessons)
18.10Graphing from gradient-intercept form y=mx+b
18.11Graphing linear functions using a single point and gradient
18.12Word problems of graphing linear functions
18.13Parallel and perpendicular lines in linear functions (free lessons)
18.14Applications of linear relations

19Geometry and Measurement

19.1Parallel and perpendicular line segments
19.2Perpendicular bisectors
19.3Angle bisectors

20Angles, Lines, and Transversals

20.1Pairs of lines and angles
20.2Parallel lines and transversals
20.3Parallel line proofs
20.4Perpendicular line proofs (free lessons)

21Properties of triangles

21.1Classifying triangles
21.2Isosceles and equilateral triangles

22Circles

22.1Circles and circumference
22.2Arcs of a circle
22.3Areas and sectors of circles

23Symmetry and Surface Area

23.1Line symmetry (free lessons)
23.2Rotational symmetry and transformations
23.3Surface area of 3-dimensional shapes (free lessons)

24Introduction to 3-Dimensional Figures

24.1Introduction to surface area of 3-dimensional shapes (free lessons)
24.2Nets of 3-dimensional shapes
24.3Surface area of prisms
24.4Surface area of cylinders

25Volume

25.1Introduction to volume
25.2Volume of prisms
25.3Volume of cylinders
25.4Word problems relating volume of prisms and cylinders

26Data and Graphs

26.1Reading and drawing histograms
26.2Reading and drawing line graphs
26.3Box-and-whisker plots and scatter plots
26.4Stem-and-leaf plots
26.5Reading and drawing Venn diagrams

27Statistics

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

28Introduction to Probability

28.1Introduction to probability
28.2Organizing outcomes
28.3Probability of independent events
28.4Comparing experimental and theoretical probability
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