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First Year Maths Topics

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video
Number Theory
Divisibility Rules
Determining Common Factors
Determining Common Multiples
Introduction to exponents
video
Adding and Subtracting Integers
Introduction to integer addition
Adding integers
Introduction to integer subtraction
Subtracting integers
Application of integer operations
video
Multiplying and Dividing Integers
Understanding integer multiplication
Multiplying integers
Understanding integer division
Dividing integers
Applications of integer operations
video
Operations with Decimals
Adding and subtracting decimals
Multiplying decimals
Dividing decimals
Order of operations (BIDMAS)
video
Adding and Subtracting Fractions
Using models to add and subtract fractions
Adding fractions with like denominators
Subtracting fractions with like denominators
Adding and subtracting fractions with unlike denominators
Adding and subtracting mixed numbers
video
Multiplying and Dividing Fractions
Multiplying fractions and whole numbers
Dividing fractions with whole numbers
Multiplying proper fractions
Multiplying improper fractions and mixed numbers
Dividing fractions and mixed numbers
Applications of fraction operations
video
Rational Numbers
Comparing and ordering rational numbers
Solving problems with rational numbers in decimal form
Solving problems with rational numbers in fraction form
Determine square roots of rational numbers
video
Powers, and Exponents
Using exponents to describe numbers
Exponent rules
Order of operations with exponents
Using exponents to solve problems
video
Number System and Radicals
Understanding the number systems
Prime factorization
Greatest Common Factors (GCF)
Least Common Multiple (LCM)
Rational vs. Irrational numbers
Converting repeating decimals to fractions
video
Ratios, Rates, and Proportions
Ratios
Rates
Proportions
video
Pythagorean Theorem
Squares and square roots
Pythagorean theorem
Estimating square roots
Using the pythagorean relationship
Applications of pythagorean theorem
video
Proportional Relationships
Identifying proportional relationships
Understanding graphs of proportional relationships
Graphing and writing equations of proportional relationships
Applications of proportional relationships
video
Fractions, Decimals, and Percents
Representing percents
Percent of a number
Converting among fractions, decimals, and percents
Applications of percents
Taxes, discounts, tips and more
Simple interest
video
Measuring Systems
Metric systems
Imperial systems
Conversions between metric and imperial systems
Conversions involve squares and cubic
video
Coordinates, Quadrants, and Transformations
Cartesian plane
Draw on coordinate planes
Introduction to transformations
Horizontal and vertical distances
video
Linear Equations
Model and solve one-step linear equations: ax = b, x/a = b
Solving two-step linear equations using addition and subtraction: ax + b = c
Solving two-step linear equations using multiplication and division: x/a + b = c
Solving two-step linear equations using distributive property: a(x + b) = c
video
Linear Inequalities
Express linear inequalities graphically and algebraically
Solving one-step linear inequalities
Solving multi-step linear inequalities
Compound inequalities
video
Linear Functions
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)M=(2x1​+x2​​,2y1​+y2​​)
Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}m=x2​−x1​y2​−y1​​
Gradient intercept form: y = mx + b
General form: Ax + By + C = 0
Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)y−y1​=m(x−x1​)
Rate of change
Graphing linear functions using table of values
Graphing linear functions using x- and y-intercepts
Graphing from gradient-intercept form y=mx+b
Graphing linear functions using a single point and gradient
Word problems of graphing linear functions
Parallel and perpendicular lines in linear functions
Applications of linear relations
video
Geometry and Measurement
Parallel and perpendicular line segments
Perpendicular bisectors
Angle bisectors
video
Angles, Lines, and Transversals
Pairs of lines and angles
Parallel lines and transversals
Parallel line proofs
Perpendicular line proofs
video
Properties of triangles
Classifying triangles
Isosceles and equilateral triangles
video
Circles
Circles and circumference
Arcs of a circle
Areas and sectors of circles
video
Symmetry and Surface Area
Line symmetry
Rotational symmetry and transformations
Surface area of 3-dimensional shapes
video
Introduction to 3-Dimensional Figures
Introduction to surface area of 3-dimensional shapes
Nets of 3-dimensional shapes
Surface area of prisms
Surface area of cylinders
video
Volume
Introduction to volume
Volume of prisms
Volume of cylinders
Word problems relating volume of prisms and cylinders
video
Data and Graphs
Reading and drawing bar graphs
Reading and drawing histograms
Reading and drawing line graphs
Box-and-whisker plots and scatter plots
Stem-and-leaf plots
Pie charts
Reading and drawing Venn diagrams
Frequency tables and dot plots
video
Statistics
Median and mode
Mean
Range and outliers
Application of averages
video
Introduction to Probability
Introduction to probability
Organizing outcomes
Probability of independent events
Comparing experimental and theoretical probability

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