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Mathematics - US - 0444 - Advanced - Concept Videos
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All Topics
10:00
Apply the Pythagorean Theorem to find missing sides
10:00
Use trigonometric ratios (sine, cosine, tangent) to solve right-angled triangles
10:00
Know exact values for sine, cosine, and tangent of 0°, 30°, 45°, 60°, 90°
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Solve problems involving bearings
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Understand and use the concepts of angle of elevation and angle of depression
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Extend sine and cosine values to angles between 0° and 360°
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Use the relationship between sine and cosine of complementary angles
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Graph and understand the properties of sine, cosine, and tangent functions
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Apply the Sine Rule for solving triangles (ASA, SSA cases)
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Apply the Cosine Rule for solving triangles (SAS, SSS cases)
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Use the formula for the area of a triangle (1/2 * ab * sinC)
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Describe and perform stretches
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Describe and perform translations using column vectors
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Describe and perform reflections in a given axis or line
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Describe and perform rotations about a point
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Describe and perform enlargements (dilations) with scale factors
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Find the inverse of a given transformation
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Find the single transformation equivalent to a sequence of transformations
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Understand directed line segment notation and component form of vectors
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Use appropriate symbols for vectors and their magnitudes
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Find the components of a vector by subtracting coordinates of an initial point from a terminal point
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Use position vectors
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Calculate the magnitude of a vector
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Understand vector subtraction as v - w = v + (-w)
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Multiply a vector by a scalar
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Add and subtract vectors algebraically (component form) and geometrically (parallelogram rule)
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Draw a straight line of best fit by eye through the mean on a scatter diagram
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Read and interpret data from graphs and tables
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Understand discrete and continuous data
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Calculate mean, mode, median, and range from discrete data
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Calculate mean, modal class, median, and range from grouped and continuous data
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Construct and interpret histograms with frequency density on the vertical axis
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Interpret histograms with unequal class intervals
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Create and interpret cumulative frequency tables and curves
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Determine median, quartiles, percentiles, and interquartile range
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Use statistics (median, mean, interquartile range) to compare different data sets
10:00
Understand and describe correlation (positive, negative, or zero) using scatter diagrams
10:00
Construct and interpret compound bar charts, dot plots, line graphs, pie charts, scatter diagrams
10:00
Angle properties of triangles, quadrilaterals, and polygons
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Interior and exterior angles of a polygon
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Make formal geometric constructions using a compass and straight edge
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Copy and bisect a segment or an angle
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Construct perpendicular lines and perpendicular bisectors
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Construct equilateral triangles, squares, and hexagons inscribed in circles
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Construct inscribed and circumscribed circles of a triangle
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Construct tangent lines from a point outside a circle
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Tangent perpendicular to radius at the point of contact
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Tangents from a point
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Angle in a semicircle
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Angles at the center and at the circumference on the same arc
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Cyclic quadrilateral properties
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Equal chords are equidistant from the center
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The perpendicular bisector of a chord passes through the center
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Tangents from an external point are equal in length
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Calculate lengths of similar figures using scale factors
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Use area and volume scale factors for similar figures and solids
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Recognize and use congruence in solving geometric problems
10:00
Know definitions of acute, obtuse, right angle, reflex, equilateral, isosceles, congruent, similar,
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Know definitions of pentagon, hexagon, octagon, rectangle, square, kite, rhombus, parallelogram, tra
10:00
Understand definitions of angle, circle, perpendicular line, parallel line, and line segment
10:00
Line and rotational symmetry in 2D and 3D
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Recognize symmetry properties of prisms and pyramids
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Angles around a point
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Angles on a straight line and intersecting straight lines
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Vertically opposite angles
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Alternate and corresponding angles on parallel lines
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Use function notation
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Understand domain and range
10:00
Use mapping diagrams
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Graph an equation in two variables as the set of all its solutions
10:00
Construct tables of values and graphs for functions of the form ax^n where n = -2, -1, 0, 1, 2, 3
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Solve equations approximately using graphical methods
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Write a function that describes a relationship between two quantities
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Compare properties of two functions represented in different ways (algebraically, graphically, numer
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Recognize linear, quadratic, cubic, reciprocal, exponential, and trigonometric functions from their
10:00
Interpret key features of function graphs (intercepts, increasing/decreasing behavior, maxima/minima
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Relate the domain of a function to its graph and quantitative relationships
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Calculate and interpret the average rate of change of a function over a specified interval
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Estimate rate of change using a graph
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Understand and compare the behavior of linear, quadratic, and exponential functions
10:00
Observe that exponential growth eventually exceeds polynomial growth
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Use properties of exponents to interpret expressions for exponential functions
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Construct linear and exponential functions given graphs, descriptions, or two input-output pairs
10:00
Simplify expressions for composite functions such as f(g(x))
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Find and interpret inverse functions
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Describe changes to the graph of y = f(x) when transformed as y = f(x) + k, y = kf(x), and y = f(x +
10:00
Graph the solutions to a linear inequality in two variables as a half-plane
10:00
Graph the solution set of a system of inequalities as the intersection of corresponding half-planes
10:00
Converting between units (e.g., currency, time, length)
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Understanding units in problems
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Choosing appropriate levels of accuracy
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Units of time: seconds, minutes, hours, days, months, years
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24-hour and 12-hour clock formats
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Understanding and solving problems related to motion
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Using the speed formula correctly
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Natural numbers, integers, prime numbers, square numbers
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Rational and irrational numbers, real numbers
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Sum or product of two rational numbers is rational
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Sum of a rational and an irrational number is irrational
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Product of a non-zero rational and an irrational number is irrational
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Symbols: =, ≠, ⩽, ⩾, <, >
10:00
Four operations and parentheses
10:00
Applies to integers, fractions, and decimals
10:00
Greatest Common Factor (GCF)
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Least Common Multiple (LCM)
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Understanding and solving problems using ratios
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Proportions in real-world contexts
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Convert between decimals, fractions, ratios, and percentages
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Ordering different forms by magnitude
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Calculating percentage increases and decreases
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Applications like interest and profit
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Includes reverse percentages
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Includes both simple and compound interest
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Includes percentiles
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Scientific notation (Standard Form)
10:00
Basic exponent rules
10:00
Positive, negative, zero, and fractional exponents
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Calculation and simplification of square root and cube root expressions
10:00
Simplify radical expressions
10:00
Understand and convert between metric units (mm, cm, m, km)
10:00
Understand and convert between area and volume units (mm², cm², m², ha, km², mm³, cm³, ml, l, m³)
10:00
Calculate perimeter and area of rectangles and triangles
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Calculate area of compound shapes derived from rectangles and triangles
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Calculate area of trapezoids and parallelograms
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Calculate circumference and area of circles
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Calculate arc length and area of a sector (sector angles in degrees only)
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Calculate surface area and volume of prisms and pyramids (including cuboids, cylinders, and cones)
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Calculate surface area and volume of spheres
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Calculate areas and volumes of compound shapes
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Describe objects using geometric shapes and their properties
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Identify the shapes of 2D cross sections of 3D objects
10:00
Identify 3D objects generated by rotations of 2D shapes
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Apply concepts of density based on area and volume in modeling situations
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Apply geometric methods to solve design problems
10:00
Writing, showing, and interpreting inequalities on the real number line
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Create and solve linear inequalities
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Create expressions and solve linear equations, including fractional expressions
10:00
Explain algebraic steps of a solution
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Interpret solutions in a given context
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Rules of exponents, including negative and fractional exponents
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Basic exponent calculations
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Rearrange and evaluate formulae, including algebraic manipulation to prove identities
10:00
Make a variable the subject of an equation
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Create and solve systems of linear equations algebraically and graphically
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Identify terms, factors, and coefficients
10:00
Expansion of parentheses, including the square of a binomial
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Simplify expressions
10:00
Simplification using factorization
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Addition or subtraction of fractions with linear denominators
10:00
Multiplication or division and simplification of two fractions
10:00
Create and solve quadratic equations by inspection, factorization, quadratic formula, and completing
10:00
Write quadratic expressions in the form (x-a)^2 + b and state the minimum value
10:00
Solve simple rational and radical equations and identify extraneous solutions
10:00
Continuation of sequences of numbers or patterns
10:00
Recognize patterns and generalize to algebraic statements
10:00
Determine the nth term of a sequence
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Derive and use the formula for the sum of a finite geometric series
10:00
Express direct and inverse variation in algebraic terms
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Use variation formulas to find unknown quantities
10:00
Factorization using common factors, difference of squares, trinomials, and four-term expressions
10:00
Understand probability P(A) as a fraction, decimal, or percentage
10:00
Interpret probability values and their significance
10:00
Calculate probability using the rule P(A) = 1 – P(A')
10:00
Use relative frequency as an estimate of probability
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Calculate the expected number of occurrences in probability experiments
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Apply the addition rule P(A or B) = P(A) + P(B) – P(A and B)
10:00
Apply the multiplication rule P(A and B) = P(A) × P(B)
10:00
Understand and determine if two events are independent
10:00
Use possibility diagrams to list all outcomes
10:00
Construct and interpret tree diagrams for successive selections with or without replacement
10:00
Plot points and read coordinates in the Cartesian plane
10:00
Calculate the distance between two points using the distance formula
10:00
Find the midpoint of a line segment
10:00
Find the point on a directed line segment that partitions the segment in a given ratio
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Calculate the slope (gradient) of a line segment
10:00
Interpret and obtain the equation of a straight line in the form y = mx + b
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Interpret and obtain the equation of a straight line in the form ax + by = d (where a, b, and d are
10:00
Find the equation of a straight line given two points
10:00
Understand and find the slope of parallel lines
10:00
Find the equation of a line parallel to a given line that passes through a given point
10:00
Understand the relationship between slopes of perpendicular lines
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