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Mathematics - International - 0607 - Advanced - Concept Videos
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All Topics
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Square numbers
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Natural numbers
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Cube numbers
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Prime numbers
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Triangle numbers
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Integers (positive, zero, and negative)
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Common factors
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Common multiples
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Rational and irrational numbers
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Reciprocals
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Percentage increase/decrease
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Simple and compound interest
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Reverse percentages
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Calculating percentages of a quantity
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Expressing one quantity as a percentage of another
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Efficient calculator use
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Entering values correctly
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Interpreting calculator displays
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Set notation and terminology
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Venn diagrams (limited to two or three sets)
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Universal set, subsets, intersection, and union
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Squares and square roots
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Cubes and cube roots
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Other powers and roots
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Time calculations (seconds, minutes, hours, days, etc.)
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12-hour and 24-hour clock conversions
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Reading timetables
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Proper and improper fractions
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Mixed numbers
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Decimal and percentage conversions
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Calculations with money
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Currency conversions
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Understanding exponential growth and decay
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Applications in depreciation and population changes
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Understanding and simplifying surds
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Rationalizing the denominator
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Comparing and ordering numbers using =, ≠, >, <, ≥, ≤
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Operations with integers, fractions and decimals
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Order of operations (including brackets)
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Understanding and using indices (positive, zero, negative, and fractional)
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Applying rules of indices
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Expressing numbers in standard form (A × 10ⁿ)
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Converting to and from standard form
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Calculating with standard form
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Rounding values (decimal places and significant figures)
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Estimating calculations
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Rounding answers appropriately
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Simplifying ratios
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Dividing a quantity in a given ratio
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Using proportional reasoning
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Common rates (e.g. hourly wages, exchange rates, flow rates)
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Solving problems involving average speed
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Understanding positive, negative, and zero correlation
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Drawing and using a straight line of best fit
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Using a graphic display calculator to find and apply the equation of linear regression
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Drawing and interpreting scatter diagrams
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Drawing and interpreting cumulative frequency tables and diagrams
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Estimating and interpreting the median, percentiles, quartiles and interquartile range from cumulati
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Classifying and tabulating statistical data
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Reading, interpreting, and drawing inferences from tables and statistical diagrams
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Comparing sets of data using tables, graphs and statistical measures
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Understanding restrictions on drawing conclusions from data
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Distinguishing between discrete and continuous data
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Calculating mean, median, mode, quartiles, range, and interquartile range for individual data
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Calculating an estimate of the mean for grouped discrete or continuous data
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Identifying the modal class from a grouped frequency distribution
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Using a graphic display calculator to calculate mean, median, and quartiles for discrete data
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Using a graphic display calculator to calculate mean for grouped data
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Drawing and interpreting bar charts, pie charts, pictograms, stem-and-leaf diagrams and simple frequ
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Constructing, solving, and interpreting linear inequalities
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Solving inequalities using a graphic display calculator
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Representing inequalities graphically
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Listing inequalities that define a given region
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Representing and interpreting inequalities on a number line
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Continuing number sequences and patterns
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Recognizing patterns and term-to-term rules
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Finding and using the nth term for sequences (linear, quadratic, cubic, exponential)
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Using subscript notation for sequences
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Expressing direct and inverse proportion in algebraic terms
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Using proportion equations to solve problems
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Identifying the best variation model for given data
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Understanding variables and expressions
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Substituting values into expressions and formulas
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Simplifying expressions by collecting like terms
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Expanding products of algebraic expressions
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Factorizing expressions (ax + bx + kay + kby, a²x² - b²y², a² + 2ab + b², ax² + bx + c, ax³ + bx² +
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Manipulating algebraic fractions
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Factorizing and simplifying rational expressions
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Understanding and using indices (positive, zero, negative, and fractional)
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Applying rules of indices
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Constructing expressions, equations, and formulas
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Solving linear equations in one unknown
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Solving fractional equations with numerical and algebraic denominators
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Solving simultaneous linear equations in two variables
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Solving quadratic equations (factorization, quadratic formula, using a graphic display calculator)
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Changing the subject of formulas (when the subject appears twice or involves powers/roots)
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Rotation of a shape about a center through multiples of 90°
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Enlargement of a shape from a center using a positive, describing, and performing transformations
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Translation of a shape using a vector
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Performing and describing combinations of transformations
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Determining the reverse of a transformation
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Recognizing, describing and performing transformations
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Reflection of a shape in a straight line
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Describing a translation using a vector
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Adding and subtracting vectors
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Multiplying a vector by a scalar
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Calculating the magnitude of a vector using √(x² + y²)
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Angle properties in circles (segment, cyclic quadrilateral, alternate segment)
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Angle properties in circles (semicircle, tangent, center)
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Symmetry properties in circles (equal chords, perpendicular bisector)
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Symmetry properties in circles (tangents from an external point)
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Understanding and using basic geometric terms (point, vertex, line, plane, parallel, perpendicular,
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Angle properties (right, acute, obtuse, reflex, interior, exterior)
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Shape properties (similarity, congruence, scale factor)
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Recognizing and interpreting the vocabulary of triangles, quadrilaterals, polygons, and solids
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Measuring and drawing lines and angles
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Using and interpreting three-figure bearings
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Calculating lengths of similar shapes
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Using relationships between lengths, areas, and volumes of similar solids
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Simplifying and solving problems involving similarity
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Recognizing line symmetry and order of rotational symmetry in two-dimensional shapes
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Identifying symmetry properties of prisms, cylinders, pyramids, and cones
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Calculating unknown angles using basic properties (angles at a point, angles on a straight line, ver
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Calculating unknown angles in shapes (sum of angles in a triangle and quadrilateral)
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Using angle properties of parallel lines (corresponding, alternate and co-interior angles)
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Identifying and using angle properties of regular and irregular polygons
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Understanding the logarithmic function as the inverse of the exponential function
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Converting between exponential and logarithmic form y = a^x as x = logₐ(y)
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Solving exponential equations using logarithms
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Recognizing function types from their graphs (linear, quadratic, cubic, reciprocal, exponential, tri
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Determining one or two coefficients (a, b, c, or d) for given function graphs
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Finding values in a function from its graph
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Sketching the graph of a function using a graphic display calculator
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Producing a table of values for a function
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Plotting points on a graph
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Finding zeros, local maxima, or local minima
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Finding the intersection of function graphs
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Identifying the vertex of a quadratic function
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Understanding functions, domain, and range
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Using function notation
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Finding inverse functions f⁻¹(x)
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Forming composite functions gf(x) = g(f(x))
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Finding a quadratic function given vertex and another point
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Finding a quadratic function given x-intercepts and a point
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Determining a quadratic function when a = 1 with given vertex or x-intercepts
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Understanding the concept of asymptotes
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Identifying asymptotes parallel to the axes on a graph
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Describing and identifying transformations of graphs (translations, reflections)
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Transforming functions y = f(x) into y = f(x) + k or y = f(x + k)
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Using metric units of mass, length, area volume, and capacity in practical situations
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Converting between different units of measurement (e.g. cm² to m², m³ to liters)
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Calculating the perimeter and area of rectangles, triangles, parallelograms, and trapeziums
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Calculating the circumference and area of a circle
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Finding arc length and sector area (as fractions of a circle)
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Working with both minor and major sectors
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Calculating surface area and volume of solids (cuboid, prism, cylinder, sphere, pyramid, cone)
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Understanding and applying given formulas for curved and total surface areas and volumes
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Calculating perimeters and areas of compound shapes and parts of shapes
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Finding surface areas and volumes of compound and partial solids (e.g. frustum of a cone)
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Using and interpreting Cartesian coordinates in two dimensions
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Finding the gradient of a straight line
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Calculating the gradient from two given points
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Calculating the length of a line segment from given coordinates
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Finding the coordinates of the midpoint of a line segment
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Interpreting and obtaining the equation of a straight-line graph
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Expressing equations in different forms (ax + by = c, y = mx + c, x = k)
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Finding the equation of a straight line from its graph
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Determining the gradient and y-intercept from an equation
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Finding the gradient and equation of a line parallel to a given line
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Finding the gradient and equation of a line perpendicular to a given line
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Finding the equation of a perpendicular bisector
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Applying Pythagoras’ theorem to find unknown sides in right-angled triangles
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Finding the length of a chord in a circle
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Calculating the distance of a chord from the center of a circle
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Finding the distance between two points on a coordinate grid
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Using sine, cosine, and tangent ratios for calculations involving right-angled triangles
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Solving problems in two dimensions using trigonometry and Pythagoras’ theorem
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Understanding that the perpendicular distance from a point to a line is the shortest distance to the
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Solving problems involving angles of elevation and depression
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Knowing the exact values of sine and cosine for 0°, 30°, 45°, 60°, 90°
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Knowing the exact values of tangent for 0°, 30°, 45°, 60°
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Recognizing, sketching and interpreting the graphs of y = sin x, y = cos x, y = tan x for 0° ≤ x ≤ 3
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Solving trigonometric equations involving sin x, cos x, tan x for 0° ≤ x ≤ 360°
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Using the sine rule and cosine rule for solving triangle problems
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Calculating the area of a triangle using the formula 1/2 ab sin C
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Applying Pythagoras’ theorem and trigonometry in three-dimensional problems
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Finding the angle between a line and a plane
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Understanding and using the probability scale from 0 to 1
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Understanding and using probability notation
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Calculating the probability of a single event
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Understanding that the probability of an event not occurring is 1 - P(A)
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Understanding relative frequency as an estimate of probability
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Calculating expected frequencies using probability
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Probability of combined events using sample space and Venn diagrams
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Using probability notation for combined events including P(A ∩ B) (intersection) and P(A ∪ B) (union
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Understanding and applying probability rules including P(A or B) = P(A) + P(B) for mutually exclusiv
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