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Grade 7-12 Math Lesson Library
The maths of Grades 7 to 12: the DepEd MATATAG curriculum year by year for Grades 7 to 10 — number and algebra, measurement and geometry, and data and probability — then General Mathematics, Precalculus, Solid Mensuration and Statistics and Probability for Senior High. Every lesson is a short slide deck ending in a 5-question check.
No lesson matches that. Try a shorter word — circle, root or mean.
Sets, Subsets, and Venn Diagrams
Roster and rule form, subsets and how many a set has, union, intersection, complement and difference, and Venn diagrams for two-group survey problems.
Read the lesson »The Real Number System
Classify a number into every subset of the real numbers it belongs to, name the commutative, associative, distributive, identity and inverse properties, and use them to compute mentally.
Read the lesson »Absolute Value and Operations on Integers
Absolute value as distance from zero, adding and subtracting integers including subtracting a negative, the sign rules for multiplying and dividing, and order of operations with negatives.
Read the lesson »Operations on Fractions and Decimals
Add, subtract, multiply and divide fractions and mixed numbers, convert between fractions and decimals, and handle word problems that mix the two.
Read the lesson »Square Roots and Estimating Irrational Numbers
Exact square roots of perfect squares, telling a rational root from an irrational one, estimating a root between two integers and to the nearest tenth, and placing it on a number line.
Read the lesson »Cube Roots of Perfect Cubes
Perfect cubes and their cube roots, how a cube root differs from a square root, and why a cube root of a negative number exists when a square root does not.
Read the lesson »Scientific Notation
Write large and small numbers as a x 10 to the n, convert back to standard form, compare numbers in scientific notation, and multiply and divide them.
Read the lesson »Ratio, Rate, and Proportion
Write and simplify ratios, find a unit rate, set up and solve a proportion by cross-multiplying, and use proportion for recipes, map scales and comparing prices.
Read the lesson »Percent and Percent Problems
Percent means "per hundred". Convert between percent, decimal and fraction, use part = percent x whole, and work backwards from a sale price to the original.
Read the lesson »Algebraic Expressions and Laws of Exponents
Terms, coefficients and constants, combining like terms, evaluating an expression by substitution, and the product, quotient, power and zero laws of exponents.
Read the lesson »Linear Equations in One Variable
Solve one-step and two-step linear equations, equations needing the distributive property, and equations with the variable on both sides — then check by substituting back.
Read the lesson »Word Problems Involving Linear Equations
Turn a word problem into an equation — number and consecutive-integer problems, age problems set in the past or future, and money, perimeter and rate problems using one variable.
Read the lesson »Rearranging a Formula: Changing the Subject
Make a different variable the subject of a formula. The same moves as solving an equation, except the answer is an expression in letters rather than a number.
Read the lesson »Measurement and Unit Conversion
Convert metric units by powers of ten, convert between common English and metric units, convert units of time, and use the unit-factor method so the units cancel and prove the answer.
Read the lesson »Angles, Lines, and Angle Pairs
Complementary and supplementary angles, linear pairs and vertical angles, and solving for an unknown angle with an algebraic part-part-whole equation.
Read the lesson »Polygons, Triangles, and Quadrilaterals
Classify polygons and triangles, find interior and exterior angle sums, use the triangle angle-sum and exterior angle theorems, and apply the properties of parallelograms and trapezoids.
Read the lesson »Perimeter, Area, and Circles
Perimeter and area of triangles, rectangles, parallelograms and trapezoids, circumference and area of a circle, and working backwards from a given area to a missing dimension.
Read the lesson »Volume of Pyramids and Cylinders
Volume of square and rectangular pyramids and of cylinders, why a pyramid is exactly a third of its prism, and how to work backwards from a volume to a missing height.
Read the lesson »Data Collection and Sampling Techniques
Population and sample, primary and secondary data, and the four sampling methods — random, systematic, stratified and cluster — plus how a biased sample goes wrong.
Read the lesson »Organizing Data: Frequency Tables and Graphs
Build a frequency table with sensible class intervals, compute relative frequency as a percentage, read bar graphs, histograms and pie charts, and choose the right display for a data set.
Read the lesson »Outcomes from Experiments
Experiments, outcomes and sample space. Listing outcomes with a table or tree diagram, and finding the probability of an event as a fraction between 0 and 1.
Read the lesson »Operations on Polynomials
Classify polynomials by terms and degree, add and subtract by combining like terms, multiply with FOIL, and divide a polynomial by a monomial.
Read the lesson »Special Products
The square of a binomial, the sum and difference pattern giving a difference of squares, products with a common term, the square of a trinomial and the cube of a binomial.
Read the lesson »Factoring by Greatest Common Factor and Grouping
Find the greatest common factor of monomials, factor it out, factor four-term polynomials by grouping, and take out a common binomial factor.
Read the lesson »Factoring Differences of Squares and Cubes
Factor a difference of two squares, a sum of cubes and a difference of cubes, take the GCF out first to factor completely, and use the squares pattern for mental arithmetic.
Read the lesson »Factoring Trinomials
Factor trinomials with leading coefficient 1 by finding two numbers, use the AC method when the leading coefficient is not 1, and recognise perfect square trinomials.
Read the lesson »Simplifying Rational Algebraic Expressions
What makes an expression rational, finding the excluded values, factoring top and bottom completely, and simplifying to lowest terms by cancelling common factors.
Read the lesson »Operations on Rational Algebraic Expressions
Multiply and divide rational expressions by factoring and cancelling, add and subtract with like and unlike denominators using the LCD, and state the restrictions afterwards.
Read the lesson »Rational Algebraic Equations
Solve equations with a variable in the denominator by clearing the LCD, and check every answer against the restrictions so an extraneous root never slips through.
Read the lesson »Sequences and Their Rules
Find the rule behind a sequence, write the nth term of an arithmetic sequence, and tell arithmetic from geometric and from sequences that are neither.
Read the lesson »Linear Inequalities in One Variable
Solve linear inequalities in one variable, remember that multiplying or dividing by a negative reverses the sign, and show the solution on a number line.
Read the lesson »The Coordinate Plane and Graphing Lines
Plot points and name quadrants on the Cartesian plane, find intercepts, and graph a linear equation from a table of values or from its intercepts.
Read the lesson »Distance and the Midpoint of a Line Segment
The distance formula as the Pythagorean theorem on the coordinate plane, the midpoint as the average of the coordinates, and working backwards to a missing endpoint.
Read the lesson »Slope and Forms of Linear Equations
Compute slope from two points, write a line in slope-intercept and point-slope form, convert to standard form, and read slope as a constant rate of change.
Read the lesson »Solving Systems of Linear Equations
Solve systems of linear equations by substitution and by elimination, and recognise when a system has no solution or infinitely many.
Read the lesson »Word Problems with Systems
Turn two-unknown word problems into systems — number, money, mixture, age and cost problems — then solve and check both conditions.
Read the lesson »Linear Inequalities in Two Variables
Graph a linear inequality in two variables — solid or broken boundary line, which side to shade, and how to test a point to be sure.
Read the lesson »Money, Profit and Loss, and Best Buys
Earning money, mark-up and margin, profit and loss, comparing best buys by unit price, and what buying on terms really costs once the interest is counted.
Read the lesson »The Pythagorean Theorem
Use a squared plus b squared equals c squared to find a missing side, recognise Pythagorean triples, test whether a triangle is right-angled, and apply it to real distances.
Read the lesson »Volume of Pyramids, Cones, and Spheres
Volume of pyramids, cones and spheres, why a cone is a third of its cylinder and a sphere two thirds of it, and how to find a missing radius from a given volume.
Read the lesson »Triangle Inequality Theorems
The triangle inequality theorem and the range of a missing third side, plus the rules linking the largest angle to the longest side and the exterior angle inequality.
Read the lesson »Measures of Central Tendency of Ungrouped Data
Mean, median and mode for ungrouped data, which one to use when the data is skewed, and working backwards from a mean to a missing value.
Read the lesson »Measures of Variability for Ungrouped Data
Range, mean absolute deviation, variance and standard deviation for ungrouped data, and what spread tells you that an average cannot.
Read the lesson »Primary and Secondary Data in Graphs
Read and compare graphs built from primary and secondary data, choose the right display for a data set, and judge how far a published graph can be trusted.
Read the lesson »Probability and the Counting Principle
Theoretical and experimental probability, why they converge, and the Fundamental Counting Principle for finding how many outcomes a multi-stage choice has.
Read the lesson »Relations and Functions
Relations as ordered pairs with a domain and range, deciding whether a relation is a function, the vertical line test, and evaluating f(x) forwards and backwards.
Read the lesson »Domain, Range, and Zeros of Functions
Read the domain and range from a table, graph or equation, find the zeros of a function algebraically, and connect zeros to x-intercepts.
Read the lesson »Quadratics by Factoring and Square Roots
Solve quadratics by extracting square roots and by factoring, use the zero product property, and apply both to area word problems.
Read the lesson »Completing the Square and the Quadratic Formula
Complete the square to solve any quadratic, derive and apply the quadratic formula, and handle equations whose roots are irrational.
Read the lesson »Nature, Sum, and Product of Roots
Use the discriminant to classify the roots without solving, find a coefficient that forces a double root, and use the sum and product of roots to build or check an equation.
Read the lesson »Equations Transformable to Quadratic Equations
Equations that become quadratic once expanded or once the denominators are cleared, including rational equations with extraneous roots and work-rate problems.
Read the lesson »Quadratic Functions and Their Graphs
Vertex form and what each number does, converting from standard form by completing the square, finding intercepts and the maximum or minimum, and how shifts change the equation.
Read the lesson »Applications of Quadratic Functions
Maximum area from a fixed perimeter, projectile height and landing time, and the price that maximises revenue — all through the vertex of a quadratic.
Read the lesson »Direct, Inverse, Joint, and Combined Variation
Direct, inverse, joint and combined variation — writing the equation, finding the constant k from one pair of values, and using it to answer the question.
Read the lesson »Basic Geometric Concepts and Notation
Points, lines and planes, the notation for segments, rays and angles, betweenness and the segment addition postulate, and classifying angles.
Read the lesson »Parallel Lines Cut by a Transversal
The eight angles formed when a transversal cuts two parallel lines — corresponding, alternate interior, alternate exterior and co-interior — and how to prove lines parallel.
Read the lesson »Parallelograms and Special Quadrilaterals
Properties of parallelograms and of rectangles, rhombi and squares, the tests that prove a quadrilateral is a parallelogram, and how the family tree fits together.
Read the lesson »Trapezoids, Kites, and the Midline Theorem
Trapezoids and isosceles trapezoids, the median or midsegment, kites and their perpendicular diagonals, and the midline theorem for triangles.
Read the lesson »If-Then Statements and Reasoning
Conditional statements, their converse, inverse and contrapositive, why only the contrapositive is always equivalent, and inductive versus deductive reasoning.
Read the lesson »Triangle Congruence
Corresponding parts from a congruence statement, the SSS, SAS, ASA, AAS and HL tests, why SSA and AAA fail, and using CPCTC.
Read the lesson »Triangle Congruence Proofs
Write a two-column proof of triangle congruence — the given, the reasons you may cite, the free facts like reflexive sides and vertical angles, and finishing with CPCTC.
Read the lesson »Similar Triangles and Proportionality
Similarity as same shape with proportional sides, the AA, SSS and SAS similarity tests, finding a missing side with a proportion, and how area scales with the square of the ratio.
Read the lesson »Triangle Theorems
The isosceles triangle theorem and its converse, the angle bisector and perpendicular bisector theorems, and the four centres a triangle has.
Read the lesson »Special Right Triangles
The 45-45-90 and 30-60-90 side ratios, where they come from, and using them to find any side without trigonometry.
Read the lesson »Trigonometric Ratios of Right Triangles
Sine, cosine and tangent in a right triangle, choosing the right ratio from what you have, finding a side, and finding an angle with the inverse functions.
Read the lesson »Angles of Elevation and Depression
Angles of elevation and depression measured from the horizontal, drawing the right triangle from a worded situation, and remembering to add the observer's height.
Read the lesson »Recognizing Misleading Statistics and Graphs
Spot a truncated axis, uneven intervals, a chosen average, a missing base number and a causal claim from correlated data — and say what an honest version would show.
Read the lesson »Probability of Compound Events
Probability of compound events — the addition rule with and without overlap, the multiplication rule for independent and dependent events, and using the complement for "at least one".
Read the lesson »Quadratic Inequalities in One and Two Variables
Solve quadratic inequalities in one variable with critical numbers and a sign chart, write the solution in interval notation, and graph an inequality in two variables.
Read the lesson »Absolute Value Equations and Inequalities
Solve absolute value equations by splitting into two cases, recognise when there is no solution, and turn absolute value inequalities into compound and or or statements.
Read the lesson »Zero, Negative, and Rational Exponents
Zero and negative exponents, fractional exponents as roots and powers, simplifying with positive exponents only, and applying the laws to growth and decay models.
Read the lesson »Radical Expressions and Operations on Radicals
Simplify radicals by pulling out perfect-square or perfect-cube factors, add and subtract like radicals, multiply binomials containing radicals, and rationalise a denominator.
Read the lesson »Radical Equations
Isolate the radical and square both sides, always check for extraneous roots, handle equations with two radicals by squaring twice, and solve cube-root equations.
Read the lesson »The Quadratic Formula and the Roots
Apply the quadratic formula carefully, read the discriminant to classify the roots, and use the sum and product of roots to check an answer or build an equation.
Read the lesson »Quadratic Functions and Their Graphs
Graph a parabola from its vertex, axis and intercepts, convert between standard and vertex form, and see how the sign and size of a change the curve.
Read the lesson »Equations Reducible to Quadratic Form
Equations that become quadratic by substitution, by clearing denominators, or by squaring — including which roots must be rejected afterwards.
Read the lesson »The Equation and Graph of a Circle
The centre-radius form of a circle, writing it from a centre and radius or a point on the circle, and recovering the centre and radius from general form by completing the square.
Read the lesson »Compound Interest and Depreciation
Compound interest compared with simple interest, compounding more often than yearly, depreciation as negative growth, and working backwards to a principal or a rate.
Read the lesson »The Laws of Sines and Cosines
The law of sines for two angles and a side, the law of cosines for two sides and the included angle or all three sides, and how to choose between them.
Read the lesson »Translations, Reflections, and Rotations
Translations, reflections and rotations in the Cartesian plane, the coordinate rule for each, and why all three leave a figure congruent to the original.
Read the lesson »Central Angles and Inscribed Angles
Central angles equal their arcs, inscribed angles are half their arcs, angles on the same arc are equal, a semicircle gives a right angle, and cyclic quadrilaterals have opposite angles summing to 180 degrees.
Read the lesson »Chords, Secants, and Tangents
Intersecting chords, secants and tangents — the product rules for segment lengths, and the half-sum and half-difference rules for the angles they form.
Read the lesson »Sectors and Segments of a Circle
Arc length and sector area as a fraction of the whole circle, the area of a segment as sector minus triangle, and how to work back to a radius or a central angle.
Read the lesson »Quartiles, Deciles, and Percentiles
Quartiles, deciles and percentiles for ungrouped data — locating a position, reading a value from it, and finding the percentile rank of a score.
Read the lesson »Measures of Position for Grouped Data
Quartiles, deciles and percentiles for data already grouped into classes — cumulative frequency, locating the right class, and the interpolation formula.
Read the lesson »Box Plots and Cumulative Frequency
Build a five-number summary, draw and read a box-and-whisker plot, compare two distributions from their boxes, and read a median off a cumulative frequency curve.
Read the lesson »Interquartile Range and Outliers
The interquartile range as a measure of spread, the 1.5 x IQR rule for identifying outliers, and why an outlier moves the mean far more than the median.
Read the lesson »Evaluating Statistical Reports
Judge a published statistical claim — check the sample, the measure chosen, the scale of the graph, and whether a correlation has been dressed up as a cause.
Read the lesson »Union, Intersection, and Types of Events
Union and intersection of events, the addition rule and why overlap must be subtracted, complementary events, and the difference between independent and dependent events.
Read the lesson »Functions, Function Notation, and Evaluating Functions
What makes a relation a function, reading and using function notation, evaluating a function at a number or an expression, and writing a piecewise function for a fare that changes partway.
Read the lesson »Operations on Functions and Composition
Adding, subtracting, multiplying and dividing functions, the domain the quotient loses, and composition — why f of g means g goes first and why the order almost never commutes.
Read the lesson »Transformations of Functions
Shift, reflect, stretch and shrink the graph of any function: which change moves it up, which moves it sideways against the sign, which flips it, and how to track points and the domain and range through all of them at once.
Read the lesson »Rational Functions, Equations, and Inequalities
Rational functions and their restrictions, solving a rational equation by clearing the denominators, why every answer must be checked for extraneous roots, and why an inequality needs a sign chart instead.
Read the lesson »Intercepts, Zeroes, and Asymptotes of Rational Functions
Reading a rational function's graph from its algebra — zeroes from the top, vertical asymptotes from the bottom, the horizontal asymptote from the degrees, and the hole that appears when a factor cancels.
Read the lesson »One-to-One Functions and Their Inverses
One-to-one functions and the horizontal line test, finding an inverse by swapping x and y, why the domain and range trade places, and checking an inverse by composing the two functions.
Read the lesson »Exponential Functions, Equations, and Inequalities
What makes a function exponential, solving exponential equations by matching bases, rewriting numbers to a common base, and the sign flip that a base below 1 forces on an inequality.
Read the lesson »Graphing Exponential Functions
The shape every exponential graph shares, the point (0, 1) they all pass through, growth against decay, the horizontal asymptote, and what shifting and reflecting do to all three.
Read the lesson »Logarithms and the Laws of Logarithms
A logarithm is an exponent — converting between log and exponential form, the product, quotient and power laws, common and natural logs, and the change-of-base formula.
Read the lesson »Logarithmic Equations and Inequalities
Solving logarithmic equations by rewriting in exponential form or by equating arguments, combining several logs into one first, and why every answer must be tested against the domain.
Read the lesson »Graphing Logarithmic Functions
The logarithmic graph as the exponential reflected in y = x, the point (1, 0) they all share, the vertical asymptote, and how a shift inside the bracket moves both the asymptote and the domain.
Read the lesson »Growth, Decay, and Half-Life
Exponential growth and decay models, doubling time and half-life, reading the model straight from the wording, and using logarithms to solve for the time when the exponent is unknown.
Read the lesson »Simple Interest
Simple interest as a flat charge on the original principal, the formula I = Prt, matching the units of rate and time, and finding any one of the four quantities from the other three.
Read the lesson »Compound Interest
Compound interest as interest earning interest, the formula A = P(1 + r)ⁿ, how it pulls away from simple interest over time, and finding the principal or the rate from the amount.
Read the lesson »Compounding More Than Once a Year
Compounding more than once a year — dividing the nominal rate by the number of periods, multiplying the years by it, and why more frequent compounding pays a little more.
Read the lesson »Simple Annuities
Annuities as a stream of equal payments at equal intervals, the future and present value formulas, the difference between an ordinary annuity and an annuity due, and finding the payment from a target.
Read the lesson »General and Deferred Annuities
General annuities, where the payment interval and the compounding period differ, converting to an equivalent rate so the simple-annuity formula applies, and deferred annuities whose payments start later.
Read the lesson »Stocks and Dividends
Shares, par value and market value, working out a dividend from the par value rather than the price paid, the dividend yield, and the gain or loss made on selling.
Read the lesson »Bonds
Bonds as a loan to the issuer — face value, coupon rate and maturity, working out a coupon payment, why a bond trades above or below face value, and the current yield.
Read the lesson »Business and Consumer Loans
Consumer and business loans, seeing a loan as the present value of an annuity, the amortisation formula for the regular payment, what an amortisation schedule shows, and the true cost of borrowing.
Read the lesson »Propositions and Logical Operators
What makes a sentence a proposition, the five logical operators and their symbols, negating a statement correctly including quantifiers, and translating ordinary sentences into symbols.
Read the lesson »Truth Tables, Tautologies, and Contradictions
Building a truth table row by row, the tables for and, or and the conditional, why a false hypothesis makes a conditional true, and spotting tautologies, contradictions and logical equivalence.
Read the lesson »Conditionals and Valid Arguments
Converse, inverse and contrapositive, the two valid argument forms — modus ponens and modus tollens — the two fallacies that mimic them, and how to test any argument for validity.
Read the lesson »The Circle
The circle as a conic section, its standard and general forms, completing the square in both variables to recover the centre and radius, and the two degenerate cases a general equation can hide.
Read the lesson »The Parabola
The parabola as the set of points equidistant from a focus and a directrix, the four standard forms, finding the vertex, focus, directrix and latus rectum, and why the reflector property matters.
Read the lesson »The Ellipse
The ellipse as the set of points whose distances to two foci add to a constant, the relationship a² = b² + c², reading the major axis from the larger denominator, and eccentricity.
Read the lesson »The Hyperbola
The hyperbola as the set of points whose distances to two foci differ by a constant, why the positive term decides the opening direction, c² = a² + b², and the asymptotes that guide the branches.
Read the lesson »Recognising a Conic from Its Equation
Telling the four conics apart from a general second-degree equation by looking at the squared terms, their signs and their coefficients, and the degenerate cases that hide inside each one.
Read the lesson »Situational Problems Involving Conics
Setting up a coordinate system for a real conic — parabolic dishes and bridge cables, elliptical arches and whispering galleries — then reading the answer back out in the units of the problem.
Read the lesson »Systems of Non-Linear Equations
Solving systems where at least one equation is not linear — substitution, elimination between two conics, checking every candidate, and reading the number of solutions off the picture.
Read the lesson »Series and Sigma Notation
The difference between a sequence and a series, reading and writing sigma notation, changing the index without changing the sum, and the basic properties that let a sigma be split apart.
Read the lesson »Arithmetic and Geometric Series
Sums of arithmetic and geometric series, choosing between the two sum formulas, and the infinite geometric series that converges only when the common ratio is smaller than one in size.
Read the lesson »Mathematical Induction
Proof by mathematical induction — the base case, the inductive hypothesis and the inductive step, why both halves are needed, and how to write one out properly.
Read the lesson »The Binomial Theorem
Expanding a binomial power with Pascal's triangle and with combinations, finding a single term without expanding everything, and locating the term in which a given power appears.
Read the lesson »Angles in Standard Position and Radian Measure
Angles in standard position, converting between degrees and radians, coterminal and reference angles, and arc length and sector area, which only work in radians.
Read the lesson »The Unit Circle and the Circular Functions
The unit circle as the definition of sine and cosine for any angle, the coordinates of the special angles, the signs in each quadrant, and using reference angles to find any value.
Read the lesson »Graphs of the Circular Functions
The graphs of sine, cosine and tangent — where they come from on the unit circle, their period, range and key points, and why tangent has asymptotes where the others do not.
Read the lesson »Amplitude, Period, and Phase Shift
Reading amplitude, period, phase shift and vertical shift from y = a sin(b(x − c)) + d, why the period is 2π over b, and why the phase shift needs b factored out first.
Read the lesson »Fundamental Trigonometric Identities
The reciprocal, quotient and Pythagorean identities, the even-odd identities, and the method for proving an identity — work on one side only until it matches the other.
Read the lesson »Sum and Difference Identities
The sum and difference formulas for sine, cosine and tangent, the sign flip that catches everyone in the cosine version, and using them to find exact values for angles like 15 and 75 degrees.
Read the lesson »Double-Angle and Half-Angle Identities
Double-angle formulas for sine, cosine and tangent, the three equivalent forms of cos 2A and when each is useful, and the half-angle formulas whose sign comes from the quadrant.
Read the lesson »Inverse Trigonometric Functions
Why sine, cosine and tangent need restricted domains before they can be inverted, the principal value ranges of arcsin, arccos and arctan, and evaluating compositions of a function with its inverse.
Read the lesson »Trigonometric Equations
Solving trigonometric equations — finding every solution in an interval rather than one, factoring and using identities to reduce to a single function, and why dividing by a trig factor loses roots.
Read the lesson »The Polar Coordinate System
Locating a point by distance and direction instead of across and up, converting both ways between polar and rectangular coordinates, and why a polar point has infinitely many names.
Read the lesson »Situational Problems Involving Trigonometry
Trigonometry in real situations — bearings, angles of elevation and depression, choosing between the sine and cosine laws, and simple harmonic motion modelled by a sine function.
Read the lesson »Naming Solids, Nets, and Cross-Sections
Naming a solid by its base, unfolding it into a net, slicing it into a cross-section, and the face-vertex-edge count that checks your work.
Read the lesson »Surface Area and Volume of a Prism
Volume as base area times height for any prism, lateral area as perimeter times height, and the unit conversions that turn cubic centimetres into litres.
Read the lesson »Surface Area and Volume of a Pyramid
Why a pyramid is one third of the prism on the same base, the right triangle that turns height into slant height, and the lateral area formula that needs the slant.
Read the lesson »Surface Area and Volume of a Cylinder and a Cone
A cylinder as a prism with a circular base and a cone as a pyramid with one, the rolled-out rectangle that gives lateral area, and where the cone's slant height comes from.
Read the lesson »Surface Area and Volume of a Sphere
The two sphere formulas and how to keep them apart, the flat face a hemisphere still has, and building a composite solid out of pieces you already know.
Read the lesson »Trigonometry Inside a Solid
Finding the right triangle hidden inside a pyramid, a cone or a box, telling the slant height from the lateral edge, and the angles a face and a diagonal make with the base.
Read the lesson »Random Variables, Discrete and Continuous
Turning an outcome into a number, telling a discrete random variable from a continuous one, and listing the values a random variable can take before any probability is worked out.
Read the lesson »Discrete Probability Distributions
Building a probability distribution from the outcomes, the two conditions every valid distribution must meet, and reading probabilities off a histogram.
Read the lesson »Mean, Variance, and Standard Deviation of a Random Variable
The expected value as a weighted average, the shortcut formula for variance, and why the mean of a random variable need not be a value the variable can take.
Read the lesson »The Normal Distribution and z-Scores
The bell curve and what makes it normal, converting a raw score to a z-score, reading areas from the z-table, and the empirical 68-95-99.7 rule.
Read the lesson »Sampling Distributions and the Central Limit Theorem
Why a sample mean varies, the standard error and why dividing by root n shrinks it, and the Central Limit Theorem that makes the sample mean normal whatever the population looks like.
Read the lesson »Point Estimates and Confidence Intervals
A point estimate and why it is never enough on its own, building a confidence interval from the sample mean and the margin of error, and what 95 percent confidence actually claims.
Read the lesson »Testing a Hypothesis About a Mean
Writing the null and alternative hypotheses, computing the test statistic, comparing it against a critical value, and what a rejected or retained null actually lets you say.
Read the lesson »Correlation and the Least-Squares Regression Line
Reading a scatter plot, what the correlation coefficient r does and does not say, fitting the least-squares line, and using it to predict without going past the data.
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