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Functions as input-output models and their representations, including notation, domain and range, evaluation and graph interpretation, intercepts, inverses, intersections, maxima and minima, asymptotes, and graphing with technology.

\n"},{"id":908,"name":"Modelling","slug":"modelling","topic":2,"subjects":["AIHL","AISL"],"isVideoReady":false,"videoId":null,"concepts":[{"id":966,"name":"Piecewise Linear Models","slug":"piecewise-linear-models","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1774921314118-Artboard%2043.png?alt=media&token=e753de30-6b27-451f-bbd6-e4b08f6caea7","type":"image"},"skills":[915],"description":"

Modeling with functions that have several linear pieces, such as

f(x)=\\begin{cases}2x+1 & x<2\\\\ x+3 & x\\ge2\\end{cases}

\n","hasLesson":true},{"id":963,"name":"Cubic Models","slug":"cubic-models","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1774921398155-quadraticModels%20copy.png?alt=media&token=b5a6f44a-1b02-4c98-8046-ebeff485cc84","type":"image"},"skills":[927],"description":"

Cubic models of the form ax^3+bx^2+cx+d, including graphs with 0 or 2 turning points and the short flat section seen when there are no turning points.

\n","hasLesson":true},{"id":964,"name":"Exponential Models","slug":"exponential-models","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1774921406598-exponentialModels.png?alt=media&token=5dae0854-86d5-4130-b58a-5f24386c0d50","type":"image"},"skills":[926,901,902],"description":"

Exponential models of the form Ab^x+k for repeated multiplication by a constant factor, including exponential growth when b>1, exponential decay when 0<b<1, and graphs with horizontal asymptote y=k and y-intercept (0,A+k).

\n","hasLesson":true},{"id":962,"name":"Sinuisoidal Models","slug":"sinuisoidal-models","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1774921422992-sinusoidalModels.png?alt=media&token=593230ed-6278-44de-892e-00c5f328f78b","type":"image"},"skills":[928],"description":"

Sinusoidal models of the form y=a\\sin(bx)+c or y=a\\cos(bx)+c, including the principal axis y=c, amplitude a, and period \\frac{360}{b}^{\\circ}.

\n","hasLesson":true},{"id":961,"name":"Piecewise models","slug":"piecewise-models","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1774921434771-piecewiseModels.png?alt=media&token=d5b1b32b-2ed0-4ac5-b3fe-dd9ef1897a3d","type":"image"},"skills":[],"description":"Piecewise-linear functions as models with different behavior in different intervals.","hasLesson":true},{"id":925,"name":"Power Models & Proportionality ","slug":"power-models-proportionality-","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029212106-Artboard%2045.png?alt=media&token=ea87ff9b-8929-4296-ad61-f73b3d4c6f53","type":"image"},"skills":[1089,929,930],"description":"

Power models of the form y=ax^b or y\\propto x^b, including direct proportion y=kx^n, inverse proportion y=\\frac{k}{x^n}, and fitting a power model from data using power regression.

\n","hasLesson":true},{"id":910,"name":"Modeling foundations and linear models","slug":"modeling-foundations-and-linear-models","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1774921256837-linearModels.png?alt=media&token=643bb3a9-92ae-487b-aac0-a85f8888dc5f","type":"image"},"skills":[912,913,914],"description":"Mathematical modelling with linear models \$y=ax+b\$, using assumptions and parameters to represent real situations, and interpreting or extrapolating predictions beyond the given data when appropriate. ","hasLesson":true},{"id":965,"name":"Quadratic Models","slug":"quadratic-models","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1774921323648-quadraticModels.png?alt=media&token=392b87a5-e3aa-4eb0-a0d6-021734bf76b3","type":"image"},"skills":[922,801,802,1086],"description":"

Quadratic models in the form ax^2+bx+c, including the parabola's vertex and axis of symmetry, maximum or minimum turning point, x-intercepts or roots, and fitting a quadratic from three data points.

\n","hasLesson":true}],"description":"

Building and interpreting mathematical models from data using linear, quadratic, exponential, cubic, sinusoidal, power, direct and inverse proportion forms, including fitting models, assumptions and extrapolation.

\n"},{"id":865,"name":"Rounding & Error","slug":"rounding-error","topic":1,"subjects":["AISL","AASL","AIHL","AAHL"],"isVideoReady":false,"videoId":null,"concepts":[{"id":866,"name":"Rounding and estimation","slug":"rounding-and-estimation","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757030041198-Artboard%205.png?alt=media&token=25922b18-0ebb-4291-af0d-e8584c14c0e9","type":"image"},"skills":[869,877],"description":"

Rounding, significant figures, decimal places

","hasLesson":true},{"id":868,"name":"Scientific Notation","slug":"scientific-notation","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1773515918578-Artboard%206.png?alt=media&token=69a03129-81d4-4eeb-a181-bef451d1b1cd","type":"image"},"skills":[882,885,887],"description":"

Converting numbers to and from scientific notation \\left(a\\times10^{k}\\right)

","hasLesson":true},{"id":867,"name":"Measurement and error","slug":"measurement-and-error","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1773516589698-error.png?alt=media&token=46ea8335-6157-4026-a7ad-19c8cb5f066e","type":"image"},"skills":[878,880,894],"description":"

Approximation, absolute and percentage error using |V_A-V_E| and \\frac{|V_A-V_E|}{V_E}\\times100\\%, together with error bounds from rounding or measurement and how they propagate through calculations.

\n","hasLesson":true}],"description":"

Rounding, significant figures, and scientific notation. Absolute and percentage error.

"},{"id":30,"name":"Sequences & Series","slug":"sequences-series","topic":1,"subjects":["AAHL","AIHL","AISL","AASL","ecolint-y11-hl"],"isVideoReady":true,"videoId":"DI2cudLIWEk","concepts":[{"id":27,"name":"Arithmetic Sequences","slug":"arithmetic-sequences","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029981178-Artboard%207.png?alt=media&token=8a340859-acc8-458a-a5be-e962cb927b61","type":"image"},"skills":[602,603],"description":"

Introduction to the definition, properties, and general term of an arithmetic sequence

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Introduction to definition, identification, and general term of geometric sequences

","hasLesson":true},{"id":31,"name":"Arithmetic Series","slug":"arithmetic-series","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757030004817-Artboard%209.png?alt=media&token=4f2e2c52-6ec5-4ca1-b258-67a93d257f07","type":"image"},"skills":[607,46],"description":"

Definition of series, formula for arithmetic series

","hasLesson":true},{"id":860,"name":"Summation notation","slug":"summation-notation","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029991958-Artboard%2010.png?alt=media&token=dcfdc9b6-9e57-47bc-b6bc-9b4088d76eb5","type":"image"},"skills":[47,837,861,862,863,905],"description":"

Summation notation, properties of sums

","hasLesson":true},{"id":859,"name":"Geometric Series","slug":"geometric-series","isPaywalled":true,"isPublic":true,"thumbnail":{"type":"graph","graph":{"data":"$3d","mode":"geometry"}},"skills":[606],"description":"

Finite geometric series with sum S_{n}=\\frac{u_1(1-r^n)}{1-r}.

\n","hasLesson":true},{"id":906,"name":"Sequence Mode (Calculator)","slug":"sequence-mode-calculator","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029904498-Artboard%2011.png?alt=media&token=542aa577-0f10-43f9-b206-99a890877c96","type":"image"},"skills":[],"description":"

Working with sequences on a calculator, computations and applications of a calculator

","hasLesson":true},{"id":870,"name":"Compound interest, depreciation and inflation","slug":"compound-interest-depreciation-and-inflation","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029508658-Artboard%2012.png?alt=media&token=fb6f46c3-0587-4c9c-83b6-2dd08aad7ca4","type":"image"},"skills":[872,871,883,896,873],"description":"

Compound growth, depreciation, interest, inflation, real value

","hasLesson":true}],"description":"Arithmetic sequences u_{n}=u_1+\\left(n-1\\right)d and geometric sequences v_{n}=v_1r^{n-1}, as well as their series and the \\Sigma notation for summation."},{"id":864,"name":"Financial Mathematics","slug":"financial-mathematics","topic":1,"subjects":["AISL","AIHL"],"isVideoReady":false,"videoId":null,"concepts":[{"id":870,"name":"Compound interest, depreciation and inflation","slug":"compound-interest-depreciation-and-inflation","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029508658-Artboard%2012.png?alt=media&token=fb6f46c3-0587-4c9c-83b6-2dd08aad7ca4","type":"image"},"skills":[872,871,883,896,873],"description":"

Compound growth, depreciation, interest, inflation, real value

","hasLesson":true},{"id":874,"name":"Loans","slug":"loans","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029497952-Artboard%2029.png?alt=media&token=ed1c353b-8cec-4988-8123-d1aa20e48a65","type":"image"},"skills":[1081,891,896],"description":"

Loans as amortized borrowing: money is received as an initial balance and repaid by regular payments with interest until the balance is cleared, using TVM Solver variables such as PV, PMT, FV, N, I\\%, P/Y and C/Y, with correct positive and negative cash flow signs.

\n","hasLesson":true},{"id":890,"name":"Annuities","slug":"annuities-perpetuities","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029490725-Artboard%2030.png?alt=media&token=be15ceb4-2826-4e40-9fd2-3cd0aa66344a","type":"image"},"skills":[1082,898,896],"description":"

An annuity as the reverse of a loan, with regular end-of-period withdrawals or payments and TVM Solver calculations using PV, PMT, FV, N, I\\%, and correct positive/negative cash-flow signs.

\n","hasLesson":true}],"description":"

Compound interest and depreciation models, inflation and real value, and using the TVM Solver to work with loans and annuities with correct cash flow signs.

\n"},{"id":356,"name":"2D & 3D Geometry","slug":"2d-geometry","topic":3,"subjects":["AAHL","AASL","AIHL","AISL","ecolint-y11-hl"],"isVideoReady":true,"videoId":"GnG2jU8VpUg","concepts":[{"id":82,"name":"Right-angled triangles","slug":"right-angled-triangles","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029099320-Artboard%2046.png?alt=media&token=803487ed-7a2d-4c58-88e5-31cba1785454","type":"image"},"skills":[87,36,56,716,83,717],"description":"

Pythagoras's theorem, SOHCAHTOA, finding side length from angles

","hasLesson":true},{"id":37,"name":"Non-right-angled triangles","slug":"non-right-angled-triangles","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029088911-Artboard%2047.png?alt=media&token=80493296-567f-4f51-b0b3-4c328ab90285","type":"image"},"skills":[88,73,74],"description":"

Sine and cosine rules, finding general area of a triangle

\n","hasLesson":true},{"id":65,"name":"Radians, arcs and sectors","slug":"radians-arcs-and-sectors","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028966537-Artboard%2049.png?alt=media&token=21e1f320-b306-4587-8651-9991150cbd34","type":"image"},"skills":[492,721,4],"description":"

Arc-length and sector area using formulas in degrees:

l=\\frac{\\theta}{360^\\circ}2\\pi r

A=\\frac{\\theta}{360^\\circ}\\pi r^2

\n","hasLesson":true},{"id":722,"name":"3D volume and surface area","slug":"3d-volume-and-surface-area","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028955870-Artboard%2050.png?alt=media&token=3f2ceb70-0712-4f69-81cc-c257607a3013","type":"image"},"skills":[1080,1094,723,724,725,834,835],"description":"

Spheres, cylinders, prisms, right cones, right pyramids, and combinations of solids

","hasLesson":true},{"id":89,"name":"Angles of elevation and depression","slug":"angles-of-elevation-and-depression","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028981407-Artboard%2048.png?alt=media&token=5b9c00d8-8c4e-40c8-afef-26030c38db55","type":"image"},"skills":[90],"description":"Angles measured between a horizontal line and some elevated or depressed object.","hasLesson":true}],"description":"

2D and 3D geometry including circle measures, triangle trigonometry, bearings and angles of elevation, and volumes, surface areas and coordinates of common solids.

\n"},{"id":935,"name":"Voronoi Diagrams","slug":"voronoi-diagrams","topic":3,"subjects":["AIHL","AISL"],"isVideoReady":false,"videoId":null,"concepts":[{"id":909,"name":"Voronoi structure and construction","slug":"voronoi-structure-and-construction","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1758237746834-Artboard%2051.png?alt=media&token=9ba8047e-695d-4059-a7c6-2b2229990cf2","type":"image"},"skills":[917,918,923,920,921,949],"description":"

The terminology of Voronoi diagrams, including sites, cells, edges and vertices, with edges as perpendicular bisectors, vertices equidistant from three or more sites, adding a new site, nearest neighbor interpolation, and largest empty circle or toxic waste dump problems.

\n","hasLesson":true},{"id":939,"name":"Applications of Voronoi Diagrams","slug":"applications-of-voronoi-diagrams","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028926923-Artboard%2052.png?alt=media&token=6315d13b-6e14-473a-8bc7-ee067ccd5a72","type":"image"},"skills":[920,921],"description":"

Nearest neighbor interpolation from a Voronoi diagram, where each cell takes the value of its generating site and points on boundaries may use an average of the adjacent sites, and toxic waste dump problems (largest empty circle) solved by finding the Voronoi vertex farthest from its nearest sites.

\n","hasLesson":true}],"description":"

Voronoi diagram terminology and properties, including cells, edges and vertices, perpendicular bisectors, nearest-neighbor interpolation, largest empty circle problems and adding a new site.

\n"},{"id":346,"name":"Differentiation","slug":"differentiation","topic":5,"subjects":["AAHL","AASL","AIHL","AISL"],"isVideoReady":true,"videoId":"7GKpUTrLk_o","concepts":[{"id":111,"name":"Limits and Derivatives","slug":"limits-and-derivatives","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027621748-Artboard%2086.png?alt=media&token=f862e464-90a6-482b-9b52-1be5899b056c","type":"image"},"skills":[565,566,567,570,569,571,535,534,19],"description":"

The basic idea of a limit \\lim_{x\\to a}f(x) from tables and graphs, slope as a limit, rate of change and gradient, derivatives of x^n, and linearity for sums and scalar multiples.

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Definitions of tangent and normal, finding tangent and normal lines to a function

","hasLesson":true},{"id":331,"name":"Applications of the First Derivative","slug":"applications-of-the-first-derivative","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027540062-Artboard%2089.png?alt=media&token=8765b377-ec1c-498c-8770-e7f8904405d4","type":"image"},"skills":[573,16,531],"description":"

Increasing and decreasing intervals, stationary points (maxima and minima), and optimisation

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Differentiation as the study of rates of change, gradients and limits, including rules for basic derivatives, tangents and normals, stationary points, increasing and decreasing behavior, and simple optimisation.

\n"},{"id":114,"name":"Integration","slug":"integration","topic":5,"subjects":["AAHL","AASL","AIHL","AISL"],"isVideoReady":true,"videoId":"Ex7Qii1AXn8","concepts":[{"id":450,"name":"Definite Integrals and Basic Anti-Derivatives","slug":"definite-integrals-and-basic-anti-derivatives","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027038579-Artboard%2093.png?alt=media&token=bb418ca4-71b9-42ce-b97d-090a1379edea","type":"image"},"skills":[418,293,587,581,583,545,584,585,41,1020],"description":"

Concept of an integral, areas with definite integrals, and basic anti-derivative solving skills

\n","hasLesson":true},{"id":231,"name":"Kinematics","slug":"kinematics","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757026968679-Artboard%2095.png?alt=media&token=8619b033-cbb4-41e2-b0f2-f691121bf19f","type":"image"},"skills":[],"description":"

Displacement, distance, velocity and acceleration in one and two dimensions, including v=\\frac{\\mathrm{d}s}{\\mathrm{d}t}, a=\\frac{\\mathrm{d}v}{\\mathrm{d}t}=\\frac{\\mathrm{d}^2s}{\\mathrm{d}t^2}, average velocity and acceleration, \\int v(t)\\,\\mathrm{d}t for displacement, \\int |v(t)|\\,\\mathrm{d}t for distance, speed as |v|, and speeding up/slowing down..

\n","hasLesson":true}],"description":"

Reverse differentiation and indefinite integrals, definite integrals and area under a curve, integration rules and constants, and numerical approximation with GDC and the trapezoidal rule.

\n"},{"id":96,"name":"Probability","slug":"probability","topic":4,"subjects":["AAHL","AASL","AIHL","AISL"],"isVideoReady":true,"videoId":"nTKI6Ze6SxE","concepts":[{"id":145,"name":"Foundations of probability","slug":"foundations-of-probability","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028648442-Artboard%2065.png?alt=media&token=5706f4de-134c-4cf9-b2be-c3b79211ab31","type":"image"},"skills":[701,702,699,700,32,703],"description":"

Theoretical and experimental probability, complementary events, expected number of outcomes, sample space

","hasLesson":true},{"id":154,"name":"Combined Events","slug":"combined-events","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028633410-Artboard%2066.png?alt=media&token=875764d4-1b49-4d32-9717-25ae5901b2f5","type":"image"},"skills":[156,155,157,163,34,33,1117,704],"description":"

Venn diagrams, intersection and union of events, conditional probability, independent events

","hasLesson":true},{"id":707,"name":"Tree Diagrams","slug":"tree-diagrams","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028620712-Artboard%2067.png?alt=media&token=62bf0ee2-5ee0-4524-9d9f-97eea0a4d381","type":"image"},"skills":[708,705],"description":"

Tree diagrams, selection with/without replacement, dependence

","hasLesson":true}],"description":"

Theoretical vs experimental probability, combined events, independence vs dependence.

"},{"id":94,"name":"Descriptive Statistics","slug":"descriptive-statistics","topic":4,"subjects":["AAHL","AASL","AIHL","AISL","ecolint-y11-hl"],"isVideoReady":true,"videoId":"Q6pTmvyBjtY","concepts":[{"id":461,"name":"Population, samples and data","slug":"population-samples-and-data","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028594946-Artboard%2069.png?alt=media&token=c647fb49-123f-411f-96bd-84222ced9a3c","type":"image"},"skills":[663,664,141,668,666,667,468,470,469,471,472,23],"description":"

Understand the basics of population, data collection, and sampling.

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Learn different ways to measure the \"center,\" or typical values, of a set of data: mean, median, and mode.

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Learn the concept of dispersion, range, IQR, outliers, and box and whisker plots.

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Learn about standard deviation and variance, which we use to measure how tightly or loosely clustered the data is around the mean.

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Summarizing and interpreting data using measures of centre and spread, frequency tables and graphs, sampling methods, quartiles, IQR, box plots, cumulative frequency, and outlier analysis.

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Scatter diagrams and lines of best fit y=ax+b, by eye or with GDC, the Pearson correlation coefficient r, and making predictions with awareness of limitations.

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Calculating Spearman's rank correlation coefficient by ranking x and y values, then using Pearson's r, and understanding when to use it.

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Pearson's and Spearman's correlation coefficients, drawing and using a regression line to predict values, and recognizing the limits of extrapolation.

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Concept of the binomial distribution, binomial PDF and CDF, expectation and variance of binomial distribution

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The normal (bell-shaped) distribution X\\sim\\mathrm{N}(\\mu,\\sigma^2), its symmetry about \\mu, the empirical rule, and calculator-based normal and inverse normal probability calculations.

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Discrete random variables and probability distributions, including expected value and fair games, plus binomial and normal distributions with basic calculator-based probability calculations.

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Formulating null and alternative hypotheses H_0 and H_1, then using the p-value from the data to judge evidence against H_0 at a chosen significance level.

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Expected and observed frequencies in \\chi^2 goodness of fit and independence tests, including degrees of freedom, the test statistic, and comparing \\chi^2 to a critical value to decide whether to reject H_0.

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Student's t-tests for comparing means in the 1-sample and 2-sample cases, as well as the assumptions made by the test.

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Null and alternative hypotheses, p-values and significance levels, and chi-squared and t-tests for comparing observed vs expected data, independence, and sample means.

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