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Square roots of positive numbers, and n^{\\operatorname{\\mathrm{th}}} roots.

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Exponents & their rules, introduction to logarithms, and exponential + logarithmic functions.

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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).

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Definition of series, formula for arithmetic series

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Summation notation, properties of sums

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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

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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

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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.

\n","hasLesson":true},{"id":326,"name":"Tangents and normals","slug":"tangents-and-normals","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027557648-Artboard%2088_1.png?alt=media&token=ba008df4-2d3c-426c-bf8f-0809dadd8f51","type":"image"},"skills":[575,576],"description":"

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

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

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

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

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

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

","hasLesson":true},{"id":683,"name":"Measures of center","slug":"measures-of-center","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028579941-Artboard%2070.png?alt=media&token=1bf0b1f0-af9c-495e-bcb5-7e57ec2ae2c4","type":"image"},"skills":[121,120,119],"description":"

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

","hasLesson":true},{"id":682,"name":"Quartiles, outliers and box plots","slug":"quartiles-outliers-and-box-plots","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028567591-Artboard%2071.png?alt=media&token=289941af-343d-4b68-8b4b-0b2a5f0267f2","type":"image"},"skills":[669,670,733,1037],"description":"

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

","hasLesson":true},{"id":118,"name":"Standard Deviation and Variance","slug":"standard-deviation-and-variance","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028551868-SDVar.png?alt=media&token=91c80f18-8855-40d2-a00b-62b578ab007a","type":"image"},"skills":[672,671],"description":"

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

\n","hasLesson":true},{"id":126,"name":"Frequency tables and histograms","slug":"frequency-tables-and-histograms","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028166495-Artboard%2072.png?alt=media&token=2d41e78e-b5a6-4558-849d-c5ba24514aef","type":"image"},"skills":[127,673,674],"description":"Visualizing frequency data using tables and histograms.","hasLesson":true},{"id":1004,"name":"Cumulative frequency","slug":"cumulative-frequency","isPaywalled":false,"isPublic":true,"thumbnail":null,"skills":[675,676],"description":"Completing tables of cumulative frequency, and reading cumulative frequency diagrams.","hasLesson":true}],"description":"

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.

\n"},{"id":3,"name":"Bivariate Statistics","slug":"bivariate-statistics","topic":4,"subjects":["AISL","AIHL","AASL","AAHL"],"isVideoReady":false,"videoId":null,"concepts":[{"id":268,"name":"Linear regression and Pearson's coefficient","slug":"linear-regression-and-pearsons-coefficient","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028135613-Artboard%2074.png?alt=media&token=10413a3d-f49a-4178-a780-37cbede60ac6","type":"image"},"skills":[475,711,712,714,713,476],"description":"

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.

\n","hasLesson":true},{"id":960,"name":"Spearman's Rank Correlation Coefficient","slug":"spearmans-rank-correlation-coefficient","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1775760783749-spearman.png?alt=media&token=3e974b96-a008-4b7a-b1f5-40c52fb008e1","type":"image"},"skills":[24],"description":"

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

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

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

\n"},{"id":98,"name":"Distributions & Random Variables","slug":"distributions-random-variables","topic":4,"subjects":["AAHL","AIHL","AISL","AASL"],"isVideoReady":true,"videoId":"kFLHW61tj9o","concepts":[{"id":274,"name":"Binomial Distribution","slug":"binomial-distribution","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028018137-Artboard%2075.png?alt=media&token=cb09bf58-c604-4a22-b0a2-acd0f6653970","type":"image"},"skills":[690,691,693,1018,857],"description":"

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

","hasLesson":true},{"id":275,"name":"Normal Distribution","slug":"normal-distribution","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027990196-Artboard%2076.png?alt=media&token=06211191-fa11-4675-a226-3437a57fad92","type":"image"},"skills":[686,685,1046,687,688],"description":"

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.

\n","hasLesson":true},{"id":284,"name":"Discrete random variables","slug":"discrete-random-variables","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028049217-Artboard%2074_1.png?alt=media&token=aab272d8-f276-4926-8652-aa1cfc76c0ac","type":"image"},"skills":[678,677,679,279,287,956,957],"description":"Discrete random variables taking a finite set of values, with probability distributions in tables or as expressions where probabilities sum to 1, finding \$E(X)\$ and fair games.","hasLesson":true}],"description":"

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

\n"},{"id":2,"name":"Inference & Hypotheses","slug":"inference-hypotheses","topic":4,"subjects":["AIHL","AISL"],"isVideoReady":false,"videoId":null,"concepts":[{"id":9,"name":"Hypothesis tests and p-values","slug":"hypothesis-tests-and-p-values","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027801544-Artboard%2080.png?alt=media&token=1ec95703-fcfe-4305-9c8c-81940a0ce4dd","type":"image"},"skills":[28,72],"description":"

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.

\n","hasLesson":true},{"id":954,"name":"χ² tests","slug":"chi-squared-tests","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027788675-Artboard%2082.png?alt=media&token=8daf9484-3199-4edd-9686-083e2bf40bfb","type":"image"},"skills":[29,27,31,1045,30],"description":"

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.

\n","hasLesson":true},{"id":953,"name":"Student's t-test","slug":"students-t-test","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027745203-Artboard%2084.png?alt=media&token=4e653334-7eea-41d7-b305-8b628dfef074","type":"image"},"skills":[80,82,1048],"description":"

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

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

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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