How can we help?

Course Updates for Pre-Calculus in July 2021

Updated

We are excited to share that we've made significant enhancements to our Pre-Calculus course. One consequence of adding this new content is that it may impact learners’ Mastery percentages.

When we add new content and remove old content, Mastery percentages often change because the number of available skills changes. For example, if you mastered 90 out of 100 skills in a course, and we added 10 new skills, your mastery skill count would then be 90 out of 110. This change would change your Mastery percentage from 90% to 82%.

With this specific course update, we expect that Mastery percentages will change by a maximum of 52%. Most people will see a much smaller Mastery percentage change.

You can see exactly what content items we’ve added and removed below. Happy learning!

Articles

Exercises

Videos

Content Removed

Articles

 Adding and subtracting polynomials with two variables review Circle equation review Complex number operations review Intro to complex numbers Intro to the imaginary numbers Matrix row operations Multiplying complex numbers Parabola focus & directrix review Powers of the imaginary unit Recognizing vectors practice Representing linear systems with matrices Solving equations graphically Vector forms review Vector operations review

Exercises

 Add & subtract complex numbers Add & subtract polynomials: find the error Add & subtract polynomials: two variables Add & subtract polynomials: two variables (intro) Add vectors: magnitude & direction to component Analyze scalar multiplication Classify complex numbers Combined vector operations Dependent probability Determinant of a 2x2 matrix Determine inverse matrices Divide polynomials by monomials (with remainders) Divide polynomials with remainders Equation of a parabola from focus & directrix Explicit formulas for arithmetic sequences Explicit formulas for geometric sequences Extend arithmetic sequences Extend geometric sequences Extend geometric sequences: negatives & fractions Features of a circle from its expanded equation Features of a circle from its graph Features of a circle from its standard equation Graph a circle from its expanded equation Graph a circle from its features Graph a circle from its standard equation Independent probability Interpret equations graphically Matrix dimensions Matrix elements Matrix equations: addition & subtraction Matrix equations: scalar multiplication Matrix row operations Multiply complex numbers Multiply complex numbers (basic) Parts of complex numbers Permutations & combinations Powers of the imaginary unit Probabilities of compound events Recursive formulas for arithmetic sequences Recursive formulas for geometric sequences Represent linear systems with matrices Sequences word problems Simple probability Simplify roots of negative numbers Solve equations graphically Transform polygons using matrices Unit vectors Use arithmetic sequence formulas Use geometric sequence formulas Write standard equation of a circle

Videos

 "At least one" probability with coin flipping Adding complex numbers Adding polynomials: two variables (intro) Adding vectors algebraically & graphically Adding vectors in magnitude & direction form (1 of 2) Adding vectors in magnitude & direction form (2 of 2) Birthday probability problem Classifying complex numbers Combined vector operations Common tangent of circle & hyperbola (1 of 5) Common tangent of circle & hyperbola (2 of 5) Common tangent of circle & hyperbola (3 of 5) Common tangent of circle & hyperbola (4 of 5) Common tangent of circle & hyperbola (5 of 5) Compound events example with tree diagram Conic section from expanded equation: circle & parabola Conic section from expanded equation: ellipse Conic section from expanded equation: hyperbola Converting recursive & explicit forms of geometric sequences Dependent probability example Dependent probability: coins Determinant of a 2x2 matrix Determining invertible matrices Die rolling probability Die rolling probability with independent events Divide polynomials by monomials (with remainders) Dividing complex numbers: polar & exponential form Dividing polynomials with remainders Equation of a parabola from focus & directrix Equivalent vectors Exactly three heads in five flips Example: Combinatorics and probability Explicit & recursive formulas for geometric sequences Explicit formulas for arithmetic sequences Features of a circle from its expanded equation Features of a circle from its graph Features of a circle from its standard equation Finding an error in polynomial subtraction Focus & directrix of a parabola from equation Free-throw probability Generalizing with binomial coefficients (bit advanced) Getting exactly two heads (combinatorics) Graphing a circle from its standard equation Graphing circles from features Independent & dependent probability Interpreting equations graphically Interpreting equations graphically (example 2) Intersection of circle & hyperbola Intro to arithmetic sequences Intro to complex numbers Intro to focus & directrix Intro to geometric sequences Intro to geometric sequences (advanced) Intro to matrix inverses Intro to the imaginary numbers Intro to theoretical probability Matrix word problem: prices Matrix word problem: vector combination Multiplying complex numbers Polynomials review Powers of complex numbers Powers of the imaginary unit Probability & combinations (2 of 2) Probability with counting outcomes Probability without equally likely events Recognizing vectors Representing a line tangent to a hyperbola Representing linear systems with matrix equations Sequences intro Sequences word problem: growth pattern Simple probability: non-blue marble Simple probability: yellow marble Simplifying roots of negative numbers Solving equations graphically (1 of 2) Solving equations graphically (2 of 2) Solving linear systems with matrices Subtracting complex numbers Subtracting polynomials: two variables Subtracting polynomials: two variables (intro) The Monty Hall problem Three-pointer vs free-throw probability Transforming polygons using matrices Transforming vectors using matrices Unit vectors intro Vectors word problem: tug of war Visual representation of transformation from matrix Worked example: Scaling unit vectors Worked example: finding unit vector with given direction Writing standard equation of a circle i as the principal root of -1