Precalc

πŸ“ Foundation Check

Rate your confidence on the building blocks for each upcoming exam. Focus your review time where it matters most.

Exams 1 & 2 covered foundations that Exam 3 and 4 build on. Rate your confidence on each skill below β€” the app will point you to the right review sections so you can fill gaps before they slow you down.

Foundations for Exam 3

Trigonometry Β· April 23

Functions, Domain & Range

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Trig introduces 6 new functions. You need to be solid on what a function is, domain restrictions, and how to read function notation.

Needed for: 5-2 Unit Circle, 6-1 Graphing Sine/Cosine, 6-3 Inverse Trig
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Inverse Functions

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Section 6.3 is entirely about inverse trig functions (arcsin, arccos, arctan). You need to understand how inverses work β€” reflecting over y = x, domain/range swaps, and the horizontal line test.

Needed for: 6-3 Inverse Trig Functions
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Graph Transformations

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Trig graphs (6.1, 6.2) use shifts, stretches, and reflections β€” the same transformations from linear/quadratic graphing. Amplitude = vertical stretch, phase shift = horizontal shift.

Needed for: 6-1 Graphs of Sine/Cosine, 6-2 Graphs of Other Trig
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Solving Quadratic Equations

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Many trig equations reduce to quadratics. For example, 2sinΒ²x βˆ’ sinx βˆ’ 1 = 0 is really 2uΒ² βˆ’ u βˆ’ 1 = 0 in disguise. You need factoring and the quadratic formula.

Needed for: 7-5 Solving Trig Equations
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Fraction Arithmetic

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Radian measures like 5Ο€/6 and trig values like √3/2 require confident fraction work β€” common denominators, simplifying, multiplying. This comes up in almost every trig problem.

Needed for: 5-1 Radian Measure, 7-2 Sum/Difference Identities, 7-3 Double-Angle
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Foundations for Exam 4

Conics, Sequences & Series Β· May 14

Completing the Square

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Circles, ellipses, and hyperbolas all require converting equations like xΒ² + 6x + yΒ² βˆ’ 4y = 12 into standard form. Completing the square is THE key technique.

Needed for: Circles, 10-1 Ellipse, 10-2 Hyperbola
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Polynomial Operations & Factoring

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The Binomial Theorem (11.6) expands expressions like (x + 2)⁡. You need comfort with polynomial multiplication, factoring, and exponent rules.

Needed for: 11-6 Binomial Theorem
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Exponent Rules

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Geometric sequences follow the pattern aβ‚™ = a₁ Β· rⁿ⁻¹ β€” the same exponential growth/decay from Chapter 4. You need exponent laws to simplify terms.

Needed for: 11-3 Geometric Sequences, 11-4 Series
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Systems of Equations

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Some conic and sequence problems require solving systems (two equations, two unknowns). Make sure you can do substitution and elimination.

Needed for: 10-1 Ellipse problems, 11-2 Arithmetic Sequences
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Rational Expressions

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Series problems often involve fractions with variables. Simplifying partial sums and working with rational expressions is essential for summation notation.

Needed for: 9-3 Summation Notation, 11-4 Series
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