EXAM PREP · MULTIPLE CHOICE
Pre-Calculus
Mastery Quiz
All core topics · 40 minutes · Real exam difficulty
20Questions
40Minutes
5pts each
8Topics
📚 Key Concepts & Formulas to Memorize
| TOPIC | ESSENTIAL FORMULA / CONCEPT |
|---|---|
| Functions | Composition: (f∘g)(x) = f(g(x)) Inverse: f⁻¹ swaps x and y |
| Quadratics | x = (−b ± √(b²−4ac)) / 2a Discriminant: b²−4ac |
| Polynomials | Remainder Thm: f(c) = remainder when f(x)÷(x−c) Factor Thm: (x−c) is factor iff f(c)=0 |
| Logarithms | logₐ(xy)=logₐx+logₐy logₐ(x/y)=logₐx−logₐy logₐ(xⁿ)=n·logₐx |
| Exponentials | aˣ=aʸ ⟹ x=y (a>0, a≠1) logₐ(aˣ)=x |
| Trigonometry | sin²θ+cos²θ=1 tan θ=sinθ/cosθ sin(2θ)=2sinθcosθ |
| Sequences | Arithmetic: aₙ=a₁+(n−1)d Geometric: aₙ=a₁·rⁿ⁻¹ |
| Complex Nums | i²=−1, i³=−i, i⁴=1 (a+bi)(a−bi)=a²+b² |
✏️ Example Problem (Try Before You Start)
If \(f(x) = 2x + 1\) and \(g(x) = x^2\), what is \((f \circ g)(3)\)?
Answer choices: (A) 19 (B) 49 (C) 10 (D) 25
Solution: First compute \(g(3) = 3^2 = 9\). Then \(f(g(3)) = f(9) = 2(9)+1 = \mathbf{19}\). ✓ Answer: (A)
QUESTION 1 / 20
Functions
A
Excellent!
Score: 0 / 100
Correct: 0 / 20
Time: --:--
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