2

Exp & Log Functions

100

Find the inverse of f(x) = 2^x

f⁻¹(x) = log₂(x)

200

What is the asymptote of f(x) = log(x - 3)?

x = 3

300

Evaluate: log₁₀(1000)

3

400

Solve: 2^x = 16

x = 4

500

Rewrite: log₅(x) = 3 in exponential form    

x = 125

Exp & Log Applications

100

Write the equation for 5% growth from an initial value of 100

y = 100(1.05)^t

200

What is the initial value in y = 300(0.8)^t?

300

300

Compare growth: y = 100(1.02)^t vs y = 80(1.05)^t — which grows faster?

y = 80(1.05)^t grows faster

400

Use Newton’s Law: T(t) = 70 + (100 - 70)e^(-0.05t), find T(10)

≈ 88.2

500

Use future value formula: FV = 1000(1 + 0.05/4)^(4×3)

≈ $1159.27

Sequences & Series

100

Find the 5th term of the sequence: aₙ = 3n + 1

a₅ = 16

200

Recursive rule: a₁ = 2, aₙ = aₙ₋₁ + 4, find a₄

a₄ = 14

300

Write explicit formula for geometric sequence: 2, 6, 18, ...

aₙ = 2(3)ⁿ⁻¹

400

Find sum: 5 + 10 + 20 + 40 (geometric)

75

500

Convert to summation: 2 + 4 + 6 + ... + 20

∑ from n = 1 to 10 of 2n

Trig Fundamentals

100

Convert 180° to radians

π radians

200

What is the reference angle for 150°?

30°

300

Evaluate: sin(45°) exactly

√2 / 2

400

What are the 6 trig functions of a 30° angle?

sin = 1/2, cos = √3/2, tan = 1/√3, csc = 2, sec = 2/√3, cot = √3

500

Use the Pythagorean Identity: If sin(θ) = 3/5 and θ is in Quadrant II, find cos(θ)

cos(θ) = -4/5

Trig Graphs & Applications

100

What is the amplitude of y = 3sin(x)?

3

200

What is the period of y = sin(2x)?

π

300

What is the midline of y = -2cos(x) + 4?

y = 4

400

Does y = -sin(x) reflect over the x-axis or y-axis?

x-axis

500

Write an equation for a cosine graph with amplitude 2, period 2π, midline 1

y = 2cos(x) + 1