Grade: Grade 11 Subject: Mathematics Unit: Functions & Modeling SAT: AdvancedMath ACT: Math

Unit Quiz: Functions & Modeling

Quiz Instructions

This comprehensive assessment covers all topics from the Functions & Modeling unit. Complete all 12 questions without a calculator for the first section, then use a calculator for the remaining problems. Show all work for full credit.

  • Time: 45 minutes recommended
  • Questions 1-6: No calculator
  • Questions 7-12: Calculator allowed
  • Passing Score: 80% (10/12 correct)

Section A: No Calculator

1. Simplify: log₃(27) + log₃(9)

2. If f(x) = 2^x, find the value of f(3) - f(1).

3. Solve for x: 5^(2x-1) = 25

4. Write the exponential equation 8 = 2³ in logarithmic form.

5. If a population doubles every 4 years, by what factor will it grow in 12 years?

6. Simplify: e^(ln(5))

Section B: Calculator Allowed

7. A bacteria culture starts with 500 cells and grows at a rate of 12% per hour. Write a function P(t) for the population after t hours, then find P(5). Round to the nearest whole number.

8. The half-life of a radioactive substance is 8 days. If you start with 200 grams, how much remains after 24 days?

9. Solve for t: 1000e^(0.05t) = 2500. Round to two decimal places.

10. An investment of $5,000 earns 4.5% interest compounded continuously. How long will it take to double? Use A = Pe^(rt).

11. The decibel level of a sound is given by D = 10log(I/10^(-12)), where I is intensity in watts/m². Find the decibel level of a sound with intensity I = 10^(-5) watts/m².

12. A car depreciates according to V(t) = 28000(0.82)^t, where t is years since purchase. In what year will the car be worth less than $10,000?

Answer Key

Click to reveal answers
  1. 5 — log₃(27) = 3 and log₃(9) = 2, so 3 + 2 = 5
  2. 6 — f(3) = 8 and f(1) = 2, so 8 - 2 = 6
  3. x = 3/2 or 1.5 — 5^(2x-1) = 5², so 2x-1 = 2, x = 1.5
  4. logâ‚‚(8) = 3
  5. 8 — It doubles 3 times (12÷4 = 3), so 2³ = 8
  6. 5 — e and ln are inverse functions
  7. P(t) = 500(1.12)^t; P(5) ≈ 881
  8. 25 grams — 24÷8 = 3 half-lives, so 200 × (1/2)³ = 25
  9. t ≈ 18.33 years — ln(2.5)/0.05 ≈ 18.33
  10. ≈ 15.4 years — t = ln(2)/0.045 ≈ 15.4
  11. 70 decibels — D = 10log(10^(-5)/10^(-12)) = 10log(10^7) = 70
  12. Year 6 — Solve 10000 = 28000(0.82)^t; t ≈ 5.2, so year 6

Next Steps

  • Review any questions you missed
  • If you scored below 80%, revisit the relevant lessons
  • Move on to the next unit when ready