Pre-Calc Quiz
Questions: 16 · 10 minutes
1. A temperature cycle has a maximum of 18°C at t = 15 hours, a minimum of 10°C, and a period of 24 hours. Which model fits these conditions?
T(t) = 18 + 10cos((π/12)(t - 15))
T(t) = 14 + 4cos((π/12)(t - 15))
T(t) = 10 + 4sin((π/12)(t - 15))
T(t) = 14 + 8cos((π/24)(t - 15))
2. An arithmetic sequence has first term 7 and common difference -3. What is its tenth term?
-30
-23
-20
34
3. What is the domain of f(x) = sqrt(5 - 2x) over the real numbers?
Every real number is in the domain
Values greater than or equal to 5/2
Values strictly less than 5
Values less than or equal to 5/2
4. An account starts with $500 and grows by 6% per year, modeled by A(t) = 500(1.06)^t. Approximately how many years will it take to double?
6.0 years
10.3 years
11.9 years
17.7 years
5. What is the sum of the first five terms of the geometric sequence 3, 6, 12, 24, ...?
48
189
96
93
6. What is the horizontal asymptote of r(x) = (2x² - 3)/(x² + 4)?
y = 2
y = 0
y = -3
The graph has no horizontal asymptote
7. For values where it is defined, which expression is equivalent to (1 - cos²x)/sin x?
cos x
sin x
tan x
csc x
8. What real value of x solves log base 2 of (x - 1) plus log base 2 of (x + 1) equals 3?
x equals 3
x equals 7
x equals negative 3
x equals 2
9. If f(x) = (x - 4)/3, which formula gives the inverse function f⁻¹(x)?
Divide the input plus four by three: (x + 4)/3
Triple the input and subtract four: 3x - 4
Triple the input and add four: 3x + 4
Take the reciprocal of three times the input minus four: 1/(3x - 4)
10. What is the average rate of change of f(x) = x² - 4x from x = 1 to x = 5?
The function decreases by 2 units per unit of x
The function increases by 1 unit per unit of x
The function increases by 4 units per unit of x
The function increases by 2 units per unit of x
11. Compared with y = f(x), how is the graph of y = -2f(x + 3) + 1 transformed?
Shifted left 3, reflected across the x-axis, stretched vertically by 2, and shifted up 1
Shifted left 3, reflected across the x-axis, compressed vertically by 1/2, and shifted up 1
Shifted right 3, reflected across the x-axis, stretched vertically by 2, and shifted down 1
Shifted right 3, reflected across the y-axis, stretched vertically by 2, and shifted up 1
12. What is the vertex of the parabola y = x² - 6x + 5?
Three units left and four units below the origin: (-3, -4)
Three units right and four units above the origin: (3, 4)
Three units right and four units below the origin: (3, -4)
Three units left and five units above the origin: (-3, 5)
13. Let f(x) = x² + 1 and g(x) = 3x - 2. What is f(g(2))?
11
17
25
35
14. What is the exact value of sin(5π/6)?
Negative square root of 3 divided by 2
Negative one-half
Positive square root of 3 divided by 2
Positive one-half
15. A polynomial P satisfies P(2) = 0. Which expression must be a factor of P(x)?
A binomial with zero at negative two: x + 2
A binomial with zero at positive two: x - 2
A linear expression with zero at one-half: 2x - 1
A quadratic expression with no real zeros: x² + 2
16. Which values solve 2cos(x) = 1 on the interval 0 ≤ x < 2π?
π/3 and 5π/3
π/6 and 11π/6
2π/3 and 4π/3
π/2 and 3π/2