12th Grade Math Quiz
Questions: 16 · 10 minutes
1. Two cards are drawn from a standard 52-card deck without replacement. Given that the first card was an ace, what is the probability that the second card is also an ace?
1/13
3/52
1/17
1/4
2. Convert 150° to radians.
3π/4
5π/3
5π/6
6π/5
3. Let f(x) = 3x - 1 and g(x) = x². What is f(g(2))?
25
8
11
5
4. A teacher adds 5 points to every score in a data set. How do the mean and standard deviation change?
Both the mean and standard deviation increase by 5.
The mean stays the same, while the standard deviation increases by 5.
The mean increases by 5, while the standard deviation is multiplied by 5.
The mean increases by 5, while the standard deviation stays the same.
5. An angle θ lies in Quadrant III and cos(θ) = -√2/2. What is θ in the interval 0 ≤ θ < 2π?
π/4
5π/4
3π/4
7π/4
6. A particle's position is s(t) = t² + 3t meters. What is its instantaneous velocity at t = 4 seconds?
19 m/s
7 m/s
11 m/s
28 m/s
7. Solve the equation 2^(x + 1) = 16.
x = 15
x = 4
x = 7
x = 3
8. A game pays a net gain of $8 with probability 0.25 and a net loss of $2 with probability 0.75. What is the expected net result per play?
A loss of $0.50
A gain of $2.00
A loss of $1.50
A gain of $0.50
9. Solve log₁₀(x) + log₁₀(x - 9) = 1 over the real numbers.
x = 10
x = -1
x = 9
x = 19
10. A geometric sequence has first term 5 and common ratio 2. What is its sixth term?
50
160
320
80
11. A rectangle has a perimeter of 40 units. What is the greatest possible area of the rectangle?
100 square units
160 square units
400 square units
80 square units
12. What is the remainder when p(x) = x³ - 4x + 7 is divided by x - 2?
A remainder of 5
A remainder of 7
A remainder of 11
A remainder of 15
13. At a school event, 120 tickets were sold. Adult tickets cost $12 and student tickets cost $8, producing $1,200 in revenue. How many adult tickets were sold?
60
40
75
90
14. Water enters a tank at a net rate of r(t) = 6t - 2 liters per minute. What is the net change in the amount of water from t = 0 to t = 3 minutes?
21 liters
24 liters
16 liters
48 liters
15. What is the derivative of h(x) = x³ - 4x² + 2?
3x² - 4x
3x² - 8x + 2
x² - 8x
3x² - 8x
16. The function C(F) = (5/9)(F - 32) converts Fahrenheit temperatures to Celsius. Which equation correctly converts a Celsius temperature c to Fahrenheit?
Multiply c by 5/9, then add 32: F = (5/9)c + 32
Multiply c by 9/5, then add 32: F = (9/5)c + 32
Subtract 32 from c, then multiply by 9/5: F = (9/5)(c - 32)
Add 32 to c, then multiply by 5/9: F = (5/9)(c + 32)