Practice Test 2 - ACT Math

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. What is $f(0)$ for the piecewise function $f(x) = \begin{cases} 2x - 5 & \text{if } x < -1 \\ x^2 + 1 & \text{if } x \geq -1 \end{cases}$?
2. The function $B = 800 - 5n$ models the number of books in a library, where $B$ is the number of books and $n$ is the number of days books are borrowed. How many books are left after 50 days?
3. A circle has area $16\pi$. What is the radius of the circle?
4. In a $45$-$45$-$90$ right triangle, the hypotenuse has length $10\sqrt{2}$. What is the length of each leg?
5. How many ways can 2 people be chosen from a group of 8 to serve as a captain and co-captain?
6. What is the magnitude of vector $\mathbf{v}$ if $\mathbf{v} = \langle 3, 4 \rangle$?
7. Which expression is equivalent to $2(a + 3) + 4a$? Give your answer in simplest form.
8. A student tracks the temperature (in °C) of a cooling liquid, which changes linearly with time. The line passes through points $(0,18)$ and $(4,6)$. What is the y-intercept of the line through these points?
9. What is the least common multiple (LCM) of 9 and 12?
10. A classroom has a ratio of students wearing sneakers to students not wearing sneakers of $7:3$. If 21 students are wearing sneakers, how many students are not wearing sneakers?
11. Consider the system of equations below: $3x + 2y = 12$ and $y = x - 4$. What is the value of $x + y$ for the solution to this system?
12. A club has 8 members. How many different ways can the club choose a president, vice-president, and secretary?
13. A polynomial step requires multiplying complex numbers and simplifying. What is $(-6+2i)(-1-3i)$? Use FOIL and apply $i^2=-1$ to write $a+bi$.
14. A company uses the polynomial $p(x) = -3x^3 + 2x - 8$ to model a cost. What is the leading coefficient of $p(x)$?
15. A savings plan applies a rule $f(x)$ to the number of weeks $x$ you have saved. For the piecewise function $f(x)=\begin{cases}6-x & \text{if } x<4\\ 2x+1 & \text{if } 4\le x<9\\ x^2-10 & \text{if } x\ge 9\end{cases}$ what is $f(9)$?
16. A cube-shaped box has side length 7 units. Each face is a square with side 7 units. What is the surface area of the cube in square units?​
17. A sphere has a diameter of 10 units. What is the surface area of the sphere?
18. If 6 oranges cost $3, what is the cost of 9 oranges?
19. A bicycle costs $200. If there is a 10% discount, what is the sale price of the bicycle?
20. In an AC circuit calculation, a voltage is modeled by the complex number $3+4i$ and a current is modeled by $2-5i$. What is $(3+4i)+(2-5i)$ expressed in standard form $a+bi$?

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