Practice Test 46 - ACT Math

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

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1. Based on the piecewise function $f(x)=\begin{cases} (x+1)^2-1, & x<-1\\ 2x+5, & -1\le x<2\\ 9-x, & x\ge 2 \end{cases}$ what is the value when $x=-1$?
2. What is the magnitude of $\mathbf{u} = \langle -6, 8 \rangle$?
3. For the function $f(x) = \begin{cases} 4x + 1 & \text{if } x < 0 \\ x - 3 & \text{if } 0 \leq x < 5 \\ 2x^2 & \text{if } x \geq 5 \end{cases}$, what is f(7)?
4. Two fair, standard 6-sided dice are rolled. Given that the sum of the two dice is exactly 8, what is the probability that at least one of the dice shows a 5?
5. Which vector represents the addition of $\mathbf{a} = \langle 5, -3 \rangle$ and $\mathbf{b} = \langle -2, 4 \rangle$?
6. What is the value of $x$ in the proportion $\frac{x}{14}=\frac{5}{7}$?
7. What is $\ln(1)$?
8. In triangle JKL, angle J measures $30^\circ$, angle K measures $60^\circ$. What is the measure of angle L?
9. Which polynomial is equivalent to $(x-3)(x+2)$?
10. What is the surface area of a cylinder with a radius of 7 units and a height of 14 units?
11. What is the determinant of the matrix $\begin{bmatrix}2 & -5\\ 1 & 3\end{bmatrix}?$​
12. Which equation represents a circle with center (-5, 5) and radius 6?
13. A student writes a polynomial to model the height of a plant over time: $g(x) = -4x^2 + 6x - 1$. What is the degree of $g(x)$?
14. A student solves a simple logarithmic equation. If $\log_{5}(x)=3$, what is $x$?
15. In how many ways can you arrange the letters in the word 'CAT'?
16. In right triangle DEF, angle D is the right angle. If side DE = 3 and side DF = 4, what is the length of side EF?
17. A taxi company charges a base fare of $3 plus $2 per mile. Which equation best models the relationship between the total fare $y$ and the number of miles $x$ traveled?
18. A student has 6 different books (A, B, C, D, E, F) and wants to arrange exactly 4 of them in a row on a shelf. Since the left-to-right order matters, how many possible arrangements are there?
19. A student has 6 different songs and wants to create a playlist of 3 songs with no repeats. Since the order of songs in the playlist matters, how many playlists are possible?
20. A circle has circumference $30\pi$ cm. What is the radius of the circle?

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