Practice Test 17 - ACT Math

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

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1. What angle $\theta$ (in degrees) satisfies $\sin(\theta)=\frac{\sqrt{2}}{2}$, where $0^\circ\le \theta \le 90^\circ$?​
2. Which of the following is the product $AB$ for matrices $A = \begin{pmatrix} 0 & 2 \\ 1 & 3 \end{pmatrix}$ and $B = \begin{pmatrix} 1 & 0 \\ 2 & 1 \end{pmatrix}$?
3. What is the volume-weighted average stock price over this 6-month period, rounded to the nearest dollar?
4. A laptop was originally priced at $1,200 and is now $900. What percent discount was applied?
5. A recipe is adjusted by scaling ingredients. If $3(x - 2) = 21$, solve for $x$.
6. A bottle holds 750 ml of juice. If you pour out 150 ml, how much juice remains in the bottle?
7. A rectangle has a width of 15 cm and a diagonal of 17 cm. What is the area, in square centimeters, of the rectangle?
8. What is $-3$ times $v$ if $v=\langle -4,2\rangle$?
9. At a school store, 2 notebooks and 3 pens cost $12, and 1 notebook and 2 pens cost $7. If $x$ is the cost of a notebook and $y$ is the cost of a pen, what is $(x,y)$?
10. What is the y-intercept of the line $y = 6x + 2$?
11. What is the magnitude of $\mathbf{x} = \langle 9, 12 \rangle$?
12. What is $f(0)$ for the function $f(x) = -5x + 4$?
13. Given the functions $f(x) = 2x^2 + 1$ and $g(x) = x - 3$, what is the value of $f(g(4))$?
14. For the polynomial $g(x)=-2x^3+x-1$, which statement correctly describes the end behavior of $g(x)$?
15. A pizza shop offers 6 different toppings. A customer chooses exactly 2 different toppings, and the order of toppings does not matter. How many ways can the customer choose the toppings?
16. A store offers a bundle deal. If the bundle cost is described by $2(x + 3) = 18$, what is the value of $x$?
17. Which of the following lists the numbers $3.14$, $\pi$, and $\frac{22}{7}$ in order from least to greatest? (Note: $\pi \approx 3.14159...$)
18. A drone's horizontal movement is represented by the vector $\langle 6,\,8\rangle$. What is the magnitude of the vector $\langle 6,\,8\rangle$? Give your answer in simplest form.
19. Which congruence criterion applies to $\triangle GHI$ and $\triangle JKL$ if $GH = JK$, $\text{angle } G = \text{angle } J$, and $HI = KL$?
20. A circle has diameter $12$. What is the area of the circle?

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