Practice Test 18 - 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 the area of a circle with diameter 14?
2. In the diagram, two lines intersect, forming angles $A$, $B$, $C$, and $D$. Angle $A$ measures $100^\circ$. What is the measure of angle $C$, which is a vertical angle to $A$?
3. Which value of $x$ satisfies the equation $3x + 4 = x + 18$?
4. A complex number is given by $-9 - 12i$. To find its distance from the origin, compute its absolute value. What is the absolute value of $(-9 - 12i)$? (Simplify the radical.)
5. In the right triangle shown, the right angle is at $B$. The side lengths are $AB=3$, $BC=4$, and $AC=5$. Angle $\theta$ is at $A$ (between $AB$ and $AC$). What is $\sin(\theta)$?
6. If $\,6(x + 2) - 3 = 21\,$, what is $x$?
7. A ball is thrown upward from a height of 5 meters. Its height after $x$ seconds is modeled by the quadratic equation $y = -4x^2 + 12x + 5$, where $y$ is height in meters. According to the model, what is the height of the ball after $2$ seconds?
8. How many permutations of 5 letters taken 3 at a time?
9. A shipment is packed into identical boxes. If the total number of items is given by $6x = 54$, what is the value of $x$?
10. Which formula gives the surface area of a right circular cylinder with radius $r$ and height $h$ (including both circular bases)?
11. To remove imaginary terms from a denominator later, you plan to multiply by a conjugate. What is the complex conjugate of $8 - 11i$?
12. Two triangles are shown with side lengths. Triangle $\triangle GHI$ has $GH=7$, $HI=9$, and $GI=12$. Triangle $\triangle JKL$ has $JK=14$, $KL=18$, and $JL=20$. Are the triangles similar? If so, why?
13. What is the median of the data set [9, 5, 12, 8, 7]?
14. A coffee shop sells muffins for $3 each. Jordan buys 4 muffins and pays with a $20 bill. How much change does Jordan receive?
15. Simplify: $5a^2-3a+2a^2+7a$.
16. The times (in minutes) it took a runner to complete a short course over 8 trials were: 9, 12, 11, 10, 13, 10, 14, 8. What is the median of $\{9, 12, 11, 10, 13, 10, 14, 8\}$?
17. In the standard $(x, y)$ coordinate plane, what is the slope of the line given by the equation $5x + 2y = 10$?
18. In a circle of radius $4$, arc $\overset{\frown}{EF}$ is subtended by a central angle of $135^\circ$. What is the length of arc $\overset{\frown}{EF}$?
19. What is $\tan(\frac{\pi}{4})$?
20. What is the measure of each interior angle in a regular decagon (10-gon)?

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