Practice Test 14 - ACT Math

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

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1. A taxi charges a fixed pickup fee plus a constant rate per mile. The cost is modeled by a linear function with slope $m=4$ and $y$-intercept $b=7$. Which equation has slope $4$ and $y$-intercept $7$?
2. A teacher has 7 different problems and will assign 3 of them as a quiz in a specific order (Problem 1, then 2, then 3). Since order matters, how many different quizzes are possible?
3. A scuba diver descends at a constant rate. The depth is modeled by $y = 4x$, where $x$ is time in minutes and $y$ is depth in meters. According to the model, how deep is the diver after $7.5$ minutes?
4. The area of a rectangle is 84 square inches. If the length of the rectangle is 12 inches, what is the perimeter, in inches, of the rectangle?
5. At point $O$, two lines intersect. Angle $x$ is adjacent to an angle measuring $140^\circ$ (they form a linear pair). \ 140° -------O------- / x What is the measure of angle $x$?
6. What is $8^0$?
7. What is the absolute value of $-7i$?
8. A book has 250 pages. If you read 50 pages a day, how many days will it take to read the book?
9. On a number line, a point is at $x=-\dfrac{7}{3}$. What is the absolute value of $x$?
10. A data set is $\{11, 14, 15, 15, 16, 18\}$. What is the range of the data?
11. What is $2\mathbf{v}+\mathbf{w}$ if $\mathbf{v}=\langle 1, -3\rangle$ and $\mathbf{w}=\langle -4, 5\rangle$?
12. What is $\tan(90^\circ)$?
13. A polynomial function is $b(x) = -5x + 12$. What is the leading coefficient of $b(x)$?
14. In an AC circuit calculation, the impedance is modeled by complex numbers. What is $(3+4i)+(5-2i)$ in standard form $a+bi$?
15. A right circular cone has radius 3 units and height 12 units. The height is perpendicular to the circular base. What is the volume of the cone in cubic units?
16. A function is defined by $f(x)=x^2+2x-5$. What is $f(-1)$?
17. A student expands a polynomial used in a design formula. Which polynomial is equivalent to $3x(x-2)+4$?
18. Two triangles are shown. In $\triangle WXY$, $WX=8$ and $WY=12$, and the included angle $\angle W$ is marked as $50^\circ$. In $\triangle ZUV$, $ZU=12$ and $ZV=18$, and the included angle $\angle Z$ is also marked as $50^\circ$. Are the triangles similar? If so, why?
19. The population of a city is modeled by the equation $P = 100000 + 1200t$, where $P$ is the population and $t$ is the number of years since 2010. What is the population in 2020?
20. A game score is modeled by $h(x) = x^3 - 4x$. What is $h(-2)$?

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