Practice Test 15 - ACT Math

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

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1. A sphere has radius 5 units. What is the volume of the sphere?
2. Two triangles are shown with side lengths. $\triangle ABC$ has sides $AB=4$, $BC=7$, $AC=9$. $\triangle DEF$ has sides $DE=8$, $EF=14$, $DF=18$. Which statement is true?
3. A function is defined by $f(x)=2x-3$. What is $f(\!-x)$? Show the substitution: $f(x)=2x-3$, so $f(-x)=2(-x)-3$.
4. A student has taken 4 tests and has an average score of 82. What score must the student get on the 5th test to raise the average to exactly 84?
5. A storage tank is being filled with water at a constant rate of 10 gallons per minute. If the tank starts at 100 gallons, what is the equation for the amount of water $w$ in the tank after $t$ minutes?
6. Lines $m$ and $n$ are parallel ($\Rightarrow$). A transversal $t$ intersects them. At line $n$, an interior angle is labeled $125^\circ$. The angle labeled $x$ is the same-side interior angle at line $m$. m \Rightarrow ─────────────── x / / / t / n \Rightarrow ─────────────── $125^\circ$If lines $m$ and $n$ are parallel, what is the measure of angle $x$?
7. Which interval contains $x = 3$ in the piecewise function $f(x) = \begin{cases} x - 2 & \text{if } x < 3 \\ 2x + 5 & \text{if } x \geq 3 \end{cases}$?
8. What is the mean of the data set [11, 14, 17, 20, 23]?
9. To test a new teaching technique, teachers use it in some classes while others continue with traditional methods. Which study design would avoid bias?
10. Solve for $x$ if $\ln(x) = 1$.
11. A fair die is rolled once. If the probability of rolling a number less than 5 is $p$, what is $P(\text{not less than 5})$ in terms of $p$?
12. Simplify: $8 - (2x - 3)$
13. A polynomial used in a calculation is $x^2-6x+9$. Factor: $x^2-6x+9$.
14. What is the surface area of a sphere with radius 8 units?
15. If a product originally costs $80 and is now on sale for $60, what is the percent decrease in price?
16. In a right triangle, the legs are $6$ (opposite $\theta$) and $8$ (adjacent $\theta$). What is $\sin(\theta)$?​
17. The equation of a circle in the standard $(x, y)$ coordinate plane is $x^2 + y^2 - 10x + 6y + 18 = 0$. What is the radius of the circle?
18. A polynomial describing the area of a design is $q(x) = 5 - 2x + x^2$. What is the degree of $q(x)$?
19. A taxi fare is modeled by the linear function $f(x)=4x+7$, where $x$ is miles traveled and $f(x)$ is total cost in dollars. What is $f(0)$?
20. Which best describes the shape of the distribution of the data [10, 20, 20, 30, 40, 40, 40, 50, 60]?

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