Practice Test 21 - ACT Math

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

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1. To determine the effectiveness of a new advertising campaign, a company surveys every 10th customer who makes a purchase online. Which sampling method is being used?
2. A researcher surveyed 50 families and summarized her findings in the table. Of the families surveyed, what is the mean number of vehicles per family?
3. If $f(x) = \dfrac{3x + 2}{x - 1}$, what is the value of $f^{-1}(5)$?
4. A complex impedance is given by $-6+7i$. What is the complex conjugate of $-6+7i$ (flip the sign of the imaginary part only)?
5. A map uses a scale of $1$ inch to $4$ miles. If two towns are $7.5$ inches apart on the map, what is the actual distance between the towns in miles?
6. A deck of cards is shuffled and one card is drawn. What is the probability of drawing a King or a heart?
7. A student has 7 different pens and wants to place exactly 5 of them into a pencil case in a specific left-to-right order. How many different ordered selections are possible?
8. How many sides does a regular polygon have if each exterior angle measures $45^\circ$?
9. Which equation represents a circle with center (-4, 5) and radius 6?
10. Solve: $6 - x < 2$
11. If two dice are rolled, what is the probability of getting a sum of 7?
12. A gym charges a one-time sign-up fee plus a monthly membership cost. In the equation $y = 25x + 40$, $x$ is the number of months and $y$ is the total cost (in dollars). What is the meaning of the $y$-intercept in this context?
13. A paint mixture uses a ratio of blue to yellow of $3:2$. If the artist uses $18$ cups of blue paint, how many cups of yellow paint are needed to keep the same ratio?
14. A price increases from $40 to $50. What is the percent increase?
15. Convert $\frac{2}{3}$ to a percent.
16. What is $3\mathbf{u} - \mathbf{v}$ if $\mathbf{u} = \langle 2, 4 \rangle$ and $\mathbf{v} = \langle 1, -1 \rangle$?
17. A function is defined by $f(x)=3x-7$. What is $f(5)$? Use substitution: $f(x)=3x-7$, so $f(5)=3(5)-7$.
18. A bag contains 6 red and 4 yellow balls. What is the probability of drawing two red balls in a row without replacement?
19. Factor: $x^2 - 6x + 9$
20. If $\triangle XYZ \thicksim \triangle ABC$ with $XY = 5$ and $AB = 15$, what is the ratio of $YZ$ to $BC$?

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