Practice Test 10 - ACT Math

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

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1. A delivery van uses 12 gallons of fuel to travel 300 miles. At the same rate, how many miles can it travel on 5 gallons?
2. A point in the plane is represented by the complex number $6 - 8i$. What is the absolute value of $6 - 8i$? Use $|a+bi|=\sqrt{a^2+b^2}$ and simplify the radical.
3. What angle has $\cos(\theta) = \frac{1}{2}$?
4. Given $f(x)=x^2+2x$, what is the value of $f(2a)$? Show the substitution: $f(x)=x^2+2x$, so $f(2a)=(2a)^2+2(2a)$.
5. A music subscription discount is modeled by $5x - 10 = 2x + 8$. Which value of $x$ satisfies the equation?
6. Which of the following represents $f(x+1)$ if $f(x) = 4x^2 + x - 1$?
7. If $f(x)=\dfrac{x-6}{2}$, what is the value of $f(0)$? Substitute $x=0$: $f(0)=\dfrac{0-6}{2}$.
8. If a juice box contains 250 ml, how much juice is there in 4 juice boxes?
9. What is $f(-3)$ if $f(x) = 5x^2 - 4x + 1$?
10. If $3x - 7 = 4x + 2$, then $x = $?
11. For triangles $\triangle ABC$ and $\triangle DEF$, $\triangle ABC$ has angles $A = 70^\text{o}$, $B = 50^\text{o}$, and $\triangle DEF$ has angles $D = 70^\text{o}$, $E = 50^\text{o}$. Which criterion confirms their similarity?
12. Which expression is equivalent to $(1 + 6i)(4 - i)$?
13. If the ratio of red to blue marbles is 4:7 and there are 28 blue marbles, how many red marbles are there?
14. A snack pack is made by choosing 1 drink from 3 options and 2 different snacks from 5 options. The two snacks are chosen as a pair (order does not matter), but the drink choice is separate. What is the number of possible snack packs?
15. A group of 6 friends is trying to form a subcommittee of 3 members. How many ways can they choose the subcommittee members?
16. What is $15\%$ of 250?
17. A complex number is given by $12-5i$. What is the complex conjugate of $12-5i$ (flip the sign of the imaginary part only)?
18. Given $f(x) = x^2 - 4x$ and $g(x) = 2x + 1$, for what real value(s) of $x$ does $f(g(x)) = -3$?
19. What is $\log_{10}(0.01)$?
20. The table shows the test scores for two classes, Class A and Class B. Both classes have the same mean score. Which of the following statements about the standard deviations of the two classes is true?

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