Practice Test 12 - Pre Algebra

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

Maria's test scores decreased by $12\%$ from her first test to her second test, then increased by $25\%$ from her second test to her third test. If her third test score was $77$ , what was her first test score?
A pizza is cut into equal slices. Alex eats $\frac{1}{4}$ of the pizza, and then Ben eats $\frac{2}{3}$ of what Alex ate. What fraction of the entire pizza did Ben eat?
The number of subscribers $N$ (in thousands) to a streaming service is modeled by $N = 25t + 100$ , where $t$ is months since launch. The model uses data from the first 12 months. The company projects subscriber count for month 48. Which factor most undermines this projection's reliability?
Maria claims that $x = 5$ is the solution to the equation $2x + 3 = 13$ . She shows her work: "First, I subtract 3 from both sides to get $2x = 10$ . Then I divide both sides by 2 to get $x = 5$ . I can check this by substituting: $2(5) + 3 = 10 + 3 = 13$ , which is correct." Which statement best explains why Maria's reasoning is valid?
In the expression $\frac{1}{2}x^3 - 4x^2 + x - \frac{3}{4}$ , which term has the smallest coefficient when all coefficients are written as decimals?
A survey found that 0.064 of students prefer math, while 6.8% prefer science. If 250 students were surveyed, how many more students prefer science than math?
Maria wants to determine if there's a relationship between study time and test scores for her class of 25 students. She has collected data showing each student's hours studied and their corresponding test score. Which tool would be MOST appropriate for Maria to identify patterns in this data, and why?
Which scenario correctly demonstrates a valid interpretation of this solution set in a cooking context?
A concrete foundation is poured in the shape of a rectangular prism. The foundation is 20 feet long, 12 feet wide, and 1.5 feet deep. If concrete costs $8.50 per cubic foot, what is the total cost of the concrete needed?
The product of three rational numbers is $-\frac{12}{35}$ . Two of the numbers are $\frac{2}{5}$ and $-\frac{3}{7}$ . What is the third number?
A function has the rule $g(x) = 3x - 5$ . If $g(a) = g(2a - 4)$ , what is the value of $a$ ?
A cell phone plan charges $25 per month plus $0.15 for each text message over $200$ . If $t$ represents the total number of text messages sent in a month, which expression represents the monthly cost when $t > 200$ ?
Lisa solved $2(x + 4) - 3 = 15$ and got $x = 5$ . She wants to check her answer without substituting back into the original equation. Which method would be most effective?
A basketball player has made 15 free throws out of 25 attempts this season. Her coach claims that as she takes more free throws, her success rate will approach her "true" shooting ability. Which statement best describes the probability concept the coach is referring to?
The membership of a club increased from 180 to 225 members. Later, it decreased back to 180 members. What was the percent decrease in the second change?
Two box plots compare marathon completion times (in hours) for runners in different age groups. The younger group has Q1 = 3.2, median = 3.8, Q3 = 4.5. The older group has Q1 = 3.6, median = 4.2, Q3 = 4.8. If both groups have the same number of runners, which comparison of their performances is most justified?
Consider the expression $6(a + 2b) - 4(a + 2b) + 3$ . A student rewrites this as $(6 - 4)(a + 2b) + 3 = 2(a + 2b) + 3$ . Which property primarily justifies this transformation?
The graph of a linear function passes through points $(-2, 7)$ and $(3, -8)$ . What is the rate of change of this function?
At a printing company, Machine X prints 240 pages in 8 minutes, while Machine Y prints 180 pages in 5 minutes. If both machines run simultaneously for 20 minutes, how many more pages will the faster machine print compared to the slower machine?
A teacher designs a simulation to model the probability that in a group of 4 students, at least 3 will pass an exam where the individual pass rate is 70%. She plans to use a deck of cards where hearts and diamonds represent 'pass' and clubs and spades represent 'fail'. After explaining her method, a student points out a problem. What is the most likely issue the student identified?

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