Practice Test 5 - Pre Algebra

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

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1. A function rule states: "Subtract 3 from the input, then multiply the result by itself." If the output of this function is 16, what are the possible input values?
2. A car rental company charges a flat fee plus a rate per mile. After driving 150 miles, the total cost is $85. After driving 300 miles, the total cost is $130. Which equation represents the proportional part of this relationship, where $y$ is the variable cost and $x$ is the number of miles?
3. A recipe calls for $2.75$ cups of flour, but you want to make $130\%$ of the recipe. You only have a $\frac{1}{3}$ cup measuring tool. Approximately how many scoops will you need?
4. A square has the same area as a right triangle with legs measuring 12 cm and 16 cm. What is the side length of the square?
5. A rectangle has area 84 square units and width $w$. The length is 3 units more than twice the width. After setting up the equation $w(2w + 3) = 84$, a student realizes this creates a quadratic equation. To avoid quadratic equations, what one-step equation could be used if the width were known to be 6 units?
6. A investment account loses $15.3\%$ of its value in the first year, then gains $18.7\%$ in the second year. If the account started with $8,500, approximately what is its value after two years?
7. A bag contains red and blue marbles. After drawing 80 marbles with replacement, red appeared 32 times. Based on this information, which statement about the probability of drawing red is most reasonable?
8. A car travels 240 miles in 4 hours. At this same rate, how long will it take to travel 420 miles?
9. The mean absolute deviation (MAD) of a data set is 6.4, and the mean is 52. If every value in the data set is multiplied by 1.5, what will be the new mean absolute deviation?
10. The area of a trapezoid is given by $A = \frac{1}{2}h(b_1 + b_2)$, where $h$ is the height and $b_1$ and $b_2$ are the parallel bases. A trapezoid has an area of 84 square centimeters, a height of 8 centimeters, and one base that is 3 centimeters longer than the other base. What is the length of the shorter base?
11. A swimming pool is being filled at a rate of 12.5 gallons per minute. After 18.4 minutes, how many gallons have been added to the pool?
12. The surface area of one face of a rectangular prism is $(3z + 2)(z + 4)$. Using the distributive property, which expression correctly shows the intermediate step before combining like terms?
13. A rectangular garden has a length that is 8 feet more than twice its width. If the perimeter must be at least 76 feet to accommodate a fence, which inequality represents the constraint on the width $w$ in feet?
14. Two students are debating probability values. Student X says "A probability of 0.8 means the event will definitely happen." Student Y says "A probability of 0.8 means the event happens 80% of the time in the long run." Student Z says "A probability of 0.8 means the event is impossible." Which student demonstrates the best understanding of probability?
15. A dot pattern is arranged in a triangular formation. Level 1 has 1 dot, Level 2 has 3 dots, Level 3 has 6 dots, Level 4 has 10 dots. Jenny claims that Level $n$ has $\frac{n(n+1)}{2}$ dots. Which statement best describes the reasoning behind this formula?
16. A relation is defined by the set of ordered pairs $\{(a,3), (2,b), (c,3), (2,5)\}$ where $a$, $b$, and $c$ are real numbers. For this relation to be a function, which condition must be satisfied?
17. Consider the system of inequalities: $x + 2y \leq 6$ and $y > x - 1$. A student identifies the point $(2, 2)$ as being on the boundary of the solution region. Which analysis correctly determines the status of this point?
18. Maria's monthly salary increased from $3,200 to $3,680. If she receives another raise that is 75% as large as her first raise, what will her new monthly salary be?
19. The population density of a city is $2.4 \times 10^3$ people per square kilometer. If the city covers an area of $1.8 \times 10^2$ square kilometers, and the average household size is $3.2 \times 10^0$ people, approximately how many households are in the city?
20. A circular fountain has a circumference of $16\pi$ meters. Small lights are placed every 2 meters around the edge. If the fountain is surrounded by a circular sidewalk that extends 4 meters outward from the fountain's edge, what is the area of the sidewalk?

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