Practice Test 9 - Pre Algebra

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

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1. The decimal $0.4059$ is written in expanded form as $4 \times 10^{-1} + 0 \times 10^{-2} + 5 \times 10^{-3} + 9 \times 10^{-4}$. What is the value of the digit in the ten-thousandths place when $0.4059$ is multiplied by $10^2$?
2. A car's value depreciates linearly from $18000 when new to $12000 after 4 years. Which statement correctly interprets the slope and explains what it means for the car's value after 7 years?
3. The expression $3(x + 2y) + 4(2x - y)$ can be rewritten as $(3 + 8)x + (6 - 4)y$. Which property justifies regrouping the terms in this way?
4. Two students solve $\begin{cases} 3x + y = 7 \\ y = 2x - 3 \end{cases}$ by substitution. Student A gets $x = 2, y = 1$ while Student B gets $x = 1, y = 2$. Without solving the system yourself, how can you quickly determine which student made an error?
5. The absolute value of a number is 15. If you subtract 8 from the opposite of this number, what are the possible results?
6. A recipe calls for ingredients in the following amounts: 2 cups flour, 1 cup sugar, and $\frac{1}{2}$ cup butter. Maria wants to determine if the relationship between the number of batches made and the total amount of flour needed is proportional. She also considers whether the relationship between cups of flour and cups of sugar within the recipe is proportional. Which analysis is correct?
7. A line fitted to data relating altitude (feet above sea level) to air pressure (psi) has the equation $y = -0.0005x + 14.7$. According to this model, at what altitude would the air pressure be 13.2 psi?
8. In a factory, $\frac{5}{7}$ represents the division of 5 completed products among 7 work stations for quality testing. If the factory later produces 15 products to divide among 21 work stations using the same process, which statement best explains the relationship between $\frac{5}{7}$ and $\frac{15}{21}$?
9. A water tank initially contains 150 gallons and drains at a constant rate. After 4 hours, it contains 110 gallons. After 9 hours, it contains 60 gallons. Which equation models the amount of water $y$ (in gallons) remaining after $x$ hours?
10. A student calculated that $\frac{3}{8} + \frac{5}{12} = \frac{19}{24}$. To verify this answer using decimal approximations, which comparison would be most reliable?
11. A bakery needs to package at least $180$ cupcakes for a large order. They have boxes that hold $15$ cupcakes each and have already filled $8$ boxes. The inequality $15(8 + b) \geq 180$ represents this situation, where $b$ is additional boxes needed. What is the minimum value of $b$?
12. A water tank contains 500 gallons and drains at a rate of 12 gallons per minute. At the same time, water is being added at a rate of 8 gallons per minute. How many gallons will be in the tank after 45 minutes?
13. A delivery truck's weight changes throughout the day. It starts with $2,450$ pounds of cargo. At the first stop, it delivers $375.5$ pounds and picks up $128.25$ pounds. At the second stop, it delivers $892.75$ pounds and picks up $445.5$ pounds. At the third stop, it delivers $520.25$ pounds. If the empty truck weighs $4,200$ pounds, what is the truck's total weight after all stops?
14. A student simplifies $3(x + 4) + 2(x + 4) - (x + 4)$ by first writing it as $3A + 2A - A$ where $A = x + 4$, then getting $4A$, and finally substituting back to get $4(x + 4)$. What is the primary benefit of this approach?
15. A sports analyst compared the scoring patterns of two basketball players over a season. Player X averaged 18 points per game with games ranging from 8 to 28 points. Player Y averaged 16 points per game with games ranging from 12 to 20 points. For a coach planning game strategy, what is the most important conclusion?
16. Two hikers start at base camp (elevation 0). Hiker 1 goes to an elevation where the absolute value is 450 feet. Hiker 2 goes to the opposite elevation of Hiker 1. Then Hiker 2 climbs an additional 200 feet up. Which statement must be true?
17. Maria has $\frac{3}{4}$ of a pizza left over from dinner. She wants to divide it equally among her friends, giving each friend $\frac{1}{8}$ of the original whole pizza. How many friends can she serve?
18. A city map has a scale where 2 inches represents 3 miles. Sarah measures the distance between two landmarks on the map as 4.5 inches. She then drives the actual route, which is 20% longer than the straight-line distance due to road curves. How many miles does Sarah actually drive?
19. The product of two positive integers is 360. If their greatest common factor is 6, what is the minimum possible value of their least common multiple?
20. A function $f(x)$ has the property that $f(x + 2) = f(x) + 6$ for all values of $x$. If $f(1) = 4$, what is $f(7)$?

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