Practice Test 2 - Pre Algebra

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

A bakery uses $\frac{5}{6}$ cup of sugar per batch of cookies, meaning 5 parts sugar divided into 6 equal portions total. If the bakery wants to make multiple batches but only has a $\frac{1}{12}$ cup measuring scoop, they determine they need $\frac{10}{12}$ cup of sugar per batch. What does this tell us about $\frac{5}{6}$ and $\frac{10}{12}$ ?
Which expression is equivalent to $\frac{2^{-3} \cdot 4^2}{8^{-1}}$ ?
Maria solved the inequality $3x - 5 > 7$ and got $x > 4$ . She tested her solution by substituting $x = 5$ and found that both sides of the original inequality were satisfied. What should she conclude?
A linear function is defined by $f(x) = -\frac{2}{3}x + 4$ . If the graph of this function is drawn, which statement about its intercepts is correct?
A triangle with area 48 square inches is scaled to create a new triangle with area 12 square inches. If the original triangle had a perimeter of 32 inches, what is the difference between the original and new perimeters?
A manufacturing process requires the width $w$ of a component to satisfy $|w - 12| \leq 0.5$ . Additionally, quality control rejects components where $w < 11.7$ or $w > 12.4$ . What range of widths passes both requirements?
Marcus is planning a school fundraiser selling two types of items: keychains for $3 each and bookmarks for $2 each. He needs to raise at least $240 and wants to sell exactly 100 items total. If he sells $k$ keychains, which inequality represents the constraint for reaching his fundraising goal, and what is the minimum number of keychains he must sell?
If this situation is modeled as a system of equations and graphed, what does the intersection point represent in this real-world context?
A machine can produce 450 widgets in 6 hours. Working at the same rate, how many widgets can 3 such machines produce in 8 hours?
A researcher wants to determine if the relationship between hours of sleep and reaction time is linear. She collected data from 20 participants and now needs to decide between creating a scatter plot with trend line, calculating correlation coefficient, or making a frequency table of sleep hours. Her goal is to assess linearity and determine the strength of the relationship. What tool choice provides the most complete analysis?
Consider the system $\begin{cases} x - 2y = 4 \\ y = \frac{1}{2}x + c \end{cases}$ where $c$ is a constant. If this system has no solution, what can you conclude about the relationship between the two equations?
A student runs a simulation to estimate the probability of getting exactly 2 heads when flipping 4 coins. She uses a random number generator producing digits 0-9, where even digits represent heads and odd digits represent tails. After 500 trials, she gets 180 successes. Based on these results, what should she conclude about her simulation?
In the expression $4x^2 - 6x + 9 - 2x(x + 3)$ , which of the following correctly identifies the terms after expanding but before any combining of like terms?
The distance from Earth to the nearest star (other than the Sun) is approximately $4.1 \times 10^{13}$ kilometers. The distance from Earth to the Moon is approximately $380,000$ kilometers. How many times farther is the nearest star than the Moon?
If the actual weight at noon was $850.7$ grams, what is the range of possible actual weights (in grams) for the morning reading, assuming the scale's rounding behavior is consistent?
A elevator has a weight limit and currently contains 4 adults averaging 160 pounds each and some children averaging 80 pounds each. The elevator can safely hold a maximum of 2,000 pounds total. If $c$ represents the number of children currently in the elevator, which inequality represents the constraint on the number of additional adults $a$ that can enter?
What is the value of $\frac{(2^3)^2 - 3^4}{2^2 \times 3^2 - 2^3}$ ?
Two hikers start at the same point. One hiker walks 5 miles north, then 12 miles east. The other hiker walks directly to the first hiker's final position. How much farther did the first hiker walk compared to the second hiker?
Consider the expression $3x^2 + 7xy - 2x^2 + 5y - 4xy + 8$ . After combining like terms, how many terms in the simplified expression have a coefficient with an absolute value greater than 4?
A delivery truck can carry a maximum load of $2400$ pounds. It already has packages weighing $1650$ pounds loaded. If each additional package weighs $25$ pounds, what is the solution to the inequality representing how many more packages $p$ can be loaded?

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