Practice Test 7 - Pre Algebra

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

A pattern of hexagons is built where each hexagon shares sides with adjacent hexagons. Pattern 1 has 1 hexagon with perimeter 6. Pattern 2 has 2 hexagons sharing one side with total perimeter 10. Pattern 3 has 3 hexagons in a line with total perimeter 14. If this pattern continues, what is the total perimeter of Pattern 8?
A recipe calls for 2.4 cups of flour, but Jenny only has 65% of the amount needed. She borrows 30% of the required amount from her neighbor. What percent of the required flour does Jenny now have?
If $h$ represents the total hours parked where $h > 1$ , which statement best interprets the solution $h \leq 5.8$ ?
A submarine starts at sea level and descends 150 feet, then ascends 75 feet, then descends another 200 feet. If the absolute value of the submarine's final depth equals the distance a helicopter is above sea level, and the helicopter's altitude and the submarine's depth are opposites, what is the helicopter's altitude?
Carmen is solving the system: $\begin{cases} 2x + 3y = 12 \\ 4x + 6y = 20 \end{cases}$ . She multiplies the first equation by -2 to get $-4x - 6y = -24$ , then adds it to the second equation and gets $0 = -4$ . She concludes the system has no solution. Her friend David says she made an error because the second equation should be $4x + 6y = 24$ to be consistent. Who is correct and why?
Three friends invest different amounts for the same length of time at the same interest rate. Sarah invests $P$ and earns $60 interest. Miguel invests$ 2P $and earns$ 120 interest. Chen invests $3P$ but only earns $$150 interest. What can you conclude?
A basketball player's free throw percentage improved from 0.72 to 78%. By how many percentage points did their free throw percentage increase?
A fair coin is flipped 4 times. What is the probability of getting at most 1 head?
A line of best fit for data relating study time (hours) to test scores has slope 4.2. Based on this line, a student who studies 3 additional hours should expect their test score to increase by approximately how many points?
A rhombus has diagonals of length 18 cm and 24 cm. If two identical right triangles are removed from opposite corners, each with legs of length 3 cm and 4 cm, what is the area of the remaining figure?
A student observes that when she increases her study time, her test scores improve. She records the following data: 2 hours of study yields a score of 75, 4 hours yields 85, and 6 hours yields 95. She concludes this represents a proportional relationship and predicts that 0 hours of study would yield a score of 0. What error has the student made in her reasoning?
A bakery makes muffin batter using flour, sugar, and eggs in a 6:2:1 ratio by weight. They prepare a large batch using 18 pounds of flour. Due to an unexpected large order, they need to make 50% more batter, but they only have 4 more pounds of flour available. If they use all their available flour and maintain the same ratios for the additional batter, how much total sugar will they have used for both batches combined?
A map of a state park uses a scale of 1:50,000. On the map, the distance around a lake is measured as 8.4 cm. A ranger walks around the actual lake at an average speed of 4.5 km/h. How long will it take the ranger to walk completely around the lake?
A student solves $3(2x - 1) + 4 = 2(3x + 2) - 1$ by expanding both sides. After simplification, what conclusion should the student reach?
Marcus has a checking account with overdraft protection that charges $25 when the balance goes below zero. His account starts with $156.43. He writes checks for $89.17, $45.82, and $38.76 in that order. After the overdraft fee (if any), he deposits $75.50. What is his final balance?
A machine fills bottles at a constant rate and completes 156 bottles in 12 minutes. Due to a brief power outage, the machine stops for 2 minutes during this 12-minute period. What is the actual rate of the machine when it is running?
Two students design different simulations for the same probability problem: finding the chance that exactly 2 out of 4 randomly selected students are left-handed (8% of students are left-handed). Student A uses a random number generator 1-100, while Student B uses 1-25. Which statement about their simulation designs is most accurate?
The value of a car depreciates by 20% each year. After 2 years, the car is worth $25,600. What was the original purchase price?
The inequality $|2x - 5| \geq 3$ has solution set $x \leq 1$ or $x \geq 4$ . To confirm that both boundary values are correctly included, which verification is most complete?
Jake needs to solve the equation $3x^2 - 12x - 15 = 0$ and wants to choose between using a calculator's graphing function, factoring by hand, or creating a table of values. His teacher requires him to find the exact solutions and show his work step-by-step. Which approach should Jake choose and why?

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