HiSET Math Test with Answers PDF

Question 1

A home improvement store offers to finance the purchase of any single item with zero interest for one year, with a down payment of $50. The remainder of the purchase price will be split into 12 equal monthly payments. Which of the following equations represents the relationship between an item's purchase price, s dollars, and the amount, a dollars, of each monthly payment under this offer?

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

The relationship between an item's purchase price and each monthly payment is represented by the equation s = 12a + 50.

In this scenario, the purchase price (s dollars) is paid off in 12 equal monthly installments after a $50 down payment. Each monthly payment (a dollars) contributes to the total purchase price, with the cumulative sum reaching the initial cost plus 11 additional payments of equal value.

A) s = a-50/12
This equation incorrectly subtracts $50 from each monthly payment, which would result in a diminishing total purchase price over 12 months. However, under the zero-interest financing offer, the purchase price remains constant, and the down payment is a one-time occurrence.

B) s = a/12 -50
This equation divides each monthly payment by 12 and then subtracts $50, suggesting a reduction in both the purchase price and the monthly payments. Such an approach does not align with the terms of the financing offer, where the purchase price is to be paid off in equal installments.

C) s = 12a + 50
The correct equation reflects the cumulative nature of the monthly payments, with each installment contributing to the total purchase price. By multiplying the monthly payment by 12 and adding the initial down payment, this equation accurately represents the relationship between the purchase price and the monthly payments.

D) s = 12a - 50
In this equation, the $50 down payment is subtracted from the total purchase price, which would imply a reduction in the initial cost rather than a fixed down payment. This calculation does not adhere to the financing terms outlined in the question.

E) s = 12 (a + 50)
Multiplying the monthly payment by 12 and then adding $50 to the result misrepresents the relationship between the purchase price and the monthly payments. This equation implies that the down payment is multiplied by 12, which is not reflective of the given financing structure.

Conclusion
The correct equation s = 12a + 50 appropriately captures the relationship between an item's purchase price and the equal monthly payments required under the zero-interest financing offer. Through this equation, the cumulative effect of 12 monthly installments, along with the initial down payment, contributes to settling the total purchase price without any interest accrual.

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Question 2

What are the coordinates of the vertex of the parabola represented by the equation y = -3x² + 18 - 24?

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

(C) (3,3)

The correct answer corresponds to the vertex of the parabola formed by the given quadratic equation. The vertex of a parabola in the form y = ax² + bx + c can be found using the formula x = -b / 2a. By substituting the coefficients from the equation y = -3x² + 18x - 24, you can determine the x-coordinate of the vertex, which is 3. Substituting this x-value back into the original equation provides the corresponding y-coordinate of 3, confirming the vertex as (3, 3).

A) (6, -24)
This point does not represent the vertex of the parabola. The x-coordinate is incorrect, as the correct x-value for the vertex is 3, not 6. Additionally, the y-value of -24 does not align with the calculated y-coordinate of 3 for the vertex.

B) (4, 0)
The coordinates provided do not match the vertex of the parabola. The x-value is incorrect, as the vertex x-coordinate should be 3 rather than 4. Moreover, the y-value of 0 does not correspond to the calculated y-coordinate of 3 for the vertex.

D) (2, 0)
These coordinates are not indicative of the vertex of the parabola represented by the given equation. The x-value is inaccurately given as 2, whereas the correct x-coordinate for the vertex is 3. Additionally, the y-coordinate provided as 0 does not align with the calculated y-coordinate of 3 for the vertex.

E) (-3, -105)
The coordinates (-3, -105) do not represent the vertex of the parabola. The x-value of -3 is incorrect, as the vertex x-coordinate should be 3, not -3. Furthermore, the y-coordinate of -105 does not match the calculated y-coordinate of 3 for the vertex.

Conclusion
The vertex of a parabola is a crucial point that signifies the maximum or minimum value of the quadratic function. In this case, the correct vertex coordinates for the parabola represented by the equation y = -3x² + 18x - 24 are (3, 3). These coordinates mark the turning point of the parabolic curve, where the function reaches its extreme value.

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Question 3

In a survey of 300 people who were randomly sampled from a well-defined population, 60 said that they read a newspaper daily. If 1,000 people had been randomly sampled from the same population and asked the same question, how many would be expected to say they read a newspaper daily?

Your Answer: Option(s)

Correct Answer: Option(s) A

Rationale

180

Extrapolating from the initial survey results, where 20% of the 300 people sampled read a newspaper daily, one would expect a similar percentage to hold true for a larger sample size within the same population.

B) 200
This option overestimates the expected number of individuals who read a newspaper daily, as it assumes a constant rate of 20% without considering the impact of sample size scaling on statistical variation.

C) 360
Choosing this option implies a significant increase in the proportion of daily newspaper readers compared to the original survey, which lacks justification given the consistent behavior expected within the same population.

D) 600
Selecting 600 as the expected count greatly exaggerates the anticipated number of daily newspaper readers, reflecting a misunderstanding of how sample size influences the accuracy of projections.

E) 760
This choice presents a substantial and unwarranted rise in the projected number of individuals reading a newspaper daily, disregarding the statistical principles that govern sample representativeness.

Conclusion
By applying the percentage of daily newspaper readers from the initial survey to a larger sample size of 1,000 individuals, one can reasonably estimate that around 180 people would be expected to report reading a newspaper daily. This projection aligns with the assumption of a consistent behavior pattern within the population and the proportional increase in sample size, ensuring a reliable estimate of the expected response rate.

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Question 4

A campground rents canoes for either $20 per day or $4 per hour. For what number or numbers of hours, h, is it more expensive to rent a canoe at the daily rate than at the hourly rate?

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

For what number or numbers of hours, h, is it more expensive to rent a canoe at the daily rate than at the hourly rate?

When renting a canoe, it is more expensive to opt for the daily rate when the total cost for that day exceeds the cost of renting by the hour over the same duration. This scenario occurs when the number of hours rented exceeds 5.

A) h = 5
If h equals 5 hours, the total cost for both the daily rate and the hourly rate would be the same. This choice does not represent the point at which renting at the daily rate becomes more expensive.

B) h >= 25
Choosing h to be greater than or equal to 25 hours would lead to a higher cost when renting by the hour compared to the daily rate. This range is beyond the threshold where the daily rate becomes more expensive.

C) h > 5
This is the correct answer. When h is greater than 5 hours, the total cost of renting by the day exceeds the cost of renting by the hour for the same duration, making it more expensive to choose the daily rate.

D) h < 5
If h is less than 5 hours, it is more cost-effective to rent by the hour rather than opting for the daily rate. The daily rate becomes more expensive only after surpassing the 5-hour mark.

E) h ≤ 5
This choice includes the critical point of h being exactly 5 hours where both rental options cost the same. However, it also encompasses values where renting by the hour is cheaper, failing to capture the range where the daily rate becomes pricier.

Conclusion
The tipping point where renting a canoe at the daily rate becomes more expensive than at the hourly rate occurs when the number of hours rented surpasses 5. Beyond this threshold, opting for the daily rate results in a higher total cost for canoe rental.

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Question 5

Connor sprinted 55 yards in 6.25 seconds. What was Connor's average speed in miles per hour?

Your Answer: Option(s)

Correct Answer: Option(s) D

Rationale

Connor's average speed was 18 miles per hour.

To calculate average speed, we convert the distance covered to miles (1 yard = 0.000568182 miles) and the time taken to hours. In this case, Connor covered approximately 0.03125 miles in 6.25 seconds, which translates to an average speed of 18 mph.

A) 6
This choice is incorrect because it does not accurately represent Connor's average speed in miles per hour based on the given distance and time values.

B) 9
This option is incorrect as it does not align with the correct calculation of Connor's average speed in miles per hour using the provided data.

C) 15
This option is not the correct answer as it does not match the calculated average speed of Connor in miles per hour according to the given distance and time.

D) 18
Correct! Connor's average speed is indeed 18 miles per hour, obtained by converting the distance in yards to miles and the time in seconds to hours.

E) 26
This choice is inaccurate as it does not reflect the correct average speed of Connor in miles per hour as per the distance covered and time taken.

Conclusion
By converting the distance of 55 yards to miles and the time of 6.25 seconds to hours, we determine that Connor's average speed was 18 miles per hour. This conversion allows for a more standardized comparison of speed measurements and provides a clear understanding of Connor's pace in terms of miles covered per hour.

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The relationship between an item's purchase price and each monthly payment is represented by the equation s = 12a + 50.

(C) (3,3)

180

For what number or numbers of hours, h, is it more expensive to rent a canoe at the daily rate than at the hourly rate?

Connor's average speed was 18 miles per hour.

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