Free Standardized Achievement Mathematics Test Question and Answer — Questions and Answers

Question 1: A automobile gets 27 miles per gallon on average. Which of the following best approximates how much gas would cost for this automobile to travel 2,727 average miles at a price of $4.04 per gallon?

$408.04 (Correct answer)
$118.80
$44.44
$444.40
$109.08

Correct answer: $408.04

To calculate the total cost, first determine the total gallons of gas needed by dividing the total miles (2,727) by the car's mileage (27 miles/gallon), which equals 101 gallons. Then, multiply the total gallons (101) by the price per gallon ($4.04). This results in a total cost of $408.04.

Question 2: How much does the value of 3x2 - 2y surpass the value of 2x2 - 3y when x = 3 and y = 5?

14 (Correct answer)
20
4
16
50

Correct answer: 14

First, substitute x=3 and y=5 into the expression 3x² - 2y: 3(3)² - 2(5) = 3(9) - 10 = 27 - 10 = 17. Next, substitute into 2x² - 3y: 2(3)² - 3(5) = 2(9) - 15 = 18 - 15 = 3. Finally, subtract the second value from the first: 17 - 3 = 14.

Question 3: When 2x + 3 Equals 3x - 4 what is the value of x?

7 (Correct answer)
-7
1/5
- 1/5
1

Correct answer: 7

To solve the equation 2x + 3 = 3x - 4 for x, first subtract 2x from both sides, yielding 3 = x - 4. Then, add 4 to both sides of the equation. This isolates x, giving you x = 7.

Question 4: What do 42, 126, and 210 have in common most?

21
2
6
42 (Correct answer)
14

Correct answer: 42

To find what 42, 126, and 210 have in common most, we need to find their greatest common divisor (GCD). Factoring each number gives: 42 = 2 * 3 * 7, 126 = 2 * 3² * 7, and 210 = 2 * 3 * 5 * 7. The common prime factors are 2, 3, and 7, so their product, 2 * 3 * 7 = 42, is the greatest common divisor.

Question 5: A company's revenues increased by $3 million from the first to the second year, and they doubled from the third to the second year. What were sales in millions of dollars for the first year if sales for the third year were 38 million?

20.5
17.5
35
16 (Correct answer)
22

Correct answer: 16

Let S1, S2, and S3 represent sales for the first, second, and third years. We are given S3 = 38 million. Since sales doubled from the second to the third year, S3 = 2 * S2, so S2 = 38 / 2 = 19 million. Sales increased by $3 million from the first to the second year, meaning S2 = S1 + 3. Therefore, S1 = S2 - 3 = 19 - 3 = 16 million.

Question 6: Three of the vertices of a rectangle are displayed in the typical (x,y) coordinate plane below. Which of the following is the rectangle's fourth vertex?

(9,–3)
(3,–7) (Correct answer)
(8,–3)
(4,–8)
(5,–1)

Correct answer: (3,–7)

Given three vertices of a rectangle, (3, -3), (8, -3), and (8, -7), we can deduce the fourth. The points (3,-3) and (8,-3) form a horizontal side. The points (8,-3) and (8,-7) form a vertical side. To complete the rectangle, the fourth vertex must share the x-coordinate of (3,-3) and the y-coordinate of (8,-7), making it (3, -7).

Question 7: A high school student typically eats 67.5 pounds of sugar annually. Each track team member intends to reduce their sugar intake by at least 20% over the course of the upcoming year as part of a new nutrition strategy. What is the maximum amount of sugar that each member of the track team may take in the upcoming year, assuming that they will follow this plan and consume sugar at the same rate as the average high school student?

44
54 (Correct answer)
48
66
14

Correct answer: 54

To find the maximum amount of sugar a track team member may consume, we first calculate the reduction. A 20% reduction means they will consume 100% - 20% = 80% of their typical annual sugar intake. Therefore, multiply the average annual intake of 67.5 pounds by 0.80 (or 80%) to get the new maximum amount. This calculation yields 54 pounds.

Question 8: Between 1 and 6, how many irrational numbers are there?

3
4
1
infinitely many (Correct answer)
10

Correct answer: infinitely many

Irrational numbers are real numbers that cannot be expressed as a simple fraction. A fundamental property of real numbers is that between any two distinct real numbers, there exist infinitely many rational numbers and infinitely many irrational numbers. Since 1 and 6 are distinct real numbers, there are an infinite number of irrational numbers between them.

Question 9: The sine of angle A in the right triangle below is which of the following?

5/13
5/12
12/13 (Correct answer)
12/5
13/5

Correct answer: 12/13

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse (SOH from SOH CAH TOA). Assuming a standard 5-12-13 right triangle where 13 is the hypotenuse, if the side opposite angle A is 12, then the sine of angle A is 12/13. This matches the correct answer, indicating the specific side lengths relative to angle A.

Question 10: A DVD player with a $100 list price is discounted by 30%. What does John spend for the DVD player if he receives a 20% employee discount off the retail price?

$86.00
$56.00 (Correct answer)
$77.60
$44.00
$50.00

Correct answer: $56.00

First, calculate the price after the initial 30% discount. A $100 DVD player discounted by 30% means it costs $100 * (1 - 0.30) = $100 * 0.70 = $70. Next, John receives a 20% employee discount off this new retail price. So, he pays $70 * (1 - 0.20) = $70 * 0.80 = $56. The discounts are applied sequentially to the current price.

Question 11: What is the measurement in degrees of the sharp angle made by a 12-hour clock's hands when it reads precisely one o'clock?

60°
45°
72°
15°
30° (Correct answer)

Correct answer: 30°

A 12-hour clock face is a circle, which measures 360 degrees. Since there are 12 hours marked on the clock, the angle between each consecutive hour mark is 360 degrees / 12 hours = 30 degrees per hour. At precisely one o'clock, the minute hand points directly at the 12, and the hour hand points directly at the 1. The sharp angle between these two positions is exactly one hour mark, which is 30 degrees.

Question 12: Which of the following claims must be accurate whenever the positive numbers n, a, b, and c are such that n a, c > a, and b > c?

b < n
n + b = a + c
b – n > a –n (Correct answer)
2n > a + b
a < n

Correct answer: b – n > a –n

We are given the inequalities: n > a, c > a, and b > c. From b > c and c > a, we can deduce by the transitive property of inequalities that b > a. Now, let's examine option C: b – n > a – n. If we add 'n' to both sides of this inequality, it simplifies to b > a. Since we've already established that b > a from the given conditions, this claim must be accurate.

Question 13: What are the midpoint coordinates of a line segment whose endpoints are (-3,0) and (7,4) in the conventional (x,y)coordinate plane?

(5,5)
(5,2)
(2,2) (Correct answer)
(2,4)

Correct answer: (2,2)

The midpoint coordinates of a line segment are found by averaging the x-coordinates and averaging the y-coordinates of its endpoints. For endpoints (-3, 0) and (7, 4), the x-coordinate of the midpoint is (-3 + 7) / 2 = 4 / 2 = 2. The y-coordinate of the midpoint is (0 + 4) / 2 = 4 / 2 = 2. Therefore, the midpoint coordinates are (2, 2).

Question 14: Only the three secret substances A, B, and C, which are combined in the proportions of 2:3:5, are used to make industrial cleaners. In a 42-pound (net weight) pail of this cleaner, how many pounds of secret ingredient B are there?

12.6 (Correct answer)
14
0.2
21
18

Correct answer: 12.6

The secret substances A, B, and C are combined in the proportions of 2:3:5. This means for every 2 parts of A, there are 3 parts of B and 5 parts of C, making a total of 2 + 3 + 5 = 10 parts. To find the amount of ingredient B in a 42-pound pail, we calculate B's proportion of the total: (3 parts of B / 10 total parts) * 42 pounds. This calculation gives (3/10) * 42 = 0.3 * 42 = 12.6 pounds.

Question 15: There are 280 kids in the neighborhood recreation program who are either 11 or 12 years old. The total age of the kids is 3,238 years. How many kids aged 11 are served by the recreation program?

158
208
122 (Correct answer)

Correct answer: 122

Let 'x' be the number of 11-year-olds and 'y' be the number of 12-year-olds. We can set up a system of two linear equations: x + y = 280 (total number of kids) and 11x + 12y = 3238 (total age). From the first equation, y = 280 - x. Substituting this into the second equation gives 11x + 12(280 - x) = 3238. Solving this equation yields 11x + 3360 - 12x = 3238, which simplifies to -x = -122, so x = 122. Thus, there are 122 kids aged 11.

Question 16: Before starting her arithmetic lesson, Ms. Hernandez stated:<br> I can think of five numbers whose means are equal to their medians. What is the fifth number if the first four are 14, 8, 16, and 14?<br> What five-digit number is Ms. Hernandez considering?<br>

14
16
13
18 (Correct answer)
15

Correct answer: 18

The given numbers are 14, 8, 16, and 14. Let the fifth number be 'x'. When these five numbers are arranged in ascending order, the median is the middle (third) number. If we assume the correct answer x=18, the ordered list is 8, 14, 14, 16, 18. The median is 14. The mean is the sum of the numbers divided by five: (8 + 14 + 14 + 16 + 18) / 5 = 70 / 5 = 14. Since the mean (14) equals the median (14), 18 is the correct fifth number.

Free Standardized Achievement Mathematics Test Question and Answer

A automobile gets 27 miles per gallon on average.
Which of the following best approximates how much gas would cost for this automobile to travel 2,727 average miles at a price of $4.04 per gallon?