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Embark on a journey of mathematical excellence with our "Integrated Math 1 Practice Test." This comprehensive pre-test is meticulously designed to assess your proficiency in the foundational concepts of Integrated Math 1. Dive into a range of topics, from algebra and geometry to probability and statistics, as you explore the diverse world of mathematical principles. Whether you're a student gearing up for an Integrated Math 1 course or someone keen to enhance their math abilities, this pre-test is an invaluable resource.
With a focus on the critical components of the Integrated Math 1 curriculum, it's your ideal starting point for Read moreself-assessment and improvement. Strengthen your math skills, set the stage for success, and pave the way for mathematical excellence with our Integrated Math 1 Practice Test. Your journey to mathematical mastery begins here!
Questions and Answers
1.
In nine years Sarah will be 15 years old. How old is Sarah now?
Explanation The question states that in nine years Sarah will be 15 years old. This implies that currently, Sarah is 6 years old.
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2.
Add the following: 2/3 and 4/5.
A.
22/15
B.
6/8
C.
29/15
D.
6/15
Correct Answer
A. 22/15
Explanation To add fractions, you need to have a common denominator. In this case, the common denominator is 15. So, you need to convert both fractions to have a denominator of 15.
To convert 2/3 to have a denominator of 15, you multiply the numerator and denominator by 5. This gives you 10/15.
To convert 4/5 to have a denominator of 15, you multiply the numerator and denominator by 3. This gives you 12/15.
Now, you can add the two fractions: 10/15 + 12/15 = 22/15. Therefore, the correct answer is 22/15.
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3.
Which of the following is a perfect square?
A.
6
B.
12
C.
25
D.
32
Correct Answer
C. 25
Explanation 25 is a perfect square because it is the square of 5. In other words, 25 can be expressed as 5 multiplied by itself.
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4.
There are 2.54 cm in one inch. How many cm are in six yards?
Correct Answer 548.64 548.64 cm 548.6 548.6 cm
Explanation To convert yards to centimeters, we need to know the conversion factor between yards and centimeters. Since the conversion factor between inches and centimeters is 2.54 cm in one inch, we can use this information to find the conversion factor between yards and centimeters.
There are 36 inches in one yard (since 1 yard = 3 feet and 1 foot = 12 inches). Therefore, to convert yards to centimeters, we need to multiply the number of yards by the conversion factor of inches to centimeters (2.54 cm) and then by the conversion factor of yards to inches (36 inches).
So, to find the number of centimeters in six yards, we multiply 6 yards by 36 inches/yard and then by 2.54 cm/inch. This gives us a total of 548.64 cm. Therefore, the correct answer is 548.64 cm.
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5.
What is the absolute value of 3-7?
[ 3 - 7 ] =
Correct Answer 4
Explanation The absolute value of a number is its distance from zero on the number line, regardless of whether the number is positive or negative. In this case, the absolute value of 3-7 is the distance between 3 and 7 on the number line, which is 4.
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6.
Put these numbers in order from smallest to largest: 0.5, 0.05, 0.15, 1.0
Explanation The correct answer is 0.05, 0.15, 0.5, 1.0. The numbers are arranged in ascending order from smallest to largest.
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7.
2^{3}/4 + 6 * 3 =
Remember to use the order of operations. ( / means divided by)
Correct Answer 20 twenty
Explanation To solve this equation using the order of operations, we first perform the multiplication operation, which is 6 multiplied by 3, resulting in 18. Then, we perform the division operation, which is 23 divided by 4, resulting in 5.75. Finally, we add the two results together, giving us a final answer of 20.
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8.
Evaluate 4x - 6 when x = 5.
Correct Answer 14 fourteen
Explanation The given expression is 4x - 6. To evaluate this expression when x = 5, we substitute the value of x into the expression. Therefore, we have 4(5) - 6 = 20 - 6 = 14. So, the correct answer is 14. Another way to represent the answer is "fourteen", which is the word form of the numerical value 14.
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9.
A rectangle has a length of twelve inches and a width of four inches. What is the perimeter?
Correct Answer 32 inches 32 in. 32 in 32
Explanation The perimeter of a rectangle is calculated by adding up all the sides. In this case, the length is 12 inches and the width is 4 inches. To find the perimeter, we add the length and the width together and then double that sum since opposite sides of a rectangle are equal in length. Therefore, the perimeter is 2(12 + 4) = 2(16) = 32 inches.
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10.
What is the slope of the line with equation y = 3x - 10?
A.
-10
B.
10
C.
3
D.
-3
Correct Answer
C. 3
Explanation The slope of a line is the coefficient of the x-term in the equation of the line. In this case, the equation is y = 3x - 10, so the coefficient of the x-term is 3. Therefore, the slope of the line is 3.
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11.
There are 54 students going on a field trip. If each van can carry six students, how many vans will be necessary to carry all students?
Correct Answer 9 vans 9 nine nine vans
Explanation To determine the number of vans necessary to carry all the students, we divide the total number of students by the number of students each van can carry. In this case, since each van can carry six students, we divide 54 by 6, which equals 9. Therefore, 9 vans will be necessary to carry all the students.
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12.
Change 6 2/7 (six and two sevenths) to an improper fraction instead of a mixed number.
Correct Answer 44/7 fourty four sevenths
Explanation To convert a mixed number to an improper fraction, we multiply the whole number by the denominator of the fraction and add the numerator. In this case, we have 6 multiplied by 7 (the denominator) which equals 42, and then we add 2 (the numerator) to get 44. Therefore, the improper fraction equivalent of 6 2/7 is 44/7. The phrase "forty four sevenths" is just another way of expressing the improper fraction 44/7.
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13.
Use the Pythagorean Theorem to find the hypotenuse of a right triangle with legs that measure 3 and 4.
A.
5
B.
25
C.
7
D.
49
Correct Answer
A. 5
Explanation The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the lengths of the legs are 3 and 4. So, using the theorem, we can calculate the hypotenuse as follows: 3^2 + 4^2 = 9 + 16 = 25. Taking the square root of 25 gives us 5, which is the length of the hypotenuse. Therefore, the correct answer is 5.
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14.
What is the product of 49 written as prime factors?
A.
49 * 1
B.
7*7
C.
1 * (48 + 1)
Correct Answer
B. 7*7
Explanation The correct answer is 7*7. This is because 49 can be written as the product of its prime factors, which are both 7. Therefore, the product of 49 written as prime factors is 7*7.
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15.
What is the greatest common factor of 12 & 28?
Correct Answer 4 four
Explanation The greatest common factor (GCF) is the largest number that divides evenly into both 12 and 28. In this case, the factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 28 are 1, 2, 4, 7, 14, and 28. The largest number that appears in both lists is 4, so the GCF of 12 and 28 is 4.
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16.
Round 40.5656 to the nearest tenth.
Correct Answer 40.6
Explanation To round a number to the nearest tenth, we look at the digit in the hundredth place. If it is 5 or greater, we round up, and if it is less than 5, we round down. In this case, the digit in the hundredth place is 6, which is greater than 5. Therefore, we round up the digit in the tenth place to 1. The final rounded number is 40.6.
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17.
Change 5/1000 to a decimal.
Correct Answer .005 0.005
Explanation The correct answer is 0.005 because when we change a fraction to a decimal, we divide the numerator (5) by the denominator (1000). Dividing 5 by 1000 gives us 0.005.
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18.
Which of the following is the correct volume for a cube which has sides that mesure 3 in.?
A.
6 cubic inches
B.
9 cubic inches
C.
15 cubic inches
D.
27 cubic inches
Correct Answer
D. 27 cubic inches
Explanation The volume of a cube is calculated by multiplying the length of one side by itself three times (length x length x length). In this case, the cube has sides that measure 3 inches. Therefore, the correct volume for this cube would be 3 x 3 x 3 = 27 cubic inches.
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19.
Evaluate (- x)^{2 }when x = 3.
Correct Answer 9 nine
Explanation When evaluating (-x)^2, we first substitute the value of x, which is 3, into the expression. So, (-3)^2 is calculated. The negative sign is squared along with the number, resulting in a positive value. Therefore, (-3)^2 is equal to 9. Additionally, the word "nine" is the numerical representation of the number 9.
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20.
1/3 = _____ %
Round to the nearest whole percent.
Correct Answer 33% 33
Explanation The question asks for the percentage equivalent of 1/3, rounded to the nearest whole percent. To find this, we divide 1 by 3, which equals 0.3333... When rounded to the nearest whole percent, this becomes 33%. Therefore, the correct answer is 33%. The second option, 33, is incorrect as it does not represent a percentage.
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21.
What percent of 20 = 8?
Correct Answer 40% 40 40 percent forty percent
Explanation The correct answer is 40%, 40, 40 percent, or forty percent because all of these options represent the same value - 40% of 20.
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22.
If r = 5 and s = 8, what is the value of r^{2} - 2s?
Correct Answer 9 nine
Explanation The expression r2 - 2s can be simplified by substituting the given values of r and s. Therefore, (5)2 - 2(8) is equal to 25 - 16, which equals 9. The answer is 9.
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23.
Write the decimal number which represents "two and sixteen thousandths".
Correct Answer 2.016
Explanation The given decimal number, 2.016, represents "two and sixteen thousandths" because the digit 2 represents the whole number "two," and the digits after the decimal point, 016, represent the fraction "sixteen thousandths."
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24.
Which expression represents the following statement: Five less than twice a number.
A.
2x + 5
B.
5x - 2
C.
5x + 2
D.
2x - 5
Correct Answer
D. 2x - 5
Explanation The expression 2x - 5 represents the statement "Five less than twice a number." This can be understood by breaking down the statement. "Twice a number" is represented by 2x, and "Five less than" means subtracting 5 from that. Therefore, 2x - 5 is the correct expression.
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25.
Which of the following correctly states the following number: 22738904
A.
Two trillion seven hundred thousand nine hundred four
B.
Twenty two million seven hundred thirty eight thousand nine hundred four
C.
Twenty two million seven hundred thousand nine hundred four
D.
Twenty two trillion seven hundred thirty eight thousand nine hundred and four
Correct Answer
B. Twenty two million seven hundred thirty eight thousand nine hundred four
Explanation The correct answer is "twenty two million seven hundred thirty eight thousand nine hundred four". This is the correct statement of the number 22738904.
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26.
What is the least common denominator for the following fractions: 2/4, 1/6, 7/8
Correct Answer 24
Explanation The least common denominator is the smallest multiple that all the denominators in the fractions can divide into evenly. In this case, the denominators are 4, 6, and 8. The multiples of 4 are 4, 8, 12, 16, 20, 24, and so on. The multiples of 6 are 6, 12, 18, 24, and so on. The multiples of 8 are 8, 16, 24, and so on. The smallest multiple that all three denominators can divide into evenly is 24. Therefore, the correct answer is 24.
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27.
Which of the following choices are multiples of 7?
Check all that apply.
A.
1
B.
7
C.
28
D.
49
E.
56
F.
10
G.
14
Correct Answer(s)
B. 7 C. 28 D. 49 E. 56 G. 14
Explanation The multiples of 7 are numbers that can be divided evenly by 7 without leaving a remainder. In this case, the numbers 7, 28, 49, 56, and 14 can all be divided by 7 without leaving a remainder, so they are multiples of 7. The numbers 1 and 10 cannot be divided evenly by 7, so they are not multiples of 7.
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28.
What is the most simplified form of the following fraction: 63 / 81 ?
Type your answer as a fraction using the /
Correct Answer(s) 7/9 7 /9 7 / 9
Explanation The most simplified form of the fraction 63/81 is 7/9. This can be found by dividing both the numerator and denominator by their greatest common divisor, which in this case is 9.
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29.
Simplify 9m - 3m.
Correct Answer(s) 6m 6*m 6 m
Explanation The expression 9m - 3m represents subtracting 3m from 9m. When subtracting like terms, we subtract the coefficients (9 - 3) and keep the variable (m) the same. Therefore, the simplified expression is 6m.
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30.
Evaluate and round to the nearest whole number: 9.87 / 0.3 =
Correct Answer(s) 33
Explanation The given expression is 9.87 divided by 0.3. When we evaluate this expression, we get the result as 32.9. Since we are asked to round the answer to the nearest whole number, 32.9 would round up to 33. Therefore, the correct answer is 33.
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31.
The bill for your dinner is $45.78. If you want to include a 15% tip, what will the total for dinner and tip be?
A.
$52.64
B.
$52.65
C.
$6.86
D.
$6.87
Correct Answer
B. $52.65
32.
4 + (-7) + 2 + (-5) = ?
Correct Answer -6, - 6
Explanation The given expression involves adding positive and negative numbers. When adding positive and negative numbers, we can think of it as subtracting the absolute value of the negative number from the positive number. In this case, we have 4 + (-7) + 2 + (-5). This can be simplified as 4 - 7 + 2 - 5. Evaluating this expression, we get -6. Therefore, the correct answer is -6.
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33.
Suppose that you are asked to collect information about the colors of cars that drive by school during the day and you record the following:
What is the probability that a car is red or blue?
A.
40/180
B.
60/180
C.
5/9
D.
100
Correct Answer
C. 5/9
Explanation The probability that a car is red or blue can be calculated by adding the probabilities of the car being red and blue separately. From the given information, it is not clear how many cars are red or blue. Therefore, we cannot determine the exact probability. The correct answer cannot be determined based on the given information.
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34.
Suppose that you are asked to collect information about the colors of cars that drive by school during the day and you record the following:
What is the probability that a car is green?
A.
1/6
B.
80/180
C.
20/180
Correct Answer
A. 1/6
Explanation The probability that a car is green is 1/6. This can be determined by looking at the given information, which states that the total number of cars observed is 180. Out of these 180 cars, the number of green cars is not specified. Therefore, we can assume that there is only one green car out of the six possible colors (assuming each car can only be one color). Thus, the probability of a car being green is 1 out of 6, or 1/6.
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35.
For the line y = 2x - 3, which of the following are points on this line? (Hint: use a table like the one below to create points that are on the line)
Check all answers that apply.
A.
(0, -1)
B.
(0, -3)
C.
(1, -3)
D.
(1, -1)
E.
(4, 5)
F.
(0,0)
G.
(3, 3)
Correct Answer(s)
B. (0, -3) D. (1, -1) E. (4, 5) G. (3, 3)
Explanation The equation y = 2x - 3 represents a straight line. To determine which points lie on this line, we can substitute the given x and y values into the equation and check if the equation holds true.
For the point (0, -3), substituting x = 0 and y = -3 into the equation gives -3 = 2(0) - 3, which is true.
For the point (1, -1), substituting x = 1 and y = -1 into the equation gives -1 = 2(1) - 3, which is true.
For the point (4, 5), substituting x = 4 and y = 5 into the equation gives 5 = 2(4) - 3, which is true.
For the point (3, 3), substituting x = 3 and y = 3 into the equation gives 3 = 2(3) - 3, which is true.
Therefore, the points (0, -3), (1, -1), (4, 5), and (3, 3) are all on the line y = 2x - 3.
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36.
What is the total area of the following figure?
A.
192 sq units
B.
156 sq units
C.
128 sq units
D.
126 sq units
Correct Answer
B. 156 sq units
37.
Suppose that you are asked to collect information about the colors of cars that drive by school during the day and you record the following:
What is the probability that a car is not blue?
A.
60/180
B.
1/3
C.
50/180
D.
2/3
Correct Answer
D. 2/3
Explanation The probability that a car is not blue can be found by subtracting the probability that a car is blue from 1. Since the total number of cars observed is 180 and 60 of them are blue, the probability that a car is blue is 60/180. Therefore, the probability that a car is not blue is 1 - 60/180 = 120/180 = 2/3.
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38.
The following chart shows the pattern of a function for the x and y values. Answer the following question about this chart/pattern.
What number is being added each time?
Correct Answer 4
Explanation The number being added each time is 4. This can be determined by observing the pattern in the chart, where the y values increase by 4 each time the x value increases by 1. The word "four" in the answer options also suggests that the number being added is 4.
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39.
The following chart shows the pattern of a function for the x and y values. Answer the following question about this chart/pattern.
What function/equation would represent the rule being demonstrated that allows you to detrmine y from the value of x?
Hint: y = ___*x + ____
Write the entire equation in your answer (y=?*x+?). Do not use spaces in your answer.
Correct Answer y=4*x+13
Explanation The equation that represents the rule being demonstrated is y = 4x + 13.
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40.
The following chart shows the pattern of a function for the x and y values. Answer the following question about this chart/pattern.
What is y when x = 95? (Figure out the equation, then use it to solve for y.)
Correct Answer 393
Explanation Based on the given chart, the value of y is 393 when x is equal to 95. The equation for this pattern is not provided, so we cannot determine the equation itself. However, we can directly read the value of y from the chart for the given x value.
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