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An assessment to evaluate a student's math aptitude. The questions focus on gaining an understanding of the students ability with grade 6,7 and 8 grade math.
Questions and Answers
1.
Write this number in standard notation.
326 thousand
Explanation The number "326 thousand" can be written in standard notation as 326,000 or 326000.
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2.
Find the number for n using mental math and basic properties.
(16 + n) + 47 = 16 + (53 + 47)
Explanation The given equation is (16 + n) + 47 = 16 + (53 + 47). By applying the associative property of addition, we can rearrange the terms on the right side of the equation to get (16 + n) + 47 = (16 + 53) + 47. This simplifies to (16 + n) + 47 = 69 + 47. By combining like terms on both sides of the equation, we get (16 + n) + 47 = 116. By subtracting 47 from both sides of the equation, we get 16 + n = 69. Finally, by subtracting 16 from both sides of the equation, we find that n = 53.
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3.
Find the value of each expression. Use the order of operations.
17 - 8 + 3 =
Explanation The expression requires following the order of operations, which means performing the subtraction before the addition. Subtracting 8 from 17 gives us 9, and then adding 3 to 9 gives us a final answer of 12.
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4.
Find the value of each expression. Use the order of operations .
32 * 2 + (11 - 7) * 6 =
Explanation The given expression involves multiplication, addition, and subtraction. According to the order of operations, we first perform the operations inside the parentheses: (11 - 7) = 4. Then, we multiply 32 by 2, resulting in 64. Finally, we multiply 4 by 6, giving us 24. Adding 64 and 24 together, we get the final answer of 88.
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5.
Find the answer.
3792 divided by 24 =
Explanation To find the answer, we need to divide 3792 by 24. Dividing 3792 by 24 gives us the quotient of 158.
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6.
Evaluate each algebraic expression.
a(b + 6) for a = 8 and b = 24
Explanation To evaluate the expression a(b + 6) for a = 8 and b = 24, we substitute the given values into the expression.
So, we have 8(24 + 6).
First, we solve the parentheses, which gives us 8(30).
Then, we multiply 8 by 30, resulting in 240.
Therefore, the answer is 240.
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7.
Eva bought 5 pounds of trail mix for her camping trip. If the trail mix cost $2.19 per pound, how much did she pay?
Explanation Eva bought 5 pounds of trail mix and the cost of the trail mix per pound is $2.19. To find out how much she paid, we can multiply the cost per pound ($2.19) by the number of pounds (5). This gives us $10.95, which is the total amount she paid for the trail mix.
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8.
What is the value of x to make this equation true.
x + 22 = 49
Explanation To make the equation x + 22 = 49 true, we need to find the value of x that, when added to 22, equals 49. By subtracting 22 from both sides of the equation, we find that x = 27.
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9.
Solve for y.
3y - 18 = 54
Explanation To solve for y, we need to isolate y on one side of the equation. We can do this by adding 18 to both sides of the equation. This will cancel out the -18 on the left side, leaving us with 3y = 72. Then, we divide both sides of the equation by 3 to solve for y. This gives us y = 24. Therefore, the value of y that satisfies the equation is 24.
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10.
If a car is traveling at 35 miles an hour. How many miles has it traveled after 3 hours?
Explanation The car is traveling at a speed of 35 miles per hour. To calculate the distance traveled, we need to multiply the speed by the time. Since the car has been traveling for 3 hours, we multiply 35 miles per hour by 3 hours, which gives us a total of 105 miles traveled.
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11.
What does the number below equal? Please write in standard notation.
3^{4}
Explanation The number below, 81, is the standard notation for the given number.
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12.
Find the sum.
5 + -2
Explanation The sum of 5 and -2 is 3.
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13.
Which number below is not a prime factor of 105?
A.
5
B.
3
C.
11
D.
7
Correct Answer C. 11
Explanation The number 11 is not a prime factor of 105 because when we divide 105 by 11, it does not result in a whole number. A prime factor is a prime number that can divide a given number without leaving a remainder. In this case, 105 can be divided by 5, 3, and 7 without leaving a remainder, making them prime factors. However, when we divide 105 by 11, it results in a decimal value, indicating that 11 is not a factor of 105.
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14.
What's the LCM of 7 and 49?
A.
48
B.
51
C.
49
D.
47
Correct Answer C. 49
Explanation The LCM (Least Common Multiple) is the smallest multiple that two or more numbers have in common. In this case, the LCM of 7 and 49 would be 49, as it is the smallest number that both 7 and 49 can evenly divide into. Therefore, the correct answer is 49.
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15.
Find the greatest common factor of 15,45 and 60.
A.
3
B.
15
C.
5
D.
10
Correct Answer B. 15
Explanation The greatest common factor (GCF) is the largest number that divides evenly into all of the given numbers. In this case, 15, 45, and 60 are the numbers provided. By finding the factors of each number and identifying the common factors, we can determine the GCF. The factors of 15 are 1, 3, 5, and 15. The factors of 45 are 1, 3, 5, 9, 15, and 45. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The only common factor among all three numbers is 15, making it the greatest common factor.
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16.
Which fraction has the greatest value?
A.
3/10
B.
1/5
C.
1/6
D.
2/3
Correct Answer D. 2/3
Explanation The fraction 2/3 has the greatest value because the numerator (2) is larger than the numerators of the other fractions, and the denominator (3) is smaller than the denominators of the other fractions. This means that 2/3 represents a larger portion of a whole compared to the other fractions.
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17.
What is the least common multiple of 6 and 15?
A.
60
B.
30
C.
90
D.
120
Correct Answer B. 30
Explanation The least common multiple (LCM) is the smallest multiple that two or more numbers have in common. To find the LCM of 6 and 15, we can list the multiples of each number and find the smallest one they have in common. The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ... and the multiples of 15 are 15, 30, 45, 60, ... The smallest multiple they have in common is 30, so the LCM of 6 and 15 is 30.
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18.
Evaluate 3/4 divided by 2/7
A.
21/8
B.
8/21
C.
21/2
D.
4/21
Correct Answer A. 21/8
Explanation To evaluate 3/4 divided by 2/7, we can multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 2/7 is 7/2. So, multiplying 3/4 by 7/2, we get (3/4) * (7/2) = (3 * 7) / (4 * 2) = 21/8. Therefore, the correct answer is 21/8.
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19.
What is the product of 5/6 and 1/5 in simplest form?
A.
1/6
B.
31/30
C.
6/11
D.
5/30
Correct Answer A. 1/6
Explanation To find the product of fractions, we multiply the numerators together and the denominators together. In this case, multiplying 5/6 and 1/5 gives us (5 * 1) / (6 * 5), which simplifies to 5/30. To simplify further, we can divide both the numerator and denominator by 5, resulting in 1/6. Therefore, the product of 5/6 and 1/5 in simplest form is 1/6.
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20.
Evaluate 15/16 - 15/26
A.
85/212
B.
95/221
C.
95/215
D.
75/208
Correct Answer D. 75/208
Explanation To evaluate 15/16 - 15/26, we need to find a common denominator. The least common multiple of 16 and 26 is 208. So, we can rewrite 15/16 as 195/208 and 15/26 as 120/208. Now, we can subtract the two fractions: (195/208) - (120/208) = 75/208. Therefore, the correct answer is 75/208.
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21.
Write in standard form.
3.7 x 10^{4}
Correct Answer 37,000 37000
Explanation The correct answer is 37,000,37000. This is the standard form of the number 3.7 x 104. In standard form, a number is written as a decimal number between 1 and 10 multiplied by a power of 10. In this case, 3.7 is the decimal number and 104 is the power of 10. To convert it to standard form, we move the decimal point 4 places to the right, resulting in 37,000. Then we add the zeros from the power of 10, giving us 37,000,37000.
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22.
Write 3/40 as a percent
A.
0.75%
B.
7.5%
C.
0.075%
D.
750%
Correct Answer B. 7.5%
Explanation To convert a fraction to a percent, you need to divide the numerator by the denominator and then multiply the result by 100. In this case, 3 divided by 40 equals 0.075. Multiplying 0.075 by 100 gives us 7.5%. Therefore, the correct answer is 7.5%.
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23.
The area of a square is 36 cm2. What is the perimeter of the square?
A.
18cm
B.
24cm
C.
16cm
D.
12cm
Correct Answer B. 24cm
Explanation The area of a square is found by multiplying the length of one side by itself. In this case, if the area is 36 cm2, then the length of one side is the square root of 36, which is 6 cm. Since a square has four equal sides, the perimeter is found by multiplying the length of one side by 4, which is 24 cm.
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24.
Given that side = 6 units, what is the perimeter of a square?
A.
36 units
B.
24 units
C.
12 units
D.
10 units
Correct Answer B. 24 units
Explanation The perimeter of a square is calculated by adding up the lengths of all its sides. Since all sides of a square are equal in length, we can find the perimeter by multiplying the length of one side by 4. In this case, the length of one side is given as 6 units. Therefore, the perimeter of the square would be 6 units x 4 = 24 units.
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25.
Given that the sides of a square is 9 units each, what is the perimeter of a square?
A.
13 units
B.
81 units
C.
18 units
D.
36 units
Correct Answer D. 36 units
Explanation The perimeter of a square is calculated by adding up the lengths of all its sides. In this case, since the sides of the square are given to be 9 units each, we can calculate the perimeter by multiplying the length of one side by 4 (since a square has four equal sides). Therefore, the perimeter of the square is 9 units x 4 = 36 units.
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26.
How many kilometers are in 90miles?
A.
144.83
B.
55.93
C.
165.83
D.
171.83
Correct Answer A. 144.83
Explanation The correct answer is 144.83. To convert miles to kilometers, we can use the conversion factor 1 mile = 1.60934 kilometers. So, to find how many kilometers are in 90 miles, we multiply 90 by 1.60934, which gives us 144.83 kilometers.
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27.
How many ounces are in 15 cups?
A.
120
B.
135
C.
85
D.
115
Correct Answer A. 120
Explanation There are 8 ounces in 1 cup. Therefore, to find the number of ounces in 15 cups, we multiply 15 by 8, which equals 120.
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28.
Approximately how many kilograms are there in 100 pounds?
A.
45
B.
450
C.
220
D.
22
Correct Answer A. 45
Explanation There are approximately 45 kilograms in 100 pounds.
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29.
How many centimers are in 6.9 inches?
A.
2.72
B.
17.53
C.
33.53
D.
39.53
Correct Answer B. 17.53
Explanation The correct answer is 17.53 because 1 inch is equal to 2.54 centimeters. To convert 6.9 inches to centimeters, we multiply 6.9 by 2.54, which equals 17.526. Rounded to two decimal places, the answer is 17.53 centimeters.
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30.
How many different security codes can be created if each code has 1 letter and 2 digits? (repeated letters and digits are allowed)
A.
2600
B.
6760
C.
126
D.
520
Correct Answer A. 2600
Explanation There are 26 letters in the alphabet and 10 digits (0-9). To create a code with 1 letter and 2 digits, we have 26 choices for the letter and 10 choices for each digit. Therefore, the total number of different security codes that can be created is 26 * 10 * 10 = 2600.
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31.
In how many different orders can 5 cars be parked on the road side?
A.
120
B.
240
C.
60
D.
30
Correct Answer A. 120
Explanation There are 5 cars that can be parked on the roadside. The number of different orders in which these cars can be parked can be calculated by using the concept of permutations. Since all 5 cars are distinct, the total number of different orders is equal to the factorial of 5, which is 5! = 5 x 4 x 3 x 2 x 1 = 120. Therefore, the correct answer is 120.
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32.
Use the distributive property to compute 12(4 + 7)
A.
132
B.
144
C.
108
D.
120
Correct Answer A. 132
Explanation To compute 12(4 + 7) using the distributive property, we need to distribute the 12 to both the 4 and the 7. This means multiplying 12 by each number separately and then adding the results. 12 multiplied by 4 is 48, and 12 multiplied by 7 is 84. Adding these two results together gives us 132. Therefore, the correct answer is 132.
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33.
Is 123 a rational number?
A.
Yes
B.
No
Correct Answer A. Yes
Explanation A rational number is a number that can be expressed as a fraction, where the numerator and denominator are both integers. Since 123 can be expressed as 123/1, it is a rational number.
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34.
Which of the following fractions is not equal to 5/2?
A.
5000/2000
B.
55/22
C.
15/6
D.
25/4
Correct Answer D. 25/4
Explanation The fraction 25/4 is not equal to 5/2 because when we simplify 25/4, we get 6 and 1/4, which is not equal to 5/2. Therefore, 25/4 is the correct answer.
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35.
Which of the following fractions is not in reduced form?
A.
49/50
B.
707/909
C.
49/64
D.
101/1001
Correct Answer B. 707/909
Explanation The fraction 707/909 is not in reduced form because both numbers have a common factor of 11. If we divide both the numerator and denominator by 11, we get the reduced form of the fraction, which is 64/83.
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36.
Which of the following fractions is NOT equivalent to 6?
A.
96/16
B.
60/10
C.
48/8
D.
72/9
Correct Answer D. 72/9
Explanation The fraction 72/9 is not equivalent to 6 because when simplified, it equals 8. The other fractions can be simplified to 6: 96/16 = 6, 60/10 = 6, and 48/8 = 6.
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37.
What is the product of 4/7 and 21/32 in simplest form?
A.
3/8
B.
28/39
C.
128/147
D.
12/32
Correct Answer A. 3/8
Explanation To find the product of two fractions, you simply multiply the numerators together and the denominators together. In this case, multiplying 4/7 by 21/32 gives (4*21)/(7*32) = 84/224. To simplify this fraction, you can divide both the numerator and denominator by their greatest common divisor, which is 28. Dividing 84 by 28 and 224 by 28 gives 3/8. Therefore, the product of 4/7 and 21/32 in simplest form is 3/8.
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38.
The equation (5 + 3) +8 = 5 + (3 + 8) is true by the....
A.
Associative property
B.
Distributive property
C.
Commutative property
Correct Answer A. Associative property
Explanation The equation (5 + 3) + 8 = 5 + (3 + 8) is true by the associative property. According to the associative property of addition, the grouping of numbers does not affect the sum. In this case, both sides of the equation have the same sum of 16, but the grouping of the numbers is different. The left side groups (5 + 3) first and then adds 8, while the right side groups (3 + 8) first and then adds 5. Despite the different grouping, the sum remains the same, demonstrating the associative property.
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39.
Is 11/23 in simplest form?
A.
No
B.
Yes
Correct Answer B. Yes
Explanation The fraction 11/23 is in simplest form because the numerator and denominator do not have any common factors other than 1. Therefore, it cannot be simplified any further.
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40.
Which of the following fractions is not equivalent to 3/7?
A.
33/77
B.
30/70
C.
14/9
D.
3000/7000
Correct Answer C. 14/9
Explanation The fraction 14/9 is not equivalent to 3/7 because the numerator (14) and denominator (9) have a common factor of 7, which means the fraction can be simplified further. In contrast, the other fractions cannot be simplified any further and are equivalent to 3/7.
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41.
Evaluate: 17/38 x 11/16
A.
196/614
B.
190/610
C.
193/616
D.
187/608
Correct Answer D. 187/608
Explanation The given expression is a multiplication of two fractions. To multiply fractions, we multiply the numerators together and the denominators together. In this case, the numerator is 17 multiplied by 11 which equals 187, and the denominator is 38 multiplied by 16 which equals 608. Therefore, the simplified fraction is 187/608.
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42.
Change 2 3/4 to a fraction.
A.
11/2
B.
11/4
C.
11/3
D.
11/6
Correct Answer B. 11/4
Explanation To change a mixed number like 2 3/4 to a fraction, we first convert the whole number part to a fraction by multiplying it by the denominator of the fraction part. In this case, 2 is the whole number and 4 is the denominator, so we have 2/1 * 4/4 = 8/4. Then, we add the fraction part to the converted whole number part, which gives us 8/4 + 3/4 = 11/4. Therefore, the correct answer is 11/4.
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43.
Which of the following fractions is the largest?
A.
490/890
B.
3/5
C.
100/9999
D.
1/2
Correct Answer B. 3/5
Explanation The fraction 3/5 is the largest because it represents a greater proportion of a whole compared to the other fractions. In other words, out of the given options, 3/5 is closest to 1, which is the highest possible value for a fraction. The other fractions are smaller in comparison.
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44.
Solve the proportion: r/8 = 7/56
A.
8
B.
1
C.
56
D.
7
Correct Answer B. 1
Explanation To solve the proportion r/8 = 7/56, we can cross multiply. Multiply the numerator of the first fraction (r) by the denominator of the second fraction (56) and multiply the denominator of the first fraction (8) by the numerator of the second fraction (7). This gives us r x 56 = 8 x 7. Simplifying further, we get 56r = 56. Dividing both sides by 56, we find that r = 1.
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45.
Evaluate 5.03 x 6.1
A.
30.683
B.
30.03
C.
11.13
D.
13.13
Correct Answer A. 30.683
Explanation The correct answer is 30.683 because when you multiply 5.03 by 6.1, you get the product of 30.683.
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46.
Simplify 3(2 + 20) - (3 + (2-3)^{2})
A.
60
B.
62
C.
70
D.
64
Correct Answer B. 62
Explanation To simplify the given expression, we start by solving the innermost parentheses first. (2 + 20) equals 22, and (2-3) equals -1. So, the expression becomes 3(22) - (3 + (-1)2). Then, we simplify the expression inside the parentheses, which gives us 3(22) - (3 + (-1)2) = 3(22) - (3 + (-1)2) = 3(22) - (3 + 1) = 3(22) - 4. Finally, we multiply 3 by 22, resulting in 66, and subtract 4 from it, giving us the final answer of 62.
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47.
Evaluate 96 / 12(4) / 2
A.
2
B.
1
C.
16
D.
8
Correct Answer C. 16
Explanation The expression 96 / 12(4) / 2 can be simplified by following the order of operations. First, we need to evaluate the expression within the parentheses: 12(4) equals 48. Then, we divide 96 by 48, which equals 2. Finally, we divide 2 by 2, resulting in 1. Therefore, the correct answer is 1.
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48.
Find ( 5 - x^{2} ) / x , when x = 2
A.
1/2
B.
3
C.
9/2
D.
1
Correct Answer A. 1/2
Explanation To find the value of (5 - x^2) / x when x = 2, we substitute x = 2 into the expression. Therefore, we have (5 - 2^2) / 2 = (5 - 4) / 2 = 1/2.