The following quiz will test your knowledge of algebra prerequisites.
The questions are listed and numbered first, with the solutions listed and numbered after the end of the quiz.
Work through the problems, record your answers, and then use the solutions to grade yourself to see if you are ready for the next quiz (or if you need to review some of the algebra prerequisites).
Or, if you think this quiz is too easy, you can skip ahead to Quiz 2 (Basic Algebra).
Questions
1.) Which of the following sets does the number -5 belong to?
A. Integers
B. Rational numbers
C. Real numbers
D. All of the above
2.) Evaluate the following expression: (2 + 3)*(4 + 5)
A. 17
B. 25
C. 29
D. 45
3.) Evaluate the following expression: (1 + 23)*11 – 8
A. 69
B. 91
C. 81
D. 59
4.) Which of the following numbers is largest: 3/4, 2/3, 7/10, 4/5
A. 3/4
B. 2/3
C. 7/10
D. 4/5
5.) The number 5-2 is equivalent to which of the following?
A. 1/5
B. 1/25
C. -25
D. -10
6.) What is the perimeter of a square with side length 6?
A. 6
B. 12
C. 24
D. 36
7.) What is the area of a square with side length 10?
A. 10
B. 20
C. 40
D. 100
8.) What is the value when we add the fractions (2/5) + (3/4)?
A. 5/9
B. 5/20
C. 6/20
D. 23/20
9.) What is the decimal value of the fraction 2/5?
A. 0.2
B. 0.4
C. 0.5
D. 2.5
10.) Which fraction is equivalent to the decimal value 0.025?
A. 25/10
B. 1/25
C. 1/40
D. 25/100
11.) What percentage is 15 out of 60?
A. 20%
B. 25%
C. 30%
D. 15%
12.) What is 24% of 200?
A. 24
B. 36
C. 48
D. 52
13.) What fraction is equivalent to 0.08 / 0.4?
A. 2
B. 0.2
C. 0.02
D. 0.032
14.) What is the value of 27?
A. 64
B. 128
C. 256
D. 14
15.) A recipe calls for 2 cups of sugar for every 3 cups of flour. How many cups of flour would you need if you used 6 cups of sugar?
A. 4
B. 6
C. 8
D. 9
Solutions
Ready to see how you did? Here is the answer key for the quiz (solutions follow):
| Question | Answer |
|---|---|
| 1 | D |
| 2 | D |
| 3 | B |
| 4 | D |
| 5 | B |
| 6 | C |
| 7 | D |
| 8 | D |
| 9 | B |
| 10 | C |
| 11 | B |
| 12 | C |
| 13 | B |
| 14 | B |
| 15 | D |
Below, you can find the solutions and explanations for the quiz.
1.) Which of the following sets does the number -5 belong to?
A. Integers
B. Rational numbers
C. Real numbers
D. All of the above
The correct answer is D.
It is true that the number -5 is an integer (a whole number with no fraction or decimal part).
However, -5 can also be written as a fraction (-5 = -5/1), which means -5 is a rational number
Finally, every rational number is also a real number, so -5 is a real number.
Thus, -5 is in all 3 sets: integers, rational numbers, and real numbers.
2.) Evaluate the following expression: (2 + 3)*(4 + 5)
A. 17
B. 25
C. 29
D. 45
The correct answer is D.
We need to use the order of operations (PEMDAS) here.
Remember that PEMDAS stands for:
P = parentheses
E = exponents
M = multiplication
D = division
A = addition
S = subtraction
PEMDAS helps us to remember which operations to perform first (precedence).
Remember that M and D have the same “precedence”, so we work left to right.
Also, A and S have the same “precedence”, so we work left to right.
First, we do the calculations inside parentheses (P), always working from left to right.
This gives us:
(2 + 3)*(4 + 5)
=(5)*(4 + 5)
=(5)*(9)
Now, we do multiplication (M):
5*9
=45
3.) Evaluate the following expression: (1 + 23)*11 – 8
A. 69
B. 91
C. 81
D. 59
The correct answer is B.
As before, we need to use the order of operations (PEMDAS) here.
First, we do the calculations inside parentheses (P), always working from left to right.
Inside the parentheses, we must calculate exponents (E) first, and then addition (A).
This gives us:
(1 + 23)*11 – 8
=(1 + 8)*11 – 8
=(9)*11 – 8
Now, we do multiplication (M):
9*11 – 8
=99 – 8
Finally, we do subtraction (S):
99 – 8
=91
4.) Which of the following numbers is largest: 3/4, 2/3, 7/10, 4/5
A. 3/4
B. 2/3
C. 7/10
D. 4/5
The correct answer is D.
It is difficult to compare fractions with different denominators. We have two choices: compare fractions with the same denominator (by finding a common denominator) or compare numbers by converting to decimals.
In this case, we will convert to decimals to get an idea of how big each fraction is:
3/4 as a decimal is 0.75
2/3 as a decimal is 0.6666…
7/10 as a decimal is 0.7
4/5 as a decimal is 0.8
Out of these, 0.8 is the largest decimal value, so 4/5 is the largest fraction.
5.) The number 5-2 is equivalent to which of the following?
A. 1/5
B. 1/25
C. -25
D. -10
The correct answer is B.
Remember that the reciprocal of a number N is 1/N (the reciprocal is undefined for a = 0).
Here, 5-2 has a negative exponent. A number with a negative exponent tells us to take the reciprocal of the number and make the exponent positive (that is, 1 divided by the number with a positive exponent).
So, 5-1 would mean the reciprocal of 51, which is 1/51 or 1/5.
In this case, 5-2 means the reciprocal of 52, which is 1/52 or 1/25.
6.) What is the perimeter of a square with side length 6?
A. 6
B. 12
C. 24
D. 36
The correct answer is C.
Remember that a square is a geometric shape with 4 right angles and 4 sides of equal length.
So, all four sides of this square have a length of 6.
The perimeter of a square is the sum of all side lengths (or 4 times the side length).
Here, we get a perimeter of 6 + 6 + 6 + 6 = 4*6 = 24.
Note: no units were specified here, but the units for perimeter are linear (for example, inches, feet, yards, meters, etc.)
7.) What is the area of a square with side length 10?
A. 10
B. 20
C. 40
D. 100
The correct answer is D.
Again, recall that a square is a geometric shape with 4 right angles and 4 sides of equal length.
So, all four sides of this square have a length of 10.
The area of a square is the length multiplied by the width, or the side length squared.
Here, we get an area of 10*10 = 102 = 100.
Note: no units were specified here, but the units for area are square (for example, square inches, square feet, square yards, square meters, etc.)
8.) What is the resulting value when we add the fractions (2/5) + (3/4)?
A. 5/9
B. 5/20
C. 6/20
D. 23/20
The correct answer is D.
Remember that we cannot just add numerators or denominators. To add fractions, we need a common denominator.
After we find the common denominator, we convert the fractions to a form that uses the common denominator.
Then, we add the numerators and use the common denominator to get the sum of the fractions.
Here, the denominators are 5 and 4, so the common denominator is 20 (5*4 = 20).
Next, we convert both fractions to use the common denominator of 20:
(2/5)*(4/4) = 8/20
(3/4)*(5/5) = 15/20
So, the fraction 2/5 is equivalent to 8/20 and the fraction 3/4 is equivalent to 15/20.
Now that we have a common denominator, we can add the fractions:
(2/5) + (3/4)
=(8/20) + (15/20)
=(8 + 15)/20
=23/20
Note that we can also write the fraction 23/20 as the decimal value 1.15.
9.) What is the decimal value of the fraction 2/5?
A. 0.2
B. 0.4
C. 0.5
D. 2.5
The correct answer is B.
There are two approaches to convert a fraction to a decimal. One way is to do long division by dividing the denominator into the numerator (here, 5 into 2.0).
The other method is to convert to a denominator of 100, which we will use here.
The denominator of 2/5 is 5, so we need to multiply by 20 to get a denominator of 100:
(2/5)*(20/20) = 40/100
Now, we can move the decimal point two places to the left (in both the numerator and denominator) to get a decimal:
40/100 = 0.4/1.00 = 0.4
Remember that any number divided by 1 is just the number itself.
10.) Which fraction is equivalent to the decimal value 0.025?
A. 25/10
B. 1/25
C. 1/40
D. 25/100
The correct answer is C.
There are two approaches here. One is to convert the fraction in each answer to a decimal and see which one equals 0.025.
The other method is to convert the decimal 0.025 to a fraction without decimals, which is the method we will use here.
To convert 0.025 to a fraction without decimals, start by writing it as a fraction with a denominator of 1:
0.025 = 0.025/1
Now, we want to move the decimal point three places to the right (in both the numerator and denominator):
0.025/1 = 25/1000
Now, we want to reduce this fraction as much as possible (since it does not match any answers in its current form).
We know that 5 goes into 25, and 5 also goes into 1000, so:
25/1000 = 5*5/5*200 = 5/200
We know that 5 also goes into 200, so:
5/200 = 5*1/5*40 = 1/40
This fraction cannot be reduced any further, and it matches an answer choice, so we can stop here.
11.) What percentage is 15 out of 60?
A. 20%
B. 25%
C. 30%
D. 15%
The correct answer is B.
To find a percentage, we take the part (numerator) and divide by the whole (denominator). Then, we convert the resulting fraction or decimal to a percentage.
Here, the part is 15, and the whole is 60, so we get the fraction 15/60.
We can see that 15 goes into 60, so:
15/60 = 15*1/15*4 = 1/4
We can do long division (4 into 1.0) to get 0.25 and then convert 0.25 to the percentage 25%, which is our answer.
Remember that to convert a decimal to a percent, we move the decimal point 2 places to the right.
So 0.2 is 20%, 0.02 is 2%, and 0.002 is 0.2%.
12.) What is 24% of 200?
A. 24
B. 36
C. 48
D. 52
The correct answer is C.
To find a percentage of a number, convert the percent to a fraction or decimal, and then multiply by the number you want a percentage of.
Here, 24% is 0.24 (move the decimal point two places to the left to convert a percent to a decimal).
Then, multiply the decimal 0.24 by 200 to get:
0.24*200 = 48
We could also use the literal definition of percent (“per centum” or “out of 100”) to calculate:
24% of 200
(24/100)*(200)
=24*(200/100)
=24*2
=48
13.) What fraction is equivalent to 0.08 / 0.4?
A. 2
B. 0.2
C. 0.02
D. 0.032
The correct answer is B.
We can do long division here (0.4 into 0.08), or we can move decimal points in both the numerator and denominator to get a fraction without decimals.
Here, we need to move the decimal point 2 places right in both the numerator and denominator to get:
0.08/0.4 = 8/40
We know that 8 goes into 40, so we can reduce the fraction to:
8/40 =8*1/8*5 = 1/5
To go from 5 to 100, we would multiply by 20. So, we multiply by 20 in both the numerator and denominator to get:
(1/5)*(20/20) = 20/100
Finally, we can move the decimal points 2 places left to get:
20/100 = 0.2/1 = 0.2
14.) What is the value of 27?
A. 64
B. 128
C. 256
D. 14
The correct answer is B.
Remember that 27 means 2, multiplied by itself 7 times.
So 27 = 2*2*2*2*2*2*2.
We can list out powers of 2 (doubling every time we increase the exponent by 1) to avoid any errors:
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
15.) A recipe calls for 2 cups of sugar for every 3 cups of flour. How many cups of flour would you need if you used 6 cups of sugar?
A. 4
B. 6
C. 8
D. 9
The correct answer is D.
This problem involves the use of proportions. We will use cups of sugar in the numerator of each fraction and cups of flour in the denominator of each fraction.
So, the standard recipe is 2 cups of flour to 3 cups of sugar, or 2/3.
We have 6 cups of sugar to use, and we need x cups of flour (x is unknown).
So, 2/3 = 6/x.
After we cross multiply, we get 2x = 3*6, or 2x = 18, which means x = 9.
So, if we use 6 cups of sugar, we must use 9 cups of flour in order to follow the proportion of sugar to flour in the original recipe.
How did you do? If you are not satisfied with your score (or you want to review for more mastery), you can check out the algebra review here. [text link to algebra review]
If you are confident with your score on the Algebra Prerequisites quiz, then go ahead and take the Basic Algebra quiz here to see where you stand. [text link to basic algebra quiz]