Ultimate Exam On Algebra! Trivia Quiz
Can you pass the ultimate exam on algebra? Algebra is interesting because either you love it or hate it. It is a branch of mathematics that substitutes letters for numbers, and an algebraic equation represents a scale where what is accomplished on one side is done to the other side, and the numbers act like consonants. So have some Phi, take this quiz and see if you are an algebra whiz!
- 1.
Evaluate: 8y + 5y
- A.
12y squared
- B.
-3y
- C.
13y
- D.
40y
- E.
40y squared
Correct Answer
C. 13yExplanation
When adding and subtracting in algebraic expressions, you are only able to add and subtract like terms. These are terms in which the variables are exactly the same. In this question, 8y + 5y, the variables are y and are both the same, therefore we can just add them together as a normal addition to get 13y.Rate this question:
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- 2.
Evaluate: 24s - 12s
- A.
36s
- B.
2
- C.
2s
- D.
12s squared
- E.
12s
Correct Answer
E. 12sExplanation
The variables in this equation are both s. This means they are like terms and we are able to subtract like a normal subtraction.Rate this question:
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- 3.
Evaluate: 7fg + 2gf
- A.
9gf
- B.
14fg squared
- C.
5gf
- D.
3gf
- E.
9
Correct Answer
A. 9gfExplanation
The variables in this question are also the same, being g and f. It does not matter which way around the variables is written, as long as they are both there. We then add like normal to get 9gf - 9fg is also acceptable.Rate this question:
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- 4.
Evaluate: 9jk - kj + 5jk
- A.
40jk
- B.
13jk
- C.
14jk
- D.
46jk
- E.
45kj
Correct Answer
B. 13jkExplanation
If we look at the algebraic expression, we can see that they have all like terms. If there is no numeral in front of the variable, you know that it is 1. Therefore the algebraic expression changes to 9jk - 1kj + 5jk, giving us the answer of 13jk.Rate this question:
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- 5.
Simplify, where possible: 10k + 2k + 8
- A.
20k
- B.
20k + 8
- C.
12k + 8
- D.
12k squared + 8
- E.
26k
Correct Answer
C. 12k + 8Explanation
First, we need to collect all our like terms. The only things we can add in this algebraic expression is 10k and 2k. This will leave us with the expression 12k + 8. Because 12k and 8 are not like terms, we cannot do anything else to simplify the answer.Rate this question:
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- 6.
4a + 6 -a
- A.
3a + 12
- B.
5a + 6
- C.
3a + 6
- D.
4a + -6
- E.
-4a + 6
Correct Answer
C. 3a + 6Explanation
4a and -a are our like terms in this algebraic expression. You can reword the question so -a is -1a. You then subtract 1a from 4a, to give the expression 3a + 6. These terms are not like and you can not do anything to simplify it more.Rate this question:
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- 7.
Simplify: 6k + 2k squared
- A.
8k squared
- B.
12k
- C.
6k + 2k squared
- D.
12k squared
- E.
8k
Correct Answer
C. 6k + 2k squaredExplanation
There are no like terms in this algebraic expression, therefore we can do nothing to simplify it.Rate this question:
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- 8.
Simplify: 8k - 2j + 2k + j
- A.
7j + k
- B.
-16kj + 2kj
- C.
10k - j
- D.
12k - 2j
- E.
7j
Correct Answer
C. 10k - jExplanation
We need to collect like terms in this algebraic expression. We change the expression to suit us. This means it will look like 8k + 2k -2j + j. 8k + 2k = 10k. -2j + j = -j. Therefore the answer is 10k - j.Rate this question:
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- 9.
Simplify: 3 x 3p
- A.
27p
- B.
9p squared
- C.
3p
- D.
3p squared
- E.
9p
Correct Answer
E. 9pExplanation
The terms do not have to be like to be able to multiply in algebra.Rate this question:
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- 10.
Simplify: 8p x 6k
- A.
48
- B.
2kp
- C.
14kp
- D.
64kp
- E.
48kp
Correct Answer
E. 48kpExplanation
The 8 and six were multiplied together and then along with it the p and k. In algebra, when multiplying algebraic expressions, we use shorthand notation. So, instead of writing k x p, we write kp.Rate this question:
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- 11.
Simplify: 15y ÷ 3
- A.
5
- B.
45y
- C.
18y
- D.
5y
- E.
3y
Correct Answer
D. 5yExplanation
When dividing, the algebraic expression is usually written as a fraction. In this case, we put 15y over 3 and find that it cancels to 5y.Rate this question:
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- 12.
33kjp ÷ 11pj
- A.
3jkp
- B.
11jkp
- C.
3k
- D.
3pj
- E.
3k squared
Correct Answer
C. 3kExplanation
When dividing, the algebraic expression is usually written as a fraction. This would be written as 33kjp over 11pj. You can instantly see that 33 ÷ 11 is 3, and the p and j cancel each other out. This leaves us with 3k.Rate this question:
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- 13.
7k + 2k ÷ 2
- A.
7k
- B.
8k
- C.
6k
- D.
10k
- E.
14k
Correct Answer
B. 8kExplanation
Using BODMAS, you do 2k ÷ 2 first, which equals k. 7k + k = 8k.Rate this question:
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- 14.
6 x 5k - 2k
- A.
20k
- B.
18k
- C.
30k
- D.
2k
- E.
28k
Correct Answer
E. 28kExplanation
Using BODMAS, you multiply 5k by six, equalling 30k. 30k minus 2k = 28k.Rate this question:
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- 15.
Find the value of 3k + j when: k = 2, j = 3
- A.
6
- B.
11
- C.
9
- D.
5
- E.
10
Correct Answer
C. 9Explanation
The first thing you should be doing is substituting the given values into the expression. For this question, you say 3 x 2 + 3. This equals 9.Rate this question:
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- 16.
Find the value of 8j ÷ k when: j = 8, k = 6
- A.
8
- B.
11
- C.
10
- D.
10 and two thirds
- E.
64
Correct Answer
D. 10 and two thirdsExplanation
First you must again subsititude the given values into the expression. This gives us 8 x 8 ÷ 6. 64 ÷ 6 is 10 and 2 thirds.Rate this question:
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- 17.
Find the value of x - y over k when: x = 20, y = 5, k = 3
- A.
8
- B.
7
- C.
15
- D.
5
- E.
3
Correct Answer
D. 5Explanation
The first thing you are doing is substituting the given values into the expression. This gives us 20 - 5 all over 3. This is equal to 15 ÷ 3, which gives us the answer 5.Rate this question:
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- 18.
Expand the following: 3(t -3)
- A.
3t - 3
- B.
3t - 9
- C.
-6t
- D.
3t + 3
- E.
3t + 9
Correct Answer
B. 3t - 9Explanation
The value outside the brackets needs to be multiplied by everything inside the brackets. 3 x t = 3t and 3 x -3 = -9. This gives the resulting answer 3t - 9.Rate this question:
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- 19.
Expand the following: 3(6 + 2k)
- A.
24
- B.
12k
- C.
18k + 6
- D.
24k
- E.
18 + 6k
Correct Answer
E. 18 + 6kExplanation
3 x 6 = 18, 3 x 2k = 6k. Therefore the answer is 18 + 6kRate this question:
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- 20.
Expand the following: -(3+2m)
- A.
3 + 2m
- B.
2m
- C.
-3 -2m
- D.
6m
- E.
-6m
Correct Answer
C. -3 -2mExplanation
You can change the question so it reads -1(3+2m). -1 x 3 = -3 and -1 x 2m = -2m. This gives us the answer -3 -2mRate this question:
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- 21.
Expand the following: -(10 - 2k)
- A.
12k
- B.
10 + -2k
- C.
-10 + 2k
- D.
20k
- E.
5k
Correct Answer
C. -10 + 2kExplanation
The expression can be written as -1(10 - 2k). -1 x 10 = -10, -1 x -2k = 2k (A negative number multiplyed by a negative number will equal a positive number). This gives us the answer -10 + 2k.Rate this question:
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- 22.
Factorise 9m + 12
- A.
3 (3m + 4)
- B.
3 (3 + 4)
- C.
1 (9m + 12)
- D.
1 (9 + 12)
- E.
4 (2m + 3)
Correct Answer
A. 3 (3m + 4)Explanation
To be able to factorize algebraic expressions, you need to find the HCF (highest common factor) In this equation the highest common factor is 3, so you put it outside the brackets. You find 3 needs to be multiplied by to get to 9m. The answer is 3m, so you put that in the brackets. Now you find what you need to do to get from 3 to 12. The answer is multiplied by positive 4. Inside the brackets now is 3m + 4. C is not correct because 1 is NOT the HCF.Rate this question:
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- 23.
Factorise: 3k + 6
- A.
3 (k + 6)
- B.
1 (3k + 6)
- C.
3 (k + 2)
- D.
3 (k + 18)
- E.
3 (2k + 2)
Correct Answer
C. 3 (k + 2)Explanation
First, you find the highest common factor, which is 3. You then factorize by using the previous question's explanation.Rate this question:
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- 24.
Simplify: w over 4 + 2w over 4.
- A.
3w over 4
- B.
4 over 3w
- C.
3 over 4
- D.
3 over 4w
- E.
2w over 4
Correct Answer
A. 3w over 4Explanation
The denominators are same, so we are able to add the two terms together.Rate this question:
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- 25.
4 over q + 5 over q
- A.
9 over q
- B.
Q over 9
- C.
20 over q
- D.
20 over q squared
- E.
-1 over q
Correct Answer
A. 9 over qExplanation
The denominators are the same, so we are able to simply add the numerators together.Rate this question:
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- 26.
P over 8 - 5 over 8
- A.
P over 8 - 5 over 8
- B.
P - 5 over 8
- C.
8 over p - 5
- D.
P + 5 over 8
- E.
5p over 8
Correct Answer
B. P - 5 over 8Explanation
The denominators are the same, so we are able to subtract the two, but since they are not like terms we leave it as p -5 over 8.Rate this question:
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- 27.
Simplify: d over e times e over g.
- A.
De over eg
- B.
D over g
- C.
G over d
- D.
Eg over de
- E.
Ed over eg
Correct Answer
B. D over gExplanation
We multiply d and e together, and e and g together. This gives us de over eg. We can cancel out the e's to give us d over g.Rate this question:
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- 28.
2 over x times 3 over x
- A.
X squared
- B.
6
- C.
3 x 2
- D.
6 over x squared
- E.
6 over x
Correct Answer
D. 6 over x squaredExplanation
We multiply 3 by 2 and x by x. This leaves us with 6 over x squared.Rate this question:
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