1.
Evaluate: 8y + 5y
Correct Answer
C. 13y
Explanation
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.
2.
Evaluate: 24s - 12s
Correct Answer
E. 12s
Explanation
The variables in this equation are both s. This means they are like terms and we are able to subtract like a normal subtraction.
3.
Evaluate: 7fg + 2gf
Correct Answer
A. 9gf
Explanation
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.
4.
Evaluate: 9jk - kj + 5jk
Correct Answer
B. 13jk
Explanation
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.
5.
Simplify, where possible: 10k + 2k + 8
Correct Answer
C. 12k + 8
Explanation
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.
6.
4a + 6 -a
Correct Answer
C. 3a + 6
Explanation
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.
7.
Simplify: 6k + 2k squared
Correct Answer
C. 6k + 2k squared
Explanation
There are no like terms in this algebraic expression, therefore we can do nothing to simplify it.
8.
Simplify: 8k - 2j + 2k + j
Correct Answer
C. 10k - j
Explanation
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.
9.
Simplify: 3 x 3p
Correct Answer
E. 9p
Explanation
The terms do not have to be like to be able to multiply in algebra.
10.
Simplify: 8p x 6k
Correct Answer
E. 48kp
Explanation
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.
11.
Simplify: 15y ÷ 3
Correct Answer
D. 5y
Explanation
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.
12.
33kjp ÷ 11pj
Correct Answer
C. 3k
Explanation
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.
13.
7k + 2k Ã· 2
Correct Answer
B. 8k
Explanation
Using BODMAS, you do 2k ÷ 2 first, which equals k. 7k + k = 8k.
14.
6 x 5k - 2k
Correct Answer
E. 28k
Explanation
Using BODMAS, you multiply 5k by six, equalling 30k. 30k minus 2k = 28k.
15.
Find the value of 3k + j when:
k = 2, j = 3
Correct Answer
C. 9
Explanation
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.
16.
Find the value of 8j ÷ k when:
j = 8, k = 6
Correct Answer
D. 10 and two thirds
Explanation
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.
17.
Find the value of x - y over k when:
x = 20, y = 5, k = 3
Correct Answer
D. 5
Explanation
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.
18.
Expand the following: 3(t -3)
Correct Answer
B. 3t - 9
Explanation
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.
19.
Expand the following: 3(6 + 2k)
Correct Answer
E. 18 + 6k
Explanation
3 x 6 = 18, 3 x 2k = 6k. Therefore the answer is 18 + 6k
20.
Expand the following: -(3+2m)
Correct Answer
C. -3 -2m
Explanation
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 -2m
21.
Expand the following: -(10 - 2k)
Correct Answer
C. -10 + 2k
Explanation
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.
22.
Factorise 9m + 12
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.
23.
Factorise: 3k + 6
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.
24.
Simplify: w over 4 + 2w over 4.
Correct Answer
A. 3w over 4
Explanation
The denominators are same, so we are able to add the two terms together.
25.
4 over q + 5 over q
Correct Answer
A. 9 over q
Explanation
The denominators are the same, so we are able to simply add the numerators together.
26.
P over 8 - 5 over 8
Correct Answer
B. P - 5 over 8
Explanation
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.
27.
Simplify: d over e times e over g.
Correct Answer
B. D over g
Explanation
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.
28.
2 over x times 3 over x
Correct Answer
D. 6 over x squared
Explanation
We multiply 3 by 2 and x by x. This leaves us with 6 over x squared.