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If I have x pencils and you have twice as many, how many pencils have you got?
Level 3-4 Algebra - Expressions
In your KS3 Maths lessons, you've probably encountered expressions. These are super important in algebra and overall in maths.
Algebra is like a secret code using symbols, often letters, to stand in for unknown numbers, called variables. These variables can change, or vary, depending on the situation. When you write down a situation as a maths sentence, it becomes an expression.
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1 .
Peter has x brothers, Paul has y brothers and Graham has z brothers. Between the three boys, how many brothers have they got?
xyz
x + y + z
x + y - z
x - y + z
Don't get baffled by complicated wording - often the answer is easier than you think
2 .
Simplify 4a + 5b + 6b + 11a
26ab
15a2 + 11b2
15a + 11b
9a + 17b
Here we are adding numbers together, NOT multiplying them together
3 .
Suzie is x years old and she has a sister called Rosie who is four years older. Rosie's mother was 28 when Rosie was born. How old is Rosie's mother now?
7x
x + 28
x - 4
x + 32
If you got the answer wrong then think carefully through each aspect of the question. Rosie's mother was 28 when Rosie was born. 4 years later, Suzie was born. Suzie is now x years old so Rosie's mother's age is now
28 + 4 + x = 32 + x
28 + 4 + x = 32 + x
4 .
What is the simplification of 3a + 4b + 6c + 3a - 6c - a - 3b?
4a + 2b - 3c
5a + b
6a - 3b
9a - 2b - c
Be careful to account for all the a's, then all the b's and then all the c's. In this case + 6c and - 6c cancel each other out and therefore they do not appear in the simplification
5 .
Simplify 5a + 7a.
12a
12aa
57a
57aa
Let us suppose that a = 3. (5 x 3) + (7 x 3) = 36. This is the same as saying 12 x 3 (12a) = 36
6 .
Which of the following is not a mathematical expression?
6
6a x 14
5a - 4b +16c x 8d
Oh my gosh!
The correct answer might well be an English expression but it is NOT a mathematical one!
7 .
Which of these is a simplification of 2a x 3a?
5a
6a
23aa
6a2
You must multiply the numbers together AND the letters. Remember a x a = a2
8 .
In an algebraic expression letters are often used to represent what?
Other letters
Only numbers greater than 1
Only numbers less than 1
Values
A letter can be used in place of any number - especially if the number has not yet been worked out
9 .
Jane is c years old and her sister Katie is three years younger so how old is Katie?
c3
c + 3
c - 3
c - 3 - 3
If she is younger then her age is less than. 3 less than is the same as minus 3
10 .
If I have x rabbits and you have twice as many, how many rabbits have you got?
2x
2 + x
2 - x
x2
You have two times the number that I have got and 2 times x is the same as 2x
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