Algebra (foundation)

Question 1

Write down an algebraic expression for five more than eight multiplied by x

Answer 1

8x + 5

Question 2

A boy went shopping with £A. He spent £B. How much has he got left?

Answer 2

£(A - B)

Question 3

Simplify

5t x 3t

Answer 3

15t²

Question 4

Simplify

3i + 2k – i + k

Answer 4

2i + 3k

Question 5

Simplify

5x² + 6x² – 7y + 4 + 2y

Answer 5

11x² – 5y + 4

Question 6

Expand

2(5 - 3w)

Answer 6

10 - 6w

Question 7

Expand

3p(4p³ - 5m)

Answer 7

12p⁴ - 15mp

Question 8

Expand and Simplify

3(4 + t) + 2(5 + t)

Answer 8

22 + 5t

Reasoning:

12 + 3t + 10 + 2t

=22 + 5t

Question 9

Expand and Simplify

t(3t – 4) + 3t(3 + 2t)

Answer 9

9t² + 5t

Reasoning:

3t² – 4t + 9t + 6t²

= 9t² + 5t

Question 10

Factorise

6m + 12t

Answer 10

6(m + 2t)

Reasoning:

The highest common factor of 6 and 12 is 6. There are no common letters.

Question 11

Factorise

6p² – 9pt

Answer 11

3p(2p – 3t)

Reasoning:

The highest common factor of 6 and 9 is 3. Both terms have a p as a common letter.

Question 12

Factorise

8ab² + 2ab – 4a²b

Answer 12

2ab(4b + 1 – 2a)

Reasoning:

The highest common factor of 8, 2 and 4 is 2. All the terms have an a and a b in common.