1. © T Madas

2. Look at the following expressions: 2ab + 2bc + 2ac abc 4(a + b + c ) Suppose that a, b and c are measuring lengths, while the numbers 2 and 4 have no units. Which expression could represent: a length? an area? a volume? Adding/subtracting lengths:gives another length Adding/subtracting areas:gives another area Adding/subtracting volumes:gives another volume Multiplying 2 lengths:gives an area Multiplying 3 lengths:gives a volume Multiplying area by length:gives a volume L x L x L=volume L+L+L=length x 4 2 and 4 have no units =length L x L =area x 2 =

3. © T Madas Look at the following expressions: 2ab + 2bc + 2ac abc 4(a + b + c ) Adding/subtracting lengths:gives another length Adding/subtracting areas:gives another area Adding/subtracting volumes:gives another volume Multiplying 2 lengths:gives an area Multiplying 3 lengths:gives a volume Multiplying area by length:gives a volume volume adding all edges surface area a b c

4. © T Madas The shape opposite is an ellipse. Which of the following expressions could give the area of this shape? a b Adding/subtracting lengths:gives another length Adding/subtracting areas:gives another area Adding/subtracting volumes:gives another volume Multiplying 2 lengths:gives an area Multiplying 3 lengths:gives a volume Multiplying area by length:gives a volume a and b are lengths π has no units

5. © T Madas Adding/subtracting lengths:gives another length Adding/subtracting areas:gives another area Adding/subtracting volumes:gives another volume Multiplying 2 lengths:gives an area Multiplying 3 lengths:gives a volume Multiplying area by length:gives a volume The shape opposite is an ellipse. Which of the following expressions could give the area of this shape? a b a and b are lengths π has no units

6. © T Madas

7. NeitherVolumeAreaLength In the following expressions x and y are lengths. All other numbers are dimensionless. Place each expression in the appropriate column.

8. © T Madas

9. The expressions below can be used to calculate lengths, areas or volumes of some shapes. The letters p, q and r represent lengths. π and 2 are numbers and have no dimensions. Circle each of the three expressions that can be used to calculate an area. π (p + q ) rq (p + q ) 2r2rq (r – q ) π pq pq r qr 2 pr 2 2 π pqr 2 πp 2rπp 2r

10. © T Madas

11. 7r 2hL7r 2hL 3πr 3h4L3πr 3h4L π rh The table below contains three algebraic expressions where r, L and h are lengths. The numbers 3, 4, 7 and π are dimensionless. Put a tick in the correct box to show whether each expression can be used for the calculation of length, area, volume or none of these. None of theseVolumeAreaLengthExpression

12. © T Madas

13. 2(r + L ) 2 h 4πr 43L4πr 43L 3rL The table below contains three algebraic expressions where r, L and h are lengths. The numbers 2, 3, 4 and π have no units. Put a tick in the correct box to show whether each expression can be used for calculating length, area, volume or none of these. None of theseVolumeAreaLengthExpression

14. © T Madas

15. The expressions below can be used to calculate lengths, areas or volumes of some shapes. The letters r and h represent lengths. The numbers 2, 3, 5 and π are dimensionless. Circle each of the three expressions that can be used to calculate an area. r (π + 2)r (π + 2) r (r + 5h ) 2πr 32πr 3 π (2h – r ) π rh r + h 3 3r 3h3r 3h 2r 332r 33 2πr 2h2πr 2h (r + h) 2 2r

16. © T Madas

17. Look at the table of expressions below. The letters a, b and h represent lengths. π a nd 2 are numbers that have no dimensions. Tick the boxes underneath the three expressions which could represent areas. ab h 2πa 22πa 2 (a + b 2 )h 2πa 32πa 3 π ab 2(a 2 + b 2 ) π ab 2

18. © T Madas

19. Look at the algebraic expression below, representing a volume: x n (x + y ) x and y are lengths and n is a number. What is the value of n ? Adding/subtracting lengths:gives another length x n (+x ) y Multiplying 2 lengths:gives an area Multiplying 3 lengths:gives a volume Multiplying area by length:gives an volume L A L x L 2

20. © T Madas