Practice equations...

Question 1

Simplify (2^-5 x 2^8)^2
Give your answer as a power of 2.

Answer 1

1) -5 + 8 = (2^3)^2
2) = 2^6

Question 2

There are 30 women and 20 men at the gym.

The mean height of all 50 people is 167.6 cm.
The mean height of the men is 182 cm.

Work out the mean height of the women.

Answer 2

1) (Total men) + (Total Women) Divided by 50
= 167.6 cm

2) (Total men) Divided by 20
= 182 cm

3) (total women) Divided by 30
= ?

4) 20 x 182 = 3640

5) 3640 + (total women)
= 8380

6) 8380 - 3640
= 4740

7) (total women)
= 4740

8) ; 3640 + 4740 divided by 50
= 176.6 cm

9) 4740 divided by 30
= 158 cm

10) Total mean height of woman
= 158 cm

Question 3

2.54 x 1.5

Answer 3

– 254 x 15 = 3810 , so 2.54 x 1.5 = 3.81

Question 4

x^5 x x^3

Answer 4

— ^5 + ^3 = x^8

Question 5

A cylinder has volume 100 cm^3, and height 5 cm.
What is the diameter?

Answer 5

(pi)r^2 5 = 100
– r^2 = 100 Divided by 5(pi)
–so, r = {20 Divided by (pi)} in a root
– = 2.52 cm.
– Diameter = 5.05 cm to 3sf

Question 6

Convert into standard form and multiply:
25 000 000 x 0. 000 000 000 24.

Answer 6

= (2.5 x 10^7) x (2.4 x 10^-10 )
= 6 x 10^-3