Number and Algebra

Question 1

What are natural numbers?

Answer 1

Positive whole numbers

Question 2

What are integers?

Answer 2

Whole numbers including negatives and zero

Question 3

What are rationals?

Answer 3

Numbers which can be written as fractions in their simplest form

Question 4

What are irrationals?

Answer 4

Numbers which can’t be written as fractions

Question 5

What are reals?

Answer 5

The rationals and irrationals put together. The reals will include every possible number you could meet in the course

Question 6

What does this symbol mean ‘N’

Answer 6

Natural numbers

Question 7

What does this symbol mean ‘Z’

Answer 7

Integers

Question 8

What does this symbol mean ‘Q’

Answer 8

Rationals

Question 9

What does this symbol mean ‘I’

Answer 9

Irrationals

Question 10

What does this symbol mean ‘P’

Answer 10

Reals

Question 11

Are recurring decimals rational numbers?

Answer 11

Recurring decimals can always be written as fractions so they are rational numbers

Question 12

Are terminating decimals rational numbers?

Answer 12

Terminating decimals can be written as fractions so they are rational numbers

Question 13

Are non-recurring, non-terminating decimals rational numbers?

Answer 13

Non-recurring, non-terminating decimals (i.e. they carry on forever + never repeat) can never be written as a fraction so they are irrational numbers

Question 14

A coat costs $300 including 5% sales tax. What is the cost of the coat before tax?

Answer 14

300 / 1.05 = 285.71

Question 15

What should you do when asked to calculate an estimate?

Answer 15

When asked to calculate an estimate, round the numbers to 1 s.f.

Question 16

What is 2^1?

Answer 16

2

Question 17

What is 2^0?

Answer 17

1

Question 18

What does a negative power mean?

Answer 18

A negative power means ‘take the reciprocol’

Question 19

What does a^-n mean?

Answer 19

1 / a^n

Question 20

Which is the power and which is the root?

3^-(2/5)

Answer 20

Remember a carrot
The roots are at the bottom
The power from the sun is at the top

2 = power
5 = root

Question 21

Why is standard form useful for converting units?

Answer 21

e.g. To convert kilometres to millimetres, you need to multiply by 1000 and 1000 again, ie. by 10^6.

So 4km = 4 x 10^6mm

Question 22

How many cm^2 is 4m^2 ?

Answer 22

4m^2 = 4 x 100 x 100 = 40,000cm^2

Question 23

How many mm^2 is 3.1cm^2 ?

Answer 23

3.1cm^3 = 3.1 x 10 x 10 x 10 = 3100mm^3

Question 24

What is 1ml in cm?

Answer 24

1ml = 1cm^3

Question 25

How many cm^3 in 1 litre?

Answer 25

1 litre = 1000 cm^3

Question 26

How do you convert a speed of 65km per hour into metres per second (m/s) ?

Answer 26

• In 1 hour, the no. of metres travelled will be a bigger number than the no. of km // so multiply by 1000
• In 1 second, the distance travelled will be less than in 1 hours, so divide by 3600
• 65kmh = (65x1000)/3600 = 18.1m per second

Question 27

How do you estimate an answer ?

Answer 27

By using 1sf throughout