Estimation and approximation

By rounding each number to 1 significant figure, estimate the value of

You must show your working.

Is your answer to part (a) an overestimate or an underestimate? Tick one box.

Give a reason for your answer.

By rounding each number to one significant figure,

You must show your working.

Here is a triangle.

Sam attempts to find the value of cos x using the cosine rule.

Identify two errors Sam has made.

To the nearest pound, Rosie has £12 She wants to buy 6 drinks. Each drink costs £1.89

Show that Rosie definitely has enough money to buy the 6 drinks.

To the nearest pound, Rosie has £12 She wants to buy 6 drinks. Each drink costs £1.89

Show that Rosie definitely has enough money to buy the 6 drinks.

Between which two consecutive integers does the square root of 210 lie?

Here are two calculations, A and B.

Use approximations to show that answer to A answer to B

Connor is estimating the answer to 385 + 1479

He rounds each number to the nearest 10

Work out his estimate.

Connor says, “My estimate will be more than the exact answer.”

How does he know this without working out the exact answer ?

Millie is estimating the value of

She rounds each decimal number to 1 significant figure.

Work out Millie’s estimate. You must show your working.

Millie says, “My estimate must be more than the exact value.” Without working out the exact value, give a reason how she can know this.

Millie is estimating the value of

She rounds each decimal number to 1 significant figure.

Work out Millie’s estimate. You must show your working.

Millie says, “My estimate must be more than the exact value.” Without working out the exact value, give a reason how she can know this.

By rounding each number to the nearest 10, estimate the value of 31 × 18

His answer is 37.65 By rounding each number to the nearest 10, show that his answer is incorrect.

By rounding each number to the nearest 10, estimate the value of 262 ÷ 19.8

The triangular cross section of a prism is an isosceles right-angled triangle.

Use approximations to estimate the value of x. You must show your working.

Circle the number that is closest to the value of 29³

27 000 90 2700 9000

An approximation for the value of π is given by

Use your calculator to show that this approximation is within 0.1 of 3.14

An approximation for the value of π is given by

Use your calculator to show that this approximation is within 0.1 of 3.14

5 50 500 5000

Use your calculator to work out 9.95² × 29.8 Give your answer as a decimal. Write down your full calculator display.

Is your answer to part (a) sensible? Use approximations to decide. You must show your working.

Tick a box.

The solution of 3^x = 300 lies between two consecutive integers. Work out the two integers.

Use approximations to 1 significant figure to estimate the value of

You must show your working.

Use approximations to 1 significant figure to check if your answer to part (a) is sensible.

By rounding each number to the nearest 10,

You must show your working.