Numeracy Unit 1 - Higher Tier

A standard piece of A4 paper is usually 0.08 mm thick.

What is 0.08 mm written in metres in standard form?

• 8 × 10⁴

• 8 × 10 ^{– 4}

• 8 × 10^–3

• 8 × 10^–5

A piece of card is 1 mm thick.

A stack of these pieces of card is 3 × 10^–2 metres high.

Calculate how many pieces of card there are in the stack.

In 2012 it was recorded that,

 

• the total mass of the paper used for printing newspapers, in the world, was

              2.88 × 10⁷ tonnes,

 

            • the world population was approximately 7.2 × 10⁹ people.

 

Use this information to calculate the mass of paper per person used to print newspapers in 2012.

Jade’s new suitcase weighs 3 kg.

When it is packed, her suitcase must not weight more than 25 kg altogether.

What percentage of the 25 kg does Jade have left for packing?

On a building site, 4 bricklayers were able to lay 2000 bricks in 8 hours.

To complete the work on time, bricklayers will need to lay 9000 bricks in 10 hours. Calculate how many bricklayers would be needed to lay 9000 bricks in 10 hours.

Inside one of the boxes is an old clock.

Gwilym takes the clock to be valued.

It is valued at £56.

The clock has decreased in value by 30% from last year.

Calculate how much the clock was worth last year.

9. The voltage, V volts, of an electric circuit is given by the formula

V = IR,

where I is the current measured in amps, and R is the resistance measured in ohms.

During an experiment,

• V was measured at 280 volts, correct to the nearest 10 volts,

• I was measured at 0∙2 amps, correct to the nearest 0∙1 amps.

Calculate the least possible value of the resistance R.

9. The voltage, V volts, of an electric circuit is given by the formula

V = IR,

where I is the current measured in amps, and R is the resistance measured in ohms.

During an experiment,

• V was measured at 280 volts, correct to the nearest 10 volts,

• I was measured at 0∙2 amps, correct to the nearest 0∙1 amps.

Calculate the greatest possible value of the resistance R.

Jade needs a new passport photograph.

A passport photograph must be 45 mm high by 35 mm wide.

Jade has a mathematically similar photograph that she could reduce in size to use as

her new passport photograph.

The height of this photograph is 9 cm.

Calculate the width of this photograph.

Give your answer in cm.

A decorative glaze covers the surfaces of each vase.

The glaze covers an area of:

• 400 cm2 on the smaller vase,

• 3600 cm2 on the larger vase.

The height of the larger vase is 48 cm.

Calculate the height of the smaller vase.