 # Exam-Style Questions.

## Problems adapted from questions set for previous Mathematics exams.

### 1.

GCSE Higher

A builder needs to lift a steel block. It is a cuboid with dimensions 2 m by 0.2 m by 0.2 m. Steel has a density of 7.6 g/cm3.

The builder's lifting gear can lift a maximum load of 500 kg. Can the lifting gear be used to lift the steel block?

### 2.

GCSE Higher

The density of lemon juice is 1.15 grams per cubic centimetre.

The density of lime juice is 1.25 grams per cubic centimetre.

The density of soda water is 0.97 grams per cubic centimetre.

400cm3 of a lemon and lime drink are made by mixing 30cm3 of lemon juice with 30cm3 of lime juice and then soda water is added to make up the rest of the drink.

Find the density of the lemon and lime drink correct to two decimal places.

### 3.

GCSE Higher

Strat drove from Wolverhampton to London via Coventry.

• The distance from Wolverhampton to Coventry is 56 km.
• The distance from Coventry to London is 156 km.
• Strat's average speed from Wolverhampton to Coventry was 63 km/h.
• Strat took 90 minutes to drive from Coventry to London.

(a) Work out Strat's average speed for his total drive from Wolverhampton to London.

Raven drove from Bedrock to Springfield via South Park.

• Raven's average speed from Bedrock to South Park was 70 km/h.
• Her average speed from South Park to Springfield was 50 km/h.

Raven says that the average speed from Bedrock to Springfield can be found by working out the mean of 70 km/h and 50 km/h.

(b) If Raven is correct, what does this tell you about the two parts of Raven's journey?

### 4.

GCSE Higher

A batch of coins is made from an alloy consisting of 270g of copper mixed with 90g of nickel.

• The density of copper is 9.0g/cm3.
• The density of nickel is 8.9g/cm3.

(a) Work out the volume of copper used in the alloy.

(b) What is the density of the alloy to three significant figures?

### 5.

GCSE Higher

9 cup cakes weigh a total of 204 g.

There are 420 calories in 100 g of cup cakes.

How many calories are there in one cup cake?         ### 6.

GCSE Higher

The distance from Wolverhampton to Cambridge is 115 miles.

Lynn drives from Wolverhampton to Cambridge leaving Wolverhampton at 10:30am. She assumes that her average speed will be 55 mph.

(a) Use Lynn's assumption about her average speed to work out her arrival time in Cambridge.

(b) Lynn's speed was actually lower than her assumption. How does this affect the arrival time?

### 7.

GCSE Higher

The following kinematics formula can be used to work out the distance travelled (displacement) of an object travelling with constant acceleration.

$$s = ut + \frac12 at^2$$

where:

• $$s$$ is the distance measured in metres;
• $$t$$ is the time measured in seconds;
• $$u$$ is the initial speed;
• $$a$$ is the acceleration;

(a) Rearrange the formula to make $$u$$ the subject.

(b) What units would be associated with speed in this case?

(c) What units would be associated with acceleration?

### 8.

GCSE Higher

Harper mixes 300g of material $$X$$ and 150g of material $$Y$$ to make 450g of a compound material.

Material $$X$$ has a density of 20g/cm3.

Material $$Y$$ has a density of 15g/cm3.

Work out the density of the compound material.

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