Exam-Style Questions.

If A is 150% more than B, what is the ratio A:B?

(a) \(1 : 150\)

(b) \(1 : 1.5\)

(c) \(2 : 3\)

(d) \(2 : 5\)

(e) \(5 : 2\)

Worked Solution

The Billing triplets are planting seedlings on the first day of the month. The three of them take two hours to plant 300 seedlings.

(a) On the second day of the month the triplets are joined by their friend Billy who helps them. Working at the same rate, how many plants should the four of them be able to plant in two hours?

(b) Working at the same rate, how much longer would it take four people to plant 1000 seedlings than it would take five people?

(c) Billy says that it took two hours for three people to plant 300 seedlings. If I assume they work all day, then in one day three people will plant 3600 seedlings because 300 × 12 = 3600.

Why is Billy's assumption not reasonable? What effect has Billy's assumption had on his answer?

Worked Solution

Bruce cycles a distance of 30 km at an average speed of 20 km/h.

He then runs a distance of 8 km at an average speed of 6 km/h.

Work out the total time Bruce takes.

Give your answer in hours and minutes

Worked Solution

A Primary school asked 9 children to remove the weeds from the school gardens. The gardens measured 100m² in total and the job was completed in 10 hours (spread over many weeks).

(a) The school was asked to find volunteers to weed another garden measuring 250m² at a nursing home. This work has to be completed in 15 hours.

Calculate the least number of children the school needs to find for this work.

(b) State one assumption you have made in your answer to part (a). How would your answer to part (a) change if you did not make this assumption?

Worked Solution

A cuboid made of solid metal measures 10.0 cm by 6.0 cm by 2.0 cm. The block’s mass is 600 g.

Work out:
(a) the volume of the cuboid
(b) the density of the metal in g/cm³
(c) the density of the metal in kg/m³

Worked Solution

People are paid to paint polygons.

There are eight people in the polygon painting posse.

All of the people paint at the same rate.

When all of the people are painting, they can paint all of the polygons in the palace in ten days.

The table shows the number of people painting each day:

Work out the total number of days taken to paint all of the polygons in the palace.

Worked Solution

$$y \propto \frac{1}{ x^2 }$$

When \(y = 9\), \(x = 3\).

(a) Find \(y\) when \(x = 1\).

(b) Find \(x\) when \(y = 2.25\).

Worked Solution

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 70 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?

Worked Solution

Mr Finknottle takes his parents for a drive in his car.

He drives the first ten miles in ten minutes then drives at an average speed of 68 miles per hour for 1 hour 45 minutes.

He finds this information about his car:

Use the information to find how many gallons of petrol he uses during the drive.

Worked Solution

The density of water (at 20°C) is 1.09 g/cm³.

The density of blood is 1.60 g/cm³.

Three litres of water are mixed with four litres of blood for a scientific experiment. Work out the density of the mixture giving your answer correct to 2 decimal places.

Worked Solution

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?

Worked Solution

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

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?

Worked Solution

Which of the following statements are correct if \(xy = c\) and \(c\) is a constant.

• (a) \(y\) is directly proportional to \(x\)
• (b) \(y\) is directly proportional to \(\frac{1}{x}\)
• (c) \(y\) is inversely proportional to \(\frac{1}{x}\)
• (d) \(x\) is directly proportional to \(y\)

Worked Solution

Henrietta sells the eggs that the chickens on her farm lay.

She has 220 chickens and each chicken lays 5 eggs each week.

Henrietta gives each chicken 80 grams of chicken feed each day which costs £5.50 for a 20 kg bag.

Work out the cost of the chicken feed for every box of six eggs she sells.

Worked Solution

If \(a\) is inversely proportional to \(b\) and \(b\) is directly proportional to \(c^2\) find a formula for \(a\) in terms of \(c\) given that \( a=20 \) and \(c = 4 \) when \(b = 8 \).

Worked Solution