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Gradient of a Line

Practise the skill of finding the gradients of straight lines shown in different ways.

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This is level 6: Calculate horizontal distance or height difference from road signs. If the answer is a fraction, type it in as a decimal. You will be awarded a trophy if you get at least 9 answers correct and you do this activity online.

1


According to the map, the next service station is 900m further along a road signed 10%. How much higher is the station than the current position?

Assume 900 metres is the horizontal distance. A gradient of 10% is equivalent to the decimal \(0.1\). Multiply 900 metres by \(0.1\)

m

2


A road sign shows a 20% gradient. A farm entrance is 350m away measured horizontally on the map. Find the increase in height.

m

3


A hill is marked with a gradient of 1:5. What is the gradient of the hill when expressed as a percentage?

%

4


A cyclist sees a 25% hill sign. If the top of the hill is 480m away horizontally, what is the vertical rise?

m

5


A road descends with a gradient of 1:4. A car park is further down the road 65m lower above sea level than the present position. What is the horizontal distance to the car park?

m

6


A warning sign gives the gradient as 30%. Over what horizontal distance would you need to travel to achieve 45m increase in height?

m

7


A mountain road has an 8% gradient. A chalet is 1.25km away measured horizontally on the map. How many metres lower is the chalet?

m

8


A lorry travels down a road marked 12%. If the horizontal distance travelled is 800 yards, by how many yards does the road fall?

yd

9


A road sign shows a 14% climb. The summit of the road is 91m higher than the present position. What is the horizontal distance to the summit?

m

10


A steep road is marked 1:7. The slope is constant for half a mile (880 yards). Find the height difference to the nearest yard of the two ends of the half mile.

yd

11


A pass begins at 240 m above sea level and rises at a gradient of 17% for a horizontal distance of 1.4km. What is the height above sea level at the end of this section?

m

12


A road drops from a mountain lodge at 920m above sea level. The warning sign says 1:3 and the horizontal distance to the valley floor is 2.4 km. What is the height of the valley floor above sea level?

m

Check

Can you correct your mistakes in order to get full marks?

This is Gradient of a Line level 6. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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When planning to use technology in your lesson always have a plan B!

Mandy Fox, Kendal

Monday, January 9, 2023

"Hi John,
I have a suggestion! Please would you consider making a second page for Gradient of a Line where the scales on the x-axis and y-axis are different.
Many thanks for all your hard work!
Mandy Fox.

[Transum: Good idea Mandy. It's on my list ...]"

Miss Jenna, Australia

Thursday, October 26, 2023

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Tuesday, October 21, 2025

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Description of Levels

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Level 1 - Find the gradient when the rise and run are given

Level 2 - Find the gradient of a line drawn on a grid of squares

Level 3 - Find the gradient of lines joining pairs of coordinates

Level 4 - Find the gradient of lines from their graphs if the axes scales are different

Level 5 - Mixed Questions including the gradients of parallel and perpendicular lines and the equation of a straight line

Level 6 - Calculate horizontal distance or height difference from road signs

Graph Match - Try this when you have mastered the skill of finding the gradient of a line.

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Help

Some more difficult questions have a hint that can help you find a way to solve the problem. If you see a  button, click it to reveal the hint.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

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