Nth Term of a Linear Sequence | How to Find It with Examples

In this article, we will discuss how to find the nth term of a linear sequence, also known as an arithmetic sequence.

Nth Term of a Linear Sequence

This fundamental concept in mathematics allows you to determine any term in a sequence without listing all the preceding terms.

We will discuss are:

How to find the nth term of a linear sequence
Solving various problems related to sequences and series

They are very important in practicing questions for coordinate geometry as well.

Here is one more link to practice a few extra questions: Maths Genie Nth Term of a Linear Sequence Questions

What Is a Linear Sequence?

A linear sequence is a list of numbers where the difference between any two consecutive terms is always the same.
This constant difference is known as the common difference.

Example of a Linear Sequence:

Consider the sequence: 2, 5, 8, 11, 14

From 2 to 5: Add 3

From 5 to 8: Add 3

From 8 to 11: Add 3

From 11 to 14: Add 3

Common Difference (A): 3

General Formula for the Nth Term

The general formula to find the nth term of a linear sequence is:

nth term = A × n + B

Where:

A is the common difference
B is a constant (the adjustment needed to match the first term)
n is the term number

Our goal is to find the values of A and B to create a formula that can calculate any term in the sequence.

Steps to Find the Nth Term

To find the general term of a sequence, follow these two main steps:

Step 1: Find the Common Difference (A)

Subtract any term from the term that follows it.
Ensure the difference is consistent throughout the sequence.

Step 2: Find the Constant Term (B)

Use the first term of the sequence.
Subtract the common difference from the first term: B = First term − A

Solved Example 1

Question: Here are the first 5 terms of an arithmetic sequence.

2, 5, 8, 11, 14

Find an expression, in term of n, for the nth term of sequence and using that find 10th term of the sequence.

Solution:

Given Sequence: 2, 5, 8, 11, 14

Step 1: Find the Common Difference (A)

5 – 2 = 3

8 – 5 = 3

• Common difference A = 3

Step 2: Find the Constant Term (B)

• First term is 2

B = 2 – 3

= −1

Step 3: Nth Term Formula:

nth term = A × n + B

nth term = 3n − 1

Finding a Specific Term

To find the 10th term:

nth term = 3 × 10 − 1

nth term = 29

Solved Example 2

Question: Here are the first 5 terms of an arithmetic sequence.

6, 11, 16, 21, 26

Find an expression, in term of n, for the nth term of sequence and using that find 52nd term of the sequence.

Solution:

Given Sequence: 6, 11, 16, 21, 26

Step 1: Find the Common Difference (A)

11 – 6 = 5

16 – 11 = 5

• Common difference A = 5

Step 2: Find the Constant Term (B)

• First term is 6

B = 6 – 5

= 1

Step 3: Nth Term Formula:

nth term = A × n + B

nth term = 5n + 1

Finding a Specific Term

To find the 52nd term:

nth term = 5 × 52 + 1

nth term = 261

Solved Example 3

Question: Here are the first 5 terms of a number sequence.

3, 7, 11, 15, 19

Write down an expression, in terms of n, for the nth term of this sequence and verify whether 319 is a term in the sequence. You must justify your answer.

Solution:

Given Sequence: 3, 7, 11, 15, 19

Step 1: Find the Common Difference (A)

7 – 3 = 4

11 – 7 = 4

• Common difference A = 4

Step 2: Find the Constant Term (B)

• First term is 3

B = 3 – 4

= -1

Step 3: Nth Term Formula:

nth term = A × n + B

nth term = 4n – 1

To check if 319 is a term in this sequence:

Set Up the Equation

4n − 1 = 319

Solve for n

Add 1 to both sides:

4n = 320

Divide both sides by 4:

n = 80

Conclusion

Since n = 80 is a whole number, 319 is the 80th term of the sequence.
Therefore, 319 is a term in the sequence.

Note: If n had not been a whole number (e.g., n = 80.5), then 319 would not be a term in the sequence.

Summary of Steps

1. Find the Common Difference (A):

Subtract consecutive terms to find A.

2. Find the Constant Term (B):

Subtract the common difference from the first term:

B = First term − A

3. Write the Nth Term Formula:

Combine A and B into the formula:

nth term = A × n + B

4. Find Any Term in the Sequence:

Substitute the desired term number (n) into the formula.

Conclusion

Finding the nth term of a linear sequence is a straightforward process once you understand the steps involved:

1. Determine the common difference between the terms.

2. Calculate the constant term by adjusting the first term.

3. Formulate the nth term using the general formula.

4. Apply the formula to find any term in the sequence or verify if a number is part of the sequence.

Practice Questions and Answers on Nth Term of a Linear Sequence

Question 1: Sequence: 4, 9, 14, 19, 24

Tasks:
- Find the nth term formula.
- Calculate the 30th term.

Question 2: Sequence: 15, 12, 9, 6, 3

Tasks:
- Find the nth term formula.
- Determine if −12 is a term in the sequence.

Question 3: Sequence: −5, 0, 5, 10, 15

Tasks:
- Find the nth term formula.
- Find the 25th term.

Question 4: Sequence: 7, 10, 13, 16, 19

Tasks:
- Find the nth term formula.
- Calculate the 15th term.

Question 5: Sequence: 20, 17, 14, 11, 8

Tasks:
- Find the nth term formula.
- Determine if −22 is a term in the sequence.

Question 6: Sequence: 1, 4, 7, 10, 13

Tasks:
- Find the nth term formula.
- Find the 100th term.

Question 7: Sequence: −2, 0, 2, 4, 6

Tasks:
- Find the nth term formula.
- Calculate the 50th term.

Question 8: Sequence: 100, 95, 90, 85, 80

Tasks:
- Find the nth term formula.
- Determine if 50 is a term in the sequence.

Question 9: Sequence: 5, 9, 13, 17, 21

Tasks:
- Find the nth term formula.
- Find the 40th term.

Question 10: Sequence: 50, 47, 44, 41, 38

Tasks:
- Find the nth term formula.
- Determine if 2 is a term in the sequence.

Solutions

Question 1:

Step 1: Find the Common Difference (A)

9 – 4 = 5

A = 5

Step 2: Find the Constant Term (B)

First term is 4

B = 4 – 5

= −1

Nth Term Formula

nth term = 5n − 1

Calculate the 30th Term

nth term = 5 × 30 − 1

= 149

Question 2:

Step 1: Find the Common Difference (A)

12 – 15 = −3

A = −3

Step 2: Find the Constant Term (B)

First term is 15

B = 15 – (−3)

= 18

Nth Term Formula

nth term = −3n + 18

Determine if −12 Is in the Sequence

Set up the equation:

−3n + 18 = −12

Solve for n:

1. Subtract 18 from both sides:

−3n = −30

2. Divide both sides by −3:

n = 10

Conclusion

Since n = 10 is a whole number, −12 is the 10th term.
Therefore, −12 is a term in the sequence.

Question 3:

Step 1: Find the Common Difference (A)

0 – (−5) = 5

A = 5

Step 2: Find the Constant Term (B)

First term is −5

B = (−5) – 5 = −10

Nth Term Formula

nth term = 5n − 10

Find the 25th Term

nth term = 5 × 25 − 10

= 115

Question 4:

Step 1: Find the Common Difference (A)

10 – 7 = 3

A = 3

Step 2: Find the Constant Term (B)

First term is 7

B = 7 – 3 = 4

Nth Term Formula

nth term = 3n + 4

Calculate the 15th Term

nth term = 3 × 15 + 4

= 49

Question 5:

Step 1: Find the Common Difference (A)

17 – 20 = −3

A = −3

Step 2: Find the Constant Term (B)

First term is 20

B = 20 – (−3) = 23

Nth Term Formula

nth term = −3n + 23

Determine if −22 Is in the Sequence

Set up the equation:

−3n + 23 = −22

Solve for n:

1. Subtract 23 from both sides:

−3n = −45

2. Divide both sides by −3:

n = 15

Conclusion

Since n = 15 is a whole number, −22 is the 15th term.
Therefore, −22 is a term in the sequence.

Question 6:

Step 1: Find the Common Difference (A)

4 – 1 = 3

A = 3

Step 2: Find the Constant Term (B)

First term is 1

B = 1 – 3 = −2

Nth Term Formula

nth term = 3n − 2

Find the 100th Term

nth term = 3 × 100 − 2

= 298

Question 7:

Step 1: Find the Common Difference (A)

• 0 minus (−2) equals 2

• A = 2

Step 2: Find the Constant Term (B)

First term is −2

B = (−2) – 2 = −4

Nth Term Formula

nth term = 2n − 4

Calculate the 50th Term

nth term = 2 × 50 − 4

= 96

Question 8:

Step 1: Find the Common Difference (A)

95 – 100 = −5

A = −5

Step 2: Find the Constant Term (B)

First term is 100

B = 100 – (−5) = 105

Nth Term Formula

nth term = −5n + 105

Determine if 50 Is in the Sequence

Set up the equation:

−5n + 105 = 50

Solve for n:

1. Subtract 105 from both sides:

−5n = −55

2. Divide both sides by −5:

n = 11

Conclusion

Since n = 11 is a whole number, 50 is the 11th term.
Therefore, 50 is a term in the sequence.

Question 9:

Step 1: Find the Common Difference (A)

9 – 5 = 4

A = 4

Step 2: Find the Constant Term (B)

First term is 5

B = 5 – 4 = 1

Nth Term Formula

nth term = 4n + 1

Find the 40th Term

nth term = 4 × 40 + 1

= 161

Question 10:

Step 1: Find the Common Difference (A)

47 – 50 = −3

A = −3

Step 2: Find the Constant Term (B)

First term is 50

B = 50 – (−3) = 53

Nth Term Formula

nth term = −3n + 53

Determine if 2 Is in the Sequence

Set up the equation:

−3n + 53 = 2

Solve for n:

1. Subtract 53 from both sides:

−3n = −51

2. Divide both sides by −3:

n = 17

Conclusion

Since n = 17 is a whole number, 2 is the 17th term.
Therefore, 2 is a term in the sequence.

Table of Content

Nth Term of a Linear Sequence
What Is a Linear Sequence?
General Formula for the Nth Term
Steps to Find the Nth Term
Solved Examples
Summary of Steps
Conclusion
Practice Questions and Answers on Nth Term of a Linear Sequence

Inequalities on a Number Line: Examples with Practice Questions

In this article, we will discuss how to solve inequalities and represent them on a number line.

Video Tutorial on GCSE Maths: Inequalities on a Number Line

Watch this Video Tutorial as we explain all types of Inequalities on a Number Line for GCSE Maths.

Inequalities on a Number Line

Inequalities are fundamental in algebra and help us understand the range of possible values that satisfy a condition.

We will discuss are:

The Basic Inequality Symbols
How to plot them on a number line
Work through examples
Including compound inequalities.

They are very important in practicing questions for coordinate geometry as well.

Here is one more link to practice a few extra questions: Maths Genie Inequalities on a Number Line Questions

Understanding Inequality Symbols

Inequalities express a relationship where two values are not equal and one is greater or lesser than the other. The primary inequality symbols are:

Less than (<): Indicates that one value is smaller than another.
Greater than (>): Indicates that one value is larger than another.
Less than or equal to (≤): Indicates that one value is smaller than or equal to another.
Greater than or equal to (≥): Indicates that one value is larger than or equal to another.

Representing Inequalities on a Number Line

A number line is a visual tool that helps illustrate the set of values that satisfy an inequality.

Key Steps to Plot an Inequality:

Draw a Number Line: Sketch a horizontal line and mark relevant numbers.
Identify Key Points: Mark the number(s) involved in the inequality.
Use Circles to Indicate Inclusion:

- Open Circle: Used when the number is not included in the solution (for < or >).
- Closed Circle: Used when the number is included in the solution (for ≤ or ≥).

4. Shade the Solution Area:

- Draw an arrow or line extending left or right to represent all possible values that satisfy the inequality.

Solved Example 1

Question: x<5

Solution:

Interpretation:

x can be any number less than 5 (e.g., 4, 0, -3, 4.9).

Steps to Plot:

Step 1: Draw a number line and label key points, including 5.

Step 2: Place an open circle at 5 because 5 is not included.

Step 3: Shade the line to the left of 5, indicating all numbers less than 5.

Solved Example 2

Question: x>5

Solution:

Interpretation:

x can be any number greater than 5 (e.g., 6, 7, 5.1).

Steps to Plot:

Step 1: Draw a number line and mark the point 5.

Step 2: Place an open circle at 5.

Step 3: Shade the line to the right of 5, showing all numbers greater than 5.

Including the Endpoint

When the inequality includes equality (≤ or ≥), the endpoint is part of the solution set.

Solved Example 3:

Question: x ≤ 5

Solution:

Interpretation:

x can be 5 or any number less than 5.

Steps to Plot:

Step 1: Draw a number line and label 5.

Step 2: Place a closed circle at 5 to include it in the solution.

Step 3: Shade the line to the left of 5.

Solved Example 4:

Question: x ≥ 5

Solution:

Interpretation:

x can be 5 or any number greater than 5.

Steps to Plot:

Step 1: Draw a number line and label 5.

Step 2: Place a closed circle at 5.

Step 3: Shade the line to the right of 5.

Summary of Symbols and Circles

Open Circle: Used for < and > (number not included).
Closed Circle: Used for ≤ and ≥ (number included).

Compound Inequalities

Compound inequalities involve two inequality symbols and define a range between two values.

Solved Example 5:

Question: 1 < x ≤ 5

Solution:

Interpretation:

x is greater than 1 but less than or equal to 5.

Steps to Plot:

Step 1: Draw a number line and label points 1 and 5.

Step 2: Place an open circle at 1 (since x is not equal to 1).

Step 3: Place a closed circle at 5 (since x can be equal to 5).

Step 4: Shade the region between 1 and 5, connecting the two circles.

Solved Example 6:

Question: −2 ≤ x < 3

Solution:

Interpretation:

x is greater than or equal to -2 but less than 3.

Steps to Plot:

Step 1: Draw a number line and mark -2 and 3.

Step 2: Place a closed circle at -2 (including -2 in the solution)

Step 3: Place an open circle at 3 (excluding 3)

Step 4: Shade the region between -2 and 3.

Important Notes on Inequality Direction

Direction Matters: The inequality symbol points towards the smaller value
Equivalent Expressions:
- x>2 is the same as 2<x
- Both indicate that x is greater than 2.

Example:

2<x Reads as “2 is less than x,” meaning x is greater than 2.
x>2: Reads as “x is greater than 2.”

Understanding this helps avoid confusion when interpreting or rearranging inequalities.

Practice Problems

Try plotting the following inequalities on a number line:

1. x ≥ −4

- Interpretation: x is -4 or any number greater.
- Plot: Closed circle at -4, shade to the right.

2. x < 0

- Interpretation: x is any number less than 0.
- Plot: Open circle at 0, shade to the left.

3. −3 < x ≤ 2

- Interpretation: x is greater than -3 and up to 2, including 2.
- Plot: Open circle at -3, closed circle at 2, shade between them.

Conclusion

Understanding how to solve inequalities and represent them on a number line is a crucial skill in algebra. Remember:

Use open circles for < and > (number not included).
Use closed circles for ≤ and ≥ (number included).
Shade appropriately to represent all possible values of x that satisfy the inequality.
Pay attention to the direction of the inequality symbol.

Practice Questions and Answers on Inequalities on a Number Line

Question 1: Represent the inequality x < 4 on a number line.

Question 2: Sketch the inequality x ≥ −3 on a number line.

Question 3: Plot the inequality x > 0 on a number line.

Question 4: Illustrate the inequality x ≤ 6 on a number line.

Question 5: Show the solution of the compound inequality −2 < x ≤ 5 on a number line.

Question 6: Represent the inequality x ≥ −7 on a number line.

Question 7: Graph the inequality x ≤ 2 on a number line.

Question 8: Plot the compound inequality 1 ≤ x < 4 on a number line.

Question 9:Illustrate the inequality x > −5 on a number line.

Question 10: Show the solution set for the compound inequality −3 ≤ x ≤ 3 on a number line.

Solutions

Question 1:

Step 1: Draw a Horizontal Number Line:

Sketch a straight horizontal line.
Mark evenly spaced intervals.

Step 2: Mark the Key Point (4):

Locate and label the point corresponding to x = 4 on the number line.

Step 3: Place an Open Circle at 4:

Draw an open (hollow) circle at the point labelled 4.
Reason: The inequality is “less than” (<), so 4 is not included in the solution set.

Step 4: Shade to the Left of 4:

Draw a line or arrow extending from the open circle to the left.
Reason: To represent all real numbers less than 4.

Question 2:

Step 1: Draw a Horizontal Number Line:

Sketch a straight horizontal line with intervals.

Step 2: Mark the Key Point (-3):

Locate and label the point corresponding to x = −3.

Step 3: Place a Closed Circle at -3:

Draw a closed (filled-in) circle at -3.
Reason: The inequality is “greater than or equal to” (≥), so -3 is included in the solution set.

Step 4: Shade to the Right of -3:

Draw a line or arrow extending from the closed circle to the right.
Reason: To represent all real numbers greater than or equal to -3.

Question 3:

Step 1: Draw a Horizontal Number Line:

Sketch the number line with appropriate intervals.

Step 2: Mark the Key Point (0):

Locate and label the point x = 0.

Step 3: Place an Open Circle at 0:

Draw an open circle at 0.
Reason: The inequality is “greater than” (>), so 0 is not included.

Step 4: Shade to the Right of 0:

Extend a line or arrow from the open circle to the right.
Reason: To represent all real numbers greater than 0.

Question 4:

Step 1: Draw a Horizontal Number Line.

Step 2: Mark the Key Point (6):

Locate and label x = 6.

Step 3: Place a Closed Circle at 6:

Draw a closed circle at 6.
Reason: The inequality is “less than or equal to” (≤), so 6 is included.

Step 4: Shade to the Left of 6:

Draw a line or arrow extending left from the closed circle.
Reason: To represent all real numbers less than or equal to 6.

Question 5:

Step 1: Draw a Horizontal Number Line.

Step 2: Mark the Key Points (-2 and 5):

Label x = −2 and x = 5.

Step 3: Place an Open Circle at -2:

Draw an open circle at -2.
Reason: The inequality is “greater than” (>), so -2 is not included.

Step 4: Place a Closed Circle at 5:

Draw a closed circle at 5.
Reason: The inequality is “less than or equal to” (≤), so 5 is included.

Step 5: Shade the Region Between -2 and 5:

Draw a line connecting the two circles.
Reason: To represent all real numbers greater than -2 and less than or equal to 5.

Question 6:

Step 1: Draw a Horizontal Number Line.

Step 2: Mark the Key Point (-7):

Label x = −7.

Step 3: Place a Closed Circle at -7:

Draw a closed circle at -7.
Reason: The inequality is “greater than or equal to” (≥), so -7 is included.

Step 4: Shade to the Right of -7:

Extend a line or arrow from the closed circle to the right.
Reason: To represent all real numbers greater than or equal to -7.

Question 7:

Step 1: Draw a Horizontal Number Line.

Step 2: Mark the Key Point (2):

Label x = 2.

Step 3: Place a Closed Circle at 2:

Draw a closed circle at 2.
Reason: The inequality is “less than or equal to” (≤), so 2 is included.

Step 4: Shade to the Left of 2:

Draw a line or arrow extending left from the closed circle.
Reason: To represent all real numbers less than or equal to 2.

Question 8:

Step 1: Draw a Horizontal Number Line.

Step 2: Mark the Key Points (1 and 4):

Label x = 1 and x = 4.

Step 3: Place a Closed Circle at 1:

Draw a closed circle at 1.
Reason: The inequality is “greater than or equal to” (≥), so 1 is included.

Step 4: Place an Open Circle at 4:

Draw an open circle at 4.
Reason: The inequality is “less than” (<), so 4 is not included.

Step 5: Shade the Region Between 1 and 4:

Draw a line connecting the two circles.
Reason: To represent all real numbers from 1 up to (but not including) 4.

Question 9:

Step 1: Draw a Horizontal Number Line.

Step 2: Mark the Key Point (-5):

Label x = −5.

Step 3: Place an Open Circle at -5:

Draw an open circle at -5.
Reason: The inequality is “greater than” ( > >), so -5 is not included.

Step 4: Shade to the Right of -5:

Extend a line or arrow from the open circle to the right.
Reason: To represent all real numbers greater than -5.

Question 10:

Step 1: Draw a Horizontal Number Line.

Step 2: Mark the Key Points (-3 and 3):

Label x = −3 and x = 3.

Step 3: Place a Closed Circle at -3:

Draw a closed circle at -3.
Reason: The inequality is “greater than or equal to” (≥), so -3 is included.

Step 4: Place a Closed Circle at 3:

Draw a closed circle at 3.
Reason: The inequality is “less than or equal to” ( ≤ ≤), so 3 is included.

Step 5: Shade the Region Between -3 and 3:

Draw a line connecting the two closed circles.
Reason: To represent all real numbers between -3 and 3, including both endpoints.

Table of Content

Video Tutorial on GCSE Maths: Inequalities on a Number Line
Inequalities on a Number Line
Understanding Inequality Symbols
Representing Inequalities on a Number Line
Compound Inequalities
Important Notes on Inequality Direction
Practice Problems
Conclusion
Practice Questions and Answers on Inequalities on a Number Line

Steps to Calculate The Bearing of an Angle? GCSE Maths

Wondering how to calculate the bearing of Y from X in your GCSE Maths problems? Let’s break it down step by step and make it simple.

Video Tutorial on Bearings

Watch this Video Tutorial as we explain step by step how to calculate the Bearing of Y from X

What Are Bearings?

So, what exactly is a bearing?
Think of a bearing as a way to describe direction—kind of like giving someone precise instructions on which way to go.
In maths, a bearing is an angle measured clockwise from the north direction.
Bearings are especially useful in navigation and mapping because they provide an exact angle between two points.

So when we talk about calculating the bearing of Y from X, we’re figuring out the direction you need to face at point X to look straight towards point Y.

Here is one more link to practice a few extra questions: Maths Genie Bearings Questions

Things to Remember When Calculating the Bearing of Y from X

When calculating a bearing, there are a three important things to remember.

Always Measure Clockwise from North: Bearings are measured starting from the north direction and moving clockwise. Think of a compass where the north is at the top, and you turn in the direction the clock’s hands move.
Use Three Digits: Bearings are expressed as three-digit numbers. If your angle is less than 100 degrees, add leading zeros. For example, 45 degrees becomes 045°.

This three-digit system helps to avoid any confusion and makes everything very clear.

3. Know the Cardinal Points: Familiarize yourself with the basic compass points:

- North (N) is 000° or 360°
- East (E) is 090°
- South (S) is 180°
- West (W) is 270°

Steps to Calculate The Bearing of Y From X

How to calculate the bearing of Y from X? Let’s walk through the steps together:

Figure out the Inital point and the Final point: For example, since we need to find the bearing of Y “FROM” X. This “From” tells us that X is our initial point and Y is our final point.

Draw the Line from X to Y
Connect point X to point Y with a straight line. This line shows the direct path from X to Y. You can also add an arrow to indicate the direction.

2. Mark the North Direction at Point X: At point X, draw a vertical line pointing upwards to represent the north direction. This is crucial because bearings are always measured clockwise from north.

Measure the Angle Clockwise from North to the Line XY
Using a protractor, measure the angle starting from the north line at point X and moving clockwise until you reach the line connecting X to Y. This angle is your bearing.

One important thing to remember is that you will always measure the clockwise angle from the north direction.
Since this is the north, we will draw a clockwise angle like this. Always remember to go clockwise—you will not use the angle that goes in the anticlockwise direction.

Express the Bearing as a Three-Digit Number
Bearings are written as three-digit numbers. If your angle is less than 100 degrees, add leading zeros to make it three digits. For example:
- If the angle is 60°, write the bearing as 060°.
- If it’s 120°, the bearing remains 120°.

Double-Check Your Measurement

It’s easy to make a mistake with angles, so take a moment to verify your measurement and ensure your protractor was aligned correctly.

Solved Example:

Question: By measuring the angles below, state the bearings of

X From Y.

Solution:

Let’s start by finding the bearing of X from Y. This means our initial point is Y and our final point is X.

Step #1: Draw a line from our initial point to our final or destination point. From the initial point, that is Y, we will measure the angle in a clockwise direction.

Step #2: Now, measuring this angle can be a bit tricky sometimes, so you can start by measuring the smaller interior angle. Let’s say this angle is 40 degrees.

Step #3: To find the bearing, that is the larger blue angle, we can subtract 40 from 360 to get 320 degrees.

Therefore, the bearing of X from Y is 320 degrees.

Solved Example:

Question: By measuring the angles below, state the bearings of

Y From X.

Solution:

Step #1: This means our initial point is X and our final point is Y. This time, the direction of the line is from X to Y, not Y to X.

Step #2: We draw the angle in the clockwise direction from X. This gives us the bearing of Y from X, which comes out to be 140 degrees.

There are actually two methods to solve this part.

The first is to use a protractor to measure the angle, as we did earlier.
Alternatively, you can use the property of parallel lines that states the sum of the interior angles between two parallel lines is 180 degrees. This property can sometimes make finding the bearing quicker.

Exam Practice Questions:

Question 1: The location C is on a bearing of 140° from A.

The bearing of C from B is 250°

Find the location C and mark it on the diagram below.

Solution:

Step #1: This question is divided into two parts, and we need to determine the location of C. We are given the bearings of C from both “A” and B, and we need to draw these bearings one by one.
Step #2: We are told that the location of C is on a bearing of 140 degrees from A. So, we take A as our initial point and draw a line at a bearing of 140 degrees from A. Using a protractor, we measure 140 degrees and then draw a dashed line in that direction. C could be located anywhere along this dashed line.

Step #3: Next, we need to find the bearing of C from B. Again, we take point B as our initial point and draw a 250-degree angle in a clockwise direction. We draw another dashed line from this point. The intersection of these two lines gives us the location of C.

Practice Questions and Answers on Bearings

Question 1: The diagram shows the position of Glasgow.

Belfast is 60 miles away from Glasgow on a bearing of 055°
Mark the position of Belfast on the diagram.

Question 2: A diagram of a bearing is shown below.

By measuring the diagram given:
(a) State the bearing of Y from X.

(b) State the bearing of X from Y

(c) Find the distance between X and Y.

Question 3:

(a) Write down the bearing of X from O.

(b) Work out the bearing of Y from O.

Question 4: Mark has been asked to find the bearing of X from Y.
Shown below is her method.

Mark answer is 080°
Explain Mark mistake.

Question 5: Starting at point E, Jacob makes a journey as follows:
8 km on a bearing of 135° to F
4 km, on a bearing of 180° to G
6 km on a bearing of 315° to H
(a) Use the space below to draw a suitable diagram to represent her journey.

(b) Jacob wants to return to E.
What is the bearing of E from H?

Question 6:

The diagram shows the position of two ports X and Y on a map.

(a) Measure the bearing of Y from X.

A rock R is on a bearing of 150° from Y.
On the map R is 6 cm from Y.
(b) Mark the position of R with a cross (×) and label it R.

Question 7: Alex has been asked to find the bearing of X from Y.
Shown below is his method.

Alex answer is 103°
Explain Alex mistake.

Question 8:

The diagram shows the position of a lighthouse X and a harbour Y.

The scale of the diagram is 1 cm represents 5 km.
(a) Work out the real distance between X and Y.

(b) Measure the bearing of Y from X.

A boat B is 20 km from Y on a bearing of 040°
(c) On the diagram, mark the position of boat B with a cross (×).
Label it B.

Question 9: The diagram shows the position of two boats, A and B.

The bearing of a boat C from boat A is 060°
The bearing of boat C from boat B is 310°
In the space above, draw an accurate diagram to show the position of boat C.
Mark the position of boat C with a cross (x). Label it C.

Question 10: The diagram shows the position of a boat A and a dock B.