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Question 37 - AQA GCSE Foundation Maths Past Paper 2 November 2021

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Question 30 - AQA GCSE Foundation Maths Past Paper 3 November 2021

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Question 23 - AQA GCSE Foundation Maths Past Paper 1 November 2021

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Question 22 - AQA GCSE Foundation Maths Past Paper 1 November 2021

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Question 17 - AQA GCSE Higher 2020 Past Paper 1 - Algebra, Equations of Straight Lines, Straight Line Graphs, Gradient of a line Question By Topic

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Question 22 - OCR GCSE Foundation 2020 Past Paper 1 - Algebra, Gradient of a line,Equations of Straight Lines Question By Topic

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Question 18 - AQA GCSE Foundation 2020 Past Paper 1 - Algebra, Equations of Straight Lines, Gradient of a line Question By Topic

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Question 31 - Edexcel GCSE Foundation 2020 Past Paper 3 - Algebra, Linear Equations, Algebraic Equations, Gradient of a line, Equations of Straight Lines Question By Topic

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Question 28 - Edexcel GCSE Higher 2020 Past Paper 2 - Geometry and Measures,Circles, Sectors and Arcs Questions By Topic

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Question 11 - OCR GCSE Foundation 2017 Past Paper 3 - Algebra, Straight Line Graphs, Gradient of a line Questions By Topic

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Understanding Gradients of Straight Lines for the GCSE Exam

1. What is the gradient of the line?

     The gradient of a line refers to the steepness or slope of that line. It is a measure of its slope. 

  • The bigger the gradient, the steeper the line.
  • Gradient of a line can be positive or negative and does not have to be a whole number.
  • When the gradient of two lines is the same, they are parallel. 
  • When the gradients have a product of -1, they are perpendicular.

2. Types of Gradients:

Understanding the different types of gradients is crucial when working with lines and their equations. Depending on the value of the gradient, there are four different types of gradient positive, negative, zero and undefined.

  1. Positive gradients: A line with a positive gradient has a slope that goes up from left to right, and  the value of the gradient is greater than zero.

GCSE Topicwise Gradient of a line Article Image 01

   2. Negative gradients: A line with a negative gradient has a slope that goes down from left to right, and the value of the gradient is less than zero.

GCSE Topicwise Gradient of a line Article Image 02

   3. Zero gradients: A line with a zero gradient is a horizontal line. For a line that has a slope of zero, the value of the gradient is zero.

GCSE Topicwise Gradient of a line Article Image 03

   4. Undefined gradients: A line with an undefined gradient is a vertical line.

GCSE Topicwise Gradient of a line Article Image 04

3. How to find the Gradient?

    The gradient of a line is calculated by dividing the difference between the y- and x-coordinates. 

    The formula for the gradient of a line can be written as:

    Gradient of a line = 

                                      GCSE Topicwise Gradient of a line Article Image 05

where (x ,y) and (x ,y) are any two points on the line.

3.1 Gradient through given line:

The gradient of the given straight line on a graph can be determined as follows:

Step 1: Take any two points on the given line and write their coordinates.

Step 2: Consider the first point’s coordinates as (x, y) and the second point’s coordinates as (x, y).

Step 3: Find the change in the y-axis: (y-y) 

Step 4: Find the change in the x-axis: (x-x)

Step 5: Substitute the change in y and x-axis in the gradient formula.

Step 6: Simplify it if required to get the value of the gradient of a given straight line. 

Let's look at some examples.

Example 1 : Calculate the gradient of the line drawn below.

GCSE Topicwise Gradient of a line Article Image 06

GCSE Topicwise Gradient of a line Article Image 07

Example 2 : Calculate the gradient of the line drawn below .

GCSE Topicwise Gradient of a line Article Image 08

GCSE Topicwise Gradient of a line Article Image 09

3.2 Gradient through Two Points:

The gradient of the straight line that passes through the given points can be determined as follows:

Step 1: Consider the first point’s coordinates as (x, y) and the second point’s coordinates as (x, y)

Step 2: Find the change in the y-axis: (y-y) 

Step 3: Find the change in the x-axis: (x-x)

Step 4: Substitute change in y and x-axis in the gradient formula.

Step 5: Simplify it to get the value of the gradient of the straight line.

Let's look at an example.

Example 1 : Find the gradient of the line that passes through (-5, 2) and (3, 4).

GCSE Topicwise Gradient of a line Article Image 10

Quiz Questions
GCSE Topicwise Gradient of a line Article Quiz Image

GCSE Topics

  • Statistical Measures (5)
  • Numbers (1,084)
  • Data Visualisation (4)
  • Algebra (1,176)
  • Ratio, Proportion and Rates of Change (443)
  • Geometry and Measures (809)
  • Statistics (274)
  • Probability (258)
  • Frequently Asked Questions
    What are the main topics in GCSE Maths?

    The main topics in GCSE Maths are:

    • Numbers
    • Algebra 
    • Ratio, Proportion and Rates of Change 
    • Geometry and Measures
    • Statistics 
    • Probability 
    • Statistical Measures 
    • Data Visualisation 

    With regular practice of GCSE Maths topic-wise questions and GCSE Maths past pacers, you can easily score high marks.

    Is GCSE Maths hard?

    Although many people think of GCSE maths as a difficult subject, with the correct training and preparation,you can master it in time. You can practice GCSE Maths  topic-wise questions daily to improve speed, accuracy, and time and to score high marks in the GCSE Maths exam.

    What is a good grade on GCSE Maths Exam?

    A grade of 4 or 5 would be considered "good" because the government has established a 4 as the passing grade; a grade of 5 is seen as a strong pass. Therefore, anything that exceeds this level would be considered good. You can practice GCSE Maths topic-wise questions to score good grades in the GCSE Maths exam.

    How can I get full marks in GCSE Maths?

    You can get a high score in GCSE Maths through meticulous practice of GCSE Maths topic-wise questions and GCSE Maths past papers.

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