Mathematics Specification A - 4MA1 PearsonEdexcel

Graphs

Overview

Graphs give you a way to see algebra. Every equation you write down corresponds to a curve or a line on a set of axes, and reading that picture tells you things the algebra alone can hide: where a quantity reaches its maximum, how fast something is changing, or where two conditions are satisfied at once.

This topic starts with the coordinate system itself and builds up through straight-line graphs to quadratics and, at Higher tier, cubics, reciprocals, and trigonometric curves. You will learn to find gradients, write equations of lines, and apply transformations to function graphs.

Objectives

Interpret information presented in a range of linear and non-linear graphs
Understand and use conventions for rectangular Cartesian coordinates
Plot points (x, y) in any of the four quadrants or locate points with given coordinates
Determine the coordinates of points identified by geometrical information
Determine the coordinates of the midpoint of a line segment, given the coordinates of the two end points
Draw and interpret straight line conversion graphs
Find the gradient of a straight line
Recognise that equations of the form y = mx + c are straight line graphs with gradient m and intercept on the y-axis at the point (0, c)
Recognise, generate points and plot graphs of linear and quadratic functions
[Higher] Recognise, plot and draw graphs with equation y = Ax^3 + Bx^2 + Cx + D and related reciprocal and trigonometric forms
[Higher] Apply to the graph of y = f(x) the transformations y = f(x) + a, y = f(ax), y = f(x + a), y = af(x) for linear, quadratic, sine and cosine functions
[Higher] Interpret and analyse transformations of functions and write the functions algebraically
[Higher] Find the gradients of non-linear graphs by drawing a tangent
[Higher] Find the intersection points of two graphs, one linear and one non-linear, and recognise that the solutions correspond to the solutions of the combined equation
[Higher] Calculate the gradient of a straight line given the coordinates of two points
[Higher] Find the equation of a straight line parallel to a given line; find the equation of a straight line perpendicular to a given line

Lesson Note

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Lesson Evaluation

Congratulations on completing the lesson on Graphs. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.

You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.

Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.

What is the gradient of the line y = -4x + 7? A) 7 B) -4 C) 4 D) -7 Answer: B
What is the midpoint of the segment from (2, 8) to (6, 2)? A) (4, 5) B) (8, 10) C) (3, 4) D) (4, 10) Answer: A
In which quadrant does the point (-3, 5) lie? A) First B) Second C) Third D) Fourth Answer: B
The line y = 2x + 1 is parallel to which of the following? A) y = -2x + 3 B) y = 2x - 5 C) y = 0.5x + 1 D) y = -0.5x + 1 Answer: B
A line has gradient 3. What is the gradient of a line perpendicular to it? A) 3 B) -3 C) 1/3 D) -1/3 Answer: D