Representing Inequalities Graphically and Solving Practical Problems

Representing Inequalities Graphically and Solving Practical Problems

Assessment

Interactive Video

Mathematics

University

Practice Problem

Hard

Created by

Wayground Content

FREE Resource

The video tutorial covers a recap of inequalities, including symbols and representation on a number line. It explains how to graph linear equations by identifying gradients and y-intercepts. The tutorial then describes how to use inequalities to define shaded regions on a graph. It also demonstrates solving area comparison problems using inequalities and graphical representation, focusing on linear and quadratic equations. The video concludes with a summary of how to represent inequalities graphically and solve practical problems.

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7 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following is NOT a method used to solve inequalities?

Ignoring variable coefficients

Using symbols and number lines

Applying the same processes as equations

Considering two-variable inequalities

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the equation of a line with a gradient of 2 passing through 4 on the y-axis?

y = 2x + 4

y = -2x + 4

y = -2x - 4

y = 2x - 4

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you represent a region below a dashed line with the equation y = 2x + 4?

y ≤ 2x + 4

y > 2x + 4

y < 2x + 4

y ≥ 2x + 4

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In comparing areas, which formula represents the area of a rectangle?

1/2 base times height

x times (x - 3)

x times (x + 3)

1/2 (x - 3) times height

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the inequality form after rearranging 2x - 4 < x^2 - 3x?

x^2 + 5x + 4 < 0

x^2 + 5x - 4 < 0

x^2 - 5x - 4 > 0

x^2 - 5x + 4 > 0

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the roots of the equation x^2 - 5x + 4 = 0?

x = 2 and x = 3

x = -1 and x = -4

x = 1 and x = 4

x = 0 and x = 5

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

For the inequality x^2 - 5x + 4 > 0, which range of x values is valid?

x = 1 or x = 4

x < 0 or x > 5

x > 1 and x < 4

x < 1 or x > 4

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