Solve Quadratics - Factorisation 1 - Numbas at mathcentre.ac.uk

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of MASH Bath: Question Bank :

Ruth Hand

said

Ready to use

4 years, 1 month ago

History

○

Ben McGovern 2 years, 6 months ago

Published this.

○

Ruth Hand 4 years, 1 month ago

Gave some feedback: Ready to use

○

Ruth Hand 4 years, 1 month ago

Created this as a copy of Quadratics: Factorisation 1.

Name	Status	Author	Last Modified
Surds: Simplifying Expressions 1a	Ready to use	Ben McGovern	15/08/2023 15:04
Surds: Simplifying Expressions 1b	Ready to use	Ben McGovern	15/08/2023 15:04
Surds: Simplifying Expressions 2b	Ready to use	Ben McGovern	15/08/2023 15:49
Surds: Simplifying Expressions 2a	Ready to use	Ben McGovern	15/08/2023 15:49
Surds: Simplifying Expressions 3a	Ready to use	Ben McGovern	15/08/2023 15:31
Surds: Simplifying Expressions 3b	Ready to use	Ben McGovern	15/08/2023 15:14
Surds: Simplifying Expressions 4a	Ready to use	Ben McGovern	15/08/2023 15:29
Surds: Simplifying Expressions 4b	Ready to use	Ben McGovern	15/08/2023 15:26
Surds: Simplifying Expressions 4c	Ready to use	Ben McGovern	15/08/2023 15:50
Surds: Simplifying Expressions 5a - Rationalising the Denominator	Ready to use	Ben McGovern	15/08/2023 15:55
Surds: Simplifying Expressions 5b - Rationalising the Denominator	Ready to use	Ben McGovern	15/08/2023 16:07
Surds: Simplifying Expressions 6 - Rationalising the Denominator	Ready to use	Ben McGovern	21/09/2022 16:31
Surds: Simplifying Expressions 7 - Rationalising the Denominator	Ready to use	Ben McGovern	21/09/2022 16:31
Quadratics: Using the Quadratic Formula	Ready to use	Ben McGovern	14/09/2022 16:14
Quadratics: Factorisation 1	Ready to use	Ben McGovern	14/08/2023 15:01
Quadratics: Factorisation 2	Ready to use	Ben McGovern	14/08/2023 15:14
Quadratics: Completing the Square 1	Ready to use	Ben McGovern	14/08/2023 14:59
Quadratics: Completing the Square 2	Ready to use	Ben McGovern	14/09/2022 16:03
Quadratics: Interpreting the Discriminant	Ready to use	Ben McGovern	14/09/2022 16:08
Quadratics: Factorisation 3 - Difference of 2 squares	Ready to use	Ben McGovern	14/08/2023 15:33
Indices: Simplification 1a	Ready to use	Ben McGovern	26/06/2023 12:12
Indices: Simplification 1b	Ready to use	Ben McGovern	26/06/2023 14:31
Indices: Simplification 1c	Ready to use	Ben McGovern	26/06/2023 14:30
Indices: Simplification 2a	Ready to use	Ben McGovern	26/06/2023 14:33
Indices: Simplification 2b	Ready to use	Ben McGovern	26/06/2023 14:36
Indices: Simplification 3a	Ready to use	Ben McGovern	26/06/2023 14:37
Indices: Simplification 3b	Ready to use	Ben McGovern	26/06/2023 14:40
Indices: Change of Notation 1	Ready to use	Ben McGovern	15/08/2023 11:43
Indices: Change of Notation 2	Ready to use	Ben McGovern	15/08/2023 11:51
Indices: Change of Notation 3	Ready to use	Ben McGovern	15/08/2023 11:54
Solve Quadratics - Factorisation 1	Ready to use	Ruth Hand	14/08/2023 15:44
Quadratics: Solving a Quadratic Equation	Ready to use	Ben McGovern	09/12/2022 16:45
Quadratics: Solving by Factorisation	Ready to use	Ben McGovern	14/09/2022 16:25
AD2 Quadratics - solve	Ready to use	Megan Oliver	09/04/2024 15:13
AD5 Difference of two squares	Ready to use	Megan Oliver	09/04/2024 15:14
AA2 Indices - divide	Ready to use	Andrew Neate	09/04/2024 15:00
AA4 Indices - Fractional 2	Ready to use	Andrew Neate	09/04/2024 15:01
AA3 Indices - Fractional 1	Ready to use	Andrew Neate	09/04/2024 15:01
AA1 Indices - times	Ready to use	Andrew Neate	28/03/2024 13:17
Calculation with indices - times	Ready to use	Will Morgan	26/06/2024 11:53
Calculation with Indices - divide	Ready to use	Will Morgan	26/06/2024 12:07

There are 209 other versions that do you not have access to.

Question statement

Solve the following quadratic equation:

$\simplify[all]{x^2+{b}x+{c}} = 0$

Give any introductory information the student needs.

			Name	Type	Generated Value

b	integer	15
c	integer	54
p	integer	6
q	integer	9

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
{p+q}

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap List of numbers
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$x=$ Unnamed gap

Advice

For a quadratic equation of the form

$x^2+bx+c = 0,$ we are able to factorise the left hand side expression into the form

$(x+p)(x+q),$ if there exists a

$p$ and

$q$ such that

$p+q=b$ and

$p \times q = c$ .

For the expression

$\simplify{x^2+{b}x+{c}},$

we need two numbers which add together to give $\var{b}$ and multiply together to give $\var{c}$ . Therefore, $p=\var{p}$ and $q=\var{q}$ , and the quadratic equation can be written in the form

$\simplify{(x+{p})(x+{q})} = 0.$

Since one of the brackets must be $0$ for their product to be $0$ we know that

$\simplify{(x+{p})}= 0 \quad \text{or} \quad \simplify{(x+{q})}= 0$

and therefore, the solutions to this quadratic equation are

$x = \simplify{{-p}} \quad \text{and} \quad x = \simplify{{-q}} .$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
List of numbers
List of numbers		Hasn't run yet

This question is used in the following exams:

Quadratic Functions pre A-level by Ruth Hand in MASH Bath: Moodle quizzes and TS.
All about quadratics by Jinhua Mathias in Maths 3-2020.
All the good stuff by Chris Templet in Chris's workspace.
Universal Algebra by Ruth Hand in MASH Bath: Moodle quizzes and TS.
Scientific Maths Training Space by Ruth Hand in MASH Bath: Moodle quizzes and TS.
EC1602 Numbas 3 by samira Al-Moustafa in samira's workspace.

Loading...

Error

Solve Quadratics - Factorisation 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben McGovern 2 years, 6 months ago

Ruth Hand 4 years, 1 month ago

Ruth Hand 4 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Solve Quadratics - Factorisation 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben McGovern 2 years, 6 months ago

Ruth Hand 4 years, 1 month ago

Ruth Hand 4 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`