AD4 Quadratics - factorise (a not 1) - Numbas at mathcentre.ac.uk

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From users who are members of Skills Audits for Maths and Stats :

Lauren Desoysa	said	Ready to use	1 year ago
Andrew Neate	said	Needs to be tested	1 year, 1 month ago

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Will Morgan 11 months, 1 week ago

Published this.

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Lauren Desoysa 1 year ago

Gave some feedback: Ready to use

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Andrew Neate 1 year, 1 month ago

Gave some feedback: Needs to be tested

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Andrew Neate 1 year, 1 month ago

Created this as a copy of Factorising Quadratic Equations with

$x^2$ Coefficients Greater than 1.

Name	Status	Author	Last Modified
Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1	Ready to use	Hannah Aldous	20/11/2019 14:39
MATH6058 Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1	draft	Catherine Palmer	25/01/2018 09:18
cormac's copy of MATH6058 Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1	draft	cormac breen	24/10/2018 13:36
Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1	draft	Ed Southwood	08/08/2022 10:18
Factorising Quadratic Equations with $x^2$ Coefficients Less than 1	draft	Ed Southwood	08/08/2022 10:18
Simon's copy of Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1	draft	Simon Thomas	07/03/2019 09:41
AD4 Quadratics - factorise (a not 1)	Ready to use	Andrew Neate	09/04/2024 15:14

There are 21 other versions that do you not have access to.

Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	3
b	integer	-1
c	integer	6
d	integer	-4
roots	list	[ 1/3, 2/3 ]

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..3)

JME function reference

Description

$a$ in $(ax+b)(cx+d)$

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`

→ Used by:

c
roots

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

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

Solve the following equation by factorisation to find $x$ .

$\simplify{{a*c}x^2+{a*d+b*c}x+{b*d}=0}\text{.}$

Input your answers in ascending order.

$x=$ Gap 0.

$x=$ Gap 1.

Advice

As this question involves a number greater than $1$ before the $x^2$ value it has a factorised form $(ax+b)(cx+d)$ .

To find $a$ and $c$ , we need to consider the factors of $\var{a*c}$ .

You may have to test a a few different options before you find one that works. In this case $a$ and $c$ are $\var{a}$ and $\var{c}$ .

This means our factorised equation must take the form

$(\var{a}x+b)(\var{c}x+d)=0\text{.}$

This expands to

$\simplify{ {a*c}x^2 + ({a}*d+{c}*b)x + a*b}$

So we must find two numbers which add together to make $\var{a*d+b*c}$ , and multiply together to make $\var{b*d}$ .

Therefore $b$ and $d$ must satisfy

$\begin{align} b \times d &=\var{b*d}\\ \simplify{{a}d+{c}b} &= \var{a*d+b*c}\text{.} \end{align}$

$b = \var{b}$ and $d = \var{d}$ satisfy these equations:

$\begin{align} \var{b} \times \var{d} &=\var{b*d}\\ \simplify[]{ {a}*{d} + {b}*{c} } &= \var{a*d+b*c} \end{align}$

So the factorised form of the equation is

$\simplify{({a}x+{b})({c}x+{d}) = 0} \text{.}$

$\simplify{({a}x+{b})({c}x+{d}) = 0}$ when either $\var{a}x+\var{b} = 0$ or $\var{c}x+ \var{d} = 0$ .

So the roots of the equation are $\var[fractionnumbers]{-b/a}$ and $\var[fractionnumbers]{-d/c}$ .

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AD4 Quadratics - factorise (a not 1)

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Taxonomy: mathcentre

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Taxonomy: Context

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Will Morgan 11 months, 1 week ago

Lauren Desoysa 1 year ago

Andrew Neate 1 year, 1 month ago

Andrew Neate 1 year, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

AD4 Quadratics - factorise (a not 1)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Will Morgan 11 months, 1 week ago

Lauren Desoysa 1 year ago

Andrew Neate 1 year, 1 month ago

Andrew Neate 1 year, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`