steve's copy of Factoring Quadratics 2 $ax^2+bx+c$ 4 questions READY

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steve kilgallon

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steve kilgallon 8 years, 8 months ago

Created this as a copy of Factoring 2 Quadratics 2 of form:

$ax^2+bx+c$ .

Name	Status	Author	Last Modified
Factorising Quadratics 1 - Basic	Ready to use	Katie Lester	01/06/2016 09:47
Factorising Quadratics 2 - Intermediate	Ready to use	Katie Lester	01/06/2016 09:47
Factorising Quadratics 3 - Challenging	Ready to use	Katie Lester	01/06/2016 09:47
Factorising Quadratics 4 - Solving by Factorising or Using Formula	Ready to use	Katie Lester	01/06/2016 09:47
Factoring 2 Quadratics 2 of form: $ax^2+bx+c$	draft	Clare Lundon	05/10/2016 22:45
Factorising Quadratics 1: $x^2+bx+c$ 3 questions READY	draft	Clare Lundon	05/10/2016 22:46
steve's copy of Factoring Quadratics 2 $ax^2+bx+c$ 4 questions READY	draft	steve kilgallon	18/07/2016 16:05
Lucy's copy of Factoring Quadratics 2 $ax^2+bx+c$ 4 questions READY	draft	Lucy Hadfield	03/08/2016 10:50
Francis 's copy of Solving Quadratic Equations using the Quadratic Formula 4 Questions READY	draft	Francis Duah	12/08/2016 17:56
Gareth's copy of Lucy's copy of Factoring Quadratics 2 $ax^2+bx+c$ 4 questions READY	draft	Gareth Woods	26/08/2016 11:21
Kjell's copy of Francis 's copy of Solving Quadratic Equations using the Quadratic Formula 4 Questions READY	draft	Kjell Hansen	05/09/2016 11:01
Kjell's copy of Kjell's copy of Francis 's copy of Solving Quadratic Equations using the Quadratic Formula 4 Questions READY	draft	Kjell Hansen	05/09/2016 11:02
Solving Quadratic Equations using the Quadratic Formula and a Calculator	draft	Francis Duah	14/09/2016 16:55
Francis 's copy of Solving Quadratic Equations using the Quadratic Formula 4 Questions READY	draft	Francis Duah	14/09/2016 16:50
Factoring 1 Quadratic of form: $ax^2+bx+c$	draft	Clare Lundon	13/10/2016 10:06
Solving Quadratic Equations using the Quadratic Formula	draft	Hannah Bartholomew	18/09/2017 11:52
Ugur's copy of Factorising Quadratics 2 - Intermediate	Ready to use	Ugur Efem	01/11/2021 12:31
Ugur's copy of Factorising Quadratics 1 - Basic	Ready to use	Ugur Efem	04/11/2021 15:33

There are 19 other versions that do you not have access to.

Question statement

Express each of the following quadratic expressions as the product of two linear factors of the form $(ax+c)(bx+d)$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	3
b	integer	1
c	integer	-1
d	integer	1
f1	integer	3
f2	integer	2
f3	integer	-1

			Name	Type	Generated Value

a2	integer	2
b2	integer	3
c2	integer	-4
d2	integer	4
f12	integer	6
f22	integer	-4
f32	integer	-16

			Name	Type	Generated Value

a3	integer	2
b3	integer	2
c3	integer	-3
d3	integer	-5
f13	integer	4
f23	integer	-16
f33	integer	15

			Name	Type	Generated Value

a4	integer	2
b4	integer	3
c4	integer	0
d4	integer	4
f14	integer	6
f24	integer	8
f34	integer	0

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2,3)

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`

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Mathematical expression
  Add
Part c) Gap-fill
1. Gap Mathematical expression
  Add
Part d) Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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

$\simplify{{f1}x^2+{f2}*x+{f3}}$

$=$ Unnamed gap

Advice

A worked example using the quadratic expression from Part a: $\simplify{{f1}x^2+{f2}x+{f3}}$

When the coefficient of $x^2$ is not $1$ in a quadratic expression such as this one it is a little more complicated.

We must produce a pair of brackets $(ax+c)(bx+d)$ which multiply out to give $\simplify{{f1}x^2+{f2}x+{f3}}$

Therefore we must find:

the two factors, a and b, of the coefficent of the $x^2$ term in the quadratic, ( $\var{f1}$ in this example ) AND

the two factors, c and d, of the constant term in the quadratic, ( $\var{f3}$ in this example),

such that $(ax+c)(bx+d)$ = $\simplify{{f1}x^2+{f2}x+{f3}}$

Here we use $\var{a}$ and $\var{b}$ as the factors of $\var{f1}$ and $\var{c}$ and $\var{d}$ as the factors of $\var{f3}$

and we must now combine them correctly such that $(ax+c)(bx+d)$ = $\simplify{{f1}x^2+{f2}x+{f3}}$

The correct combination is: $\simplify{({a}x+{c})({b}x+{d})}$

These brackets, when multiplied out, will give the original quadratic expression $\simplify{{f1}x^2+{f2}x+{f3}}$

Try it!

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steve's copy of Factoring Quadratics 2 $ax^2+bx+c$ 4 questions READY

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Taxonomy: mathcentre

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Checkpoint description

steve kilgallon 8 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

steve's copy of Factoring Quadratics 2 ax2+bx+cax^2+bx+c 4 questions READY

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

steve kilgallon 8 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

steve's copy of Factoring Quadratics 2 $ax^2+bx+c$ 4 questions READY

Generated value: `integer`