Factorising Quadratics 4 - Solving by Factorising or Using Formula

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Katie Lester

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Katie Lester

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Ready to use

9 years, 7 months ago

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Ben Brawn commented 9 years, 7 months ago

I think you should have "x=" in the statment of the quadratic formula/equation.

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Katie Lester 9 years, 7 months ago

Gave some feedback: Ready to use

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Katie Lester 9 years, 7 months ago

Created this as a copy of Factorising Quadratics 3 - Challenging.

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

Find the solutions of $x$ for the following quadratics by simplifying into two linear factors or otherwise.

You may need to use the quadratic equation, defined as:

$-b\pm\sqrt{b^2-4ac}$$2a$

Make sure you keep track of the positives and negatives.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	list	[ 3, 6, 4, 6 ]
b	list	[ -32, 30, -18, 7 ]
c	list	[ -69, 33, -82, -45 ]
disc1	number	1852
disc2	number	108
disc3	number	1636
disc4	number	1129
ansmin	number	-1.839
ansplus	number	12.51

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(1..9),4)

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: `list`

[ 3, 6, 4, 6 ]

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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Part b) Gap-fill
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Part c) Gap-fill
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Part d) Gap-fill
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2. Gap Gap 1. Number entry
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Ask the student a question, and give any hints about how they should answer this part.

Find the roots of $\simplify{{a[0]}*x^2+{b[0]}*x+{c[0]}}=0$.

Give your answers in ascending order to four significant figures.

$x=$ Gap 0. and $x=$ Gap 1.

Advice

Worked example using Part a:

Find the roots of $\simplify{{a[0]}*x^2+{b[0]}*x+{c[0]}}=0$.

The quadratic formula is given by

$-b\pm\sqrt{b^2-4ac}$$2a$

To solve this, simply input the numbers from the equation into the formula, defining the coefficient of $x^2$ as $a$, the coefficient of $x$ as $b$, and the constant as $c$.

Here, $x=$ $\simplify{-{b[0]}}$$\pm$$\sqrt{\var{b[0]}^2-4(\var{a[0]}\times\var{c[0]})}$$\simplify{2*{a[0]}}$

Inputting these figures into a calculator, starting with the minus sign before the root, gives:

$x=\var{ansmin}$,

and using the positive root version gives the other solution:

$x=\var{ansplus}$.

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:

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Factorising Quadratics 4 - Solving by Factorising or Using Formula

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Comment

Checkpoint description

Ben Brawn commented 9 years, 7 months ago

Katie Lester 9 years, 7 months ago

Katie Lester 9 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

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Error

Factorising Quadratics 4 - Solving by Factorising or Using Formula

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben Brawn commented 9 years, 7 months ago

Katie Lester 9 years, 7 months ago

Katie Lester 9 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`