Factorising Quadratics 5 - Completing the Square

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Katie Lester

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Ready to use

9 years, 6 months ago

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Katie Lester 9 years, 6 months ago

Gave some feedback: Ready to use

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Katie Lester 9 years, 6 months ago

Created this as a copy of Yameena's copy of Complete the square.

Name	Status	Author	Last Modified
Complete the square	draft	Bill Foster	06/08/2020 08:29
Factorising Quadratics 5 - Completing the Square	Ready to use	Katie Lester	01/06/2016 09:47
Lois's copy of Complete the square	draft	Lois Rollings	25/10/2017 10:26
My Completing the Square	draft	steve kilgallon	05/09/2016 16:13
Completing the Square	Ready to use	Wan Mekwi	17/09/2021 10:28

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Question statement

Put the following quadratic expression in the form $(x+a)^2+b$ for suitable numbers $a$ and $b$ .

Your answer must be input exactly in this form.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	number	-5.5
s1	integer	-1
b	number	-12.25

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
s1*random(1.0..9.5#0.5)

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: `number`

-5.5

← Depends on:

→ Used by:

Advice
"Unnamed part" - prompt
"Unnamed part" → "Unnamed gap" - Correct answer
"Unnamed part" → "Unnamed step" - prompt

Parts

Gap-fill
1. Gap Mathematical expression
  Add
1. Step Information only

Gap-fill

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

$\simplify{x^2+{2*a}x+ {a^2+b}} = \phantom{{}}$ Unnamed gap.

Advice

Given the quadratic $q(x)=\simplify{x^2+{2*a}x+ {a^2+b}}$ we complete the square by:

1. Halving the coefficient of $x$ gives $\var{a}$

2. Work out $\simplify[all]{p(x)=(x+{a})^2=x^2+{2*a}x+{a^2}}$ .
This gives the first two terms of $q(x)$ .

3. But the constant term $\simplify[all]{{a^2}}$ in $p(x)$ is not the same as in $q(x)$ , so we need to adjust by adding on $\simplify[std,!fractionNumbers]{{a^2+b}-{a^2}={b}}$ to $p(x)$ .
Hence we get

$q(x) = \simplify[all]{p(x)+{b} = (x+{a})^2+{b}}$

Give a worked solution to the whole question.

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Information only

This question is used in the following exam:

International Summer School: Quadratics 2 by Rachel Binks in MSP International Summer School.

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Factorising Quadratics 5 - Completing the Square

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Katie Lester 9 years, 6 months ago

Katie Lester 9 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

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Error

Factorising Quadratics 5 - Completing the Square

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Katie Lester 9 years, 6 months ago

Katie Lester 9 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`