Lois's copy of Complete the square

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Lois Rollings

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Lois Rollings 8 years, 8 months ago

Published this.

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Lois Rollings 9 years, 7 months ago

Created this as a 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

This question is about a quadratic expression$q(x).

Give any introductory information the student needs.

			Name	Type	Generated Value

a	number	-7
s1	integer	-1
b	number	-29

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`

-7

← Depends on:

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 Number entry
  Add

Gap-fill

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

If $q(x) =\simplify{x^2+{2*a}x+ {a^2+b}}$ , write $q(x)$ in the form $(x+a)^2+b$ for suitable numbers $a$ and $b$ .

$q(x) =$ Unnamed gap.

Advice

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

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

2. Now $\simplify[all]{p(x)=(x+{a})^2=x^2+{2*a}x+{a^2}}$ .
This matches 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

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

b) The minimum value of $q(x)$ will occur when $(x+\var{a})^2 = 0$ and $q(x)=\var{b}$

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
Mathematical expression
Mathematical expression		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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History

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Checkpoint description

Lois Rollings 8 years, 8 months ago

Lois Rollings 9 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

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Lois's copy of Complete the square

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Lois Rollings 8 years, 8 months ago

Lois Rollings 9 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`