Ugur's copy of Ugur's copy of Algebra: Solving quadratics by factorising

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Created this as a copy of Ugur's copy of Algebra: Solving quadratics by factorising.

Name	Status	Author	Last Modified
Completing the square	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Algebra: Completing the square	draft	Lovkush Agarwal	17/10/2019 17:07
Algebra: Factorising quadratics	draft	Lovkush Agarwal	23/09/2019 13:52
Algebra: Solving quadratics by factorising	Ready to use	Lovkush Agarwal	07/04/2020 10:19
Algebra: Solving quadratics by completing the square	Ready to use	Lovkush Agarwal	07/04/2020 09:59
Quadratic Factorisation	draft	Gareth Woods	14/06/2017 16:28
Harry's copy of Solving quadratics by factorising	draft	Harry Flynn	07/07/2017 09:24
Solving quadratics by factorising - AMRC	draft	Ian Loasby	24/07/2017 16:26
Katherine's copy of Solving quadratics by factorising	draft	Katherine Tomlinson	17/08/2017 16:51
Solving Equations with Hidden Quadratics	draft	Katherine Tomlinson	17/08/2017 16:33
Algebra: Quadratics, multiplying out brackets	draft	Lovkush Agarwal	20/06/2018 13:48
Factorising quadratics	draft	Owen Jepps	11/01/2018 01:23
Quadratic Factorisation and hints	draft	Owen Jepps	11/01/2018 01:30
Edward's copy of Factorising quadratics	draft	Edward Hall	12/03/2018 20:42
rema's copy of Algebra: Factorising quadratics	draft	rema Nath	28/06/2018 01:12
grant's copy of Algebra: Solving quadratics by factorising	draft	grant smith	28/06/2018 01:10
grant's copy of Algebra: Solving quadratics by completing the square	draft	grant smith	28/06/2018 01:23
rema's copy of Algebra: Factorising quadratics	draft	rema Nath	28/06/2018 01:18
Algebra: Factorising quadratics	draft	emma rand	27/07/2018 15:59
Algebra: Solving quadratics by completing the square. shorter	draft	Lovkush Agarwal	12/12/2018 12:39
Algebra: Solving quadratics by factorising. shorter	draft	Lovkush Agarwal	04/12/2019 11:43
Basic Algebraic Manipulation: Completing the square	draft	Benjamin Bui	17/01/2019 05:29
Gizem's copy of Algebra: Solving quadratics by completing the square. shorter	draft	Gizem Intepe	02/03/2019 06:07
what the heck 2	draft	John Wick	30/05/2019 11:58
John's copy of Algebra: Solving quadratics by factorising. shorter	draft	John Wick	28/03/2020 19:13
Musa's copy of 3 Solving quadratics by completing the square	draft	Musa Mammadov	27/06/2023 01:27
Solving quadratics - factorisation	Ready to use	Shaheen Charlwood	27/10/2022 18:50
Ugur's copy of Algebra: Solving quadratics by factorising	Ready to use	Ugur Efem	08/11/2021 16:44
Ugur's copy of Ugur's copy of Algebra: Solving quadratics by factorising	Ready to use	Ugur Efem	03/05/2022 11:33

There are 42 other versions that do you not have access to.

Question statement

Solve the quadratic equations by factorising. If there is more than one solution, enter them all separated by a comma.

-----------------------------------

Give any introductory information the student needs.

			Name	Type	Generated Value

num	list	Nested 5×4 list
a	list	[ 1, 1, 1, 1, 1 ]
b	list	[ 6, 1, -5, -5, -5 ]
c	list	[ 1, 4, 1, 2, 3 ]
d	list	[ 2, -5, -3, 1, 1 ]
solmax	vector	vector(-2,1.25,5,5,5)
solmin	vector	Vector with 5 components

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
[[1,random(6..7),1,random(2..5)]] +
shuffle([
  [1,random(-4..-6),1,random(-3..3 except 0)],
  [1,random(-4..-6),random(2..3),random(-1..1 except 0)],
  [1,random(1,3,5),4,random(1,3,5)*random([1,-1])],
  [1,random(-4..-6),3,random([-1,1,-2,2])]
  ])

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`

[ [ 1, 6, 1, 2 ], [ 1, 1, 4, -5 ], [ 1, -5, 1, -3 ], [ 1, -5, 2, 1 ], [ 1, -5, 3, 1 ] ]

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. List of numbers
  Add
Part b) Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. List of numbers
  Add

Gap-fill

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

Factorise $\simplify{{a[1]*c[1]}x^2+{a[1]*d[1]+b[1]*c[1]}x+ {b[1]*d[1]}}=$ Gap 0.

Hence solve $\simplify{{a[1]*c[1]}x^2+{a[1]*d[1]+b[1]*c[1]}x+ {b[1]*d[1]}}=0$ .

Gap 1.

Advice

a) Observe that

$\simplify{{a[1]*c[1]}x^2+{a[1]*d[1]+b[1]*c[1]}x+ {b[1]*d[1]}=({a[1]}x+{b[1]})({c[1]}x+{d[1]})}.$

Hence the solutions to $\simplify{{a[1]*c[1]}x^2+{a[1]*d[1]+b[1]*c[1]}x+ {b[1]*d[1]}}= 0$ are $x=\simplify{{-b[1]}/{a[1]}}$ and $x=\simplify{{-d[1]}/{c[1]}}$ .

b) Observe that

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

Hence the solutions to $\simplify{{a[2]*c[2]}x^2+{a[2]*d[2]+b[2]*c[2]}x+ {b[2]*d[2]}}= 0$ are $x=\simplify{{-b[2]}/{a[2]}}$ and $x=\simplify{{-d[2]}/{c[2]}}$ .

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
List of numbers
List of numbers		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
List of numbers
List of numbers		Hasn't run yet

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Ugur's copy of Ugur's copy of Algebra: Solving quadratics by factorising

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Taxonomy: mathcentre

Taxonomy: Kind of activity

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Ugur Efem 2 years, 10 months ago

Ugur Efem 2 years, 10 months ago

Ugur Efem 2 years, 10 months ago

Error in variable testing condition

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Generated value: `list`

Parts

Gap-fill

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Ugur's copy of Ugur's copy of Algebra: Solving quadratics by factorising

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ugur Efem 2 years, 10 months ago

Ugur Efem 2 years, 10 months ago

Ugur Efem 2 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`