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A18b - Solving quadratic equations by completing the square

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A18c - Solving quadratic equations using the quadratic formula

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Expanding, simplifying, factorising, and solving equations assorted problems

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If a cake weighs \(600\) g and a muffin weighs \(120\) g, what is the mass of 3 cakes and 2 muffins?
The answer is \(3 \times 600 + 2 \times 120 = 2040\) g
What is the mass of 6 cakes and 4 muffins?
The slow way to work this out is to do \(6 \times 600 + 4 \times 120 = 4080\) g.

A quicker way is to spot that 6 cakes and 4 muffins must weigh twice as much as 3 cakes and 2 muffins, and \(2 \times 2040 = 4080\) g.
Now suppose we know that 3 cakes and 2 muffins weigh 2040 g, but that we don't know how much an individual cake or muffin weighs. Consider the following questions:
Do you have enough information to work out how the mass of an individual cake or an individual muffin?

Do you have enough information to work out the total mass of 6 cakes and 4 muffins?

Do you have enough information to work out the total mass of 42 cakes and 28 muffins?

Do you have enough information to work out the total mass of 6 cakes and 6 muffins?

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A19a - Solving two linear simultaneous equations algebraically by elimination

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If a cake weighs \(600\) g and a muffin weighs \(120\) g, what is the mass of 3 cakes and 2 muffins? The answer is \(3 \times 600 + 2 \times 120 = 2040\) g What is the mass of 6 cakes and 4 muffins?

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Slides in PDF (one slide per page, suitable for importing into IWB software)

Worksheet (with space for student work)

Handout (slides with exercises only; 4 per page for reduced printing)

Skills drill (15 questions on one side of A4; answers included)

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A19b - Solving two linear simultaneous equations graphically or algebraically by substitution

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Skills drill (15 questions on one side of A4; answers included)

Links to past exam questions

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A19c - Solving two simultaneous equations (linear and curve) algebraically

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https://padlet.com/rdownes/Algebra1
https://padlet.com/rdownes/Algebra2
https://padlet.com/rdownes/Algebra3
https://padlet.com/rdownes/Algebra4
https://padlet.com/rdownes/Algebra5
https://padlet.com/rdownes/Algebra6
https://padlet.com/rdownes/Algebra7
https://padlet.com/rdownes/Algebra8
https://padlet.com/rdownes/Algebra9
https://padlet.com/rdownes/Algebra10
https://padlet.com/rdownes/Algebra11
https://padlet.com/rdownes/Algebra12

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Direct Measurement Video of a Rotating Water Tank: Purple Hexane and Parabolic Fish