A-level Mathematics/OCR/C1/Equations/Problems

Manipulating Equations

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Collecting Like Terms

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Simplify the following:

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Multiplication

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Simplify the following:

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Fractions

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Simplify the following:

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Solving Equations

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Changing the Subject of an Equation

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1. Solve for  :

 

2. Solve for  :

 

3. Solve for  :

 

4. Solve for  :

 

5. Solve for  :

 

Solving Quadratic Equations

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Find the Roots of:

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Simultaneous Equations

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Example 1

At a record store, 2 albums and 1 single costs £10. 1 album and 2 singles cost £8. Find the cost of an album and the cost of a single.

Taking an album as   and a single as  , the two equations would be:

 

 

You can now solve the equations and find the individual costs.

Example 2

Tom has a budget of £10 to spend on party food. He can buy 5 packets of crisps and 8 bottles of drink, or he can buy 10 packets of crisps and 6 bottles of drink.

Taking a packet of crisps as   and a bottle of drink as  , the two equations would be:

 

 

Now you can solve the equations to find the cost of each item.

Example 3

At a sweetshop, a gobstopper costs 5p more than a gummi bear. 8 gummi bears and nine gobstoppers cost £1.64.

Taking a gobstopper as   and a gummi bear as  , the two equations would be: