Summary: Mathematics
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5 Equations and inequalities
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5.1 The quadratic formula
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How do you solve an equation with the quadratic formula
1. Write the equation in the form ax2+bx+c=0
2. Write down the values of a, b and c
3. Calculate D= b2-4ac
4. The solutions are x=-b+D/2a or x=-b-D/2a -
How many solutions do you have to the quadratic equation
2 if D is more than 0
1 if D is equal to 0
0 if D is less than 0 -
5.2 Solution methods
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Rules for solving quadratic equations
1. Eliminate the fractions if there are fractions
2. Simplify as much as possible
3. Check if the equation can be arranged in the form x2=c
4. Check if you can factorise the equation
5. Use the quadratic formula or completing the square when nothing works -
5.3 Linear inequalities
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When do you have to flip the inequality sign
If x is negative -
How do you solve a linear inequality
1. Multiply the fractions and brackets out
2. Bring all the x terms to the LHS and the rest to the RHS
3. Simplify both sides
4. Divide both sides by the number in front of the x -
5.4 Inequalities and graphs
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How do you solve an inequality
1. Use the graph to find out for which values you have f(x)=g(x)
2. show the solutions to f(x)=g(x) on a number line and colour the part for which f(x)=g(x)
3. Write down the solutions to the inequality -
How do you solve the inequality f(x)-g(x)
Find out where the graph of f is below the graph of g -
How do you solve the inequality f(x)+g(x)
Find out where the graph of f is above the graph of g -
5.6 Using parameters
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What does p represent
It shows multiple functions -
6 Skills and equations
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6.2 Simplifying fractions
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Rule for multiplying fractions
Fraction*fraction=numerator*numerator/denominator*denominator
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