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1
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e
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g
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Remember the correct formula
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Make
sure that you write the equation in a standard form and write down a, b and c
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Exponential equations can also be asked:
7
3X+1•5 − 4 • 3 X+2= − 3
7
3x (3 • 5 − 4 • 9) = − 3
3x(15 − 36) = −
7
3
7
3X (−21) = − 3
1
✓common factor
✓simplification
1
3x = 9
✓change to base 3
3X = 3-2
✓ answer
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Inequalities
To get the critical values, the right hand side must be = 0 i
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standard form
Remember: When dividing or multiplying by a(-), the inequality sign changes
The solution must be in the context of inequality at all times
Example, solve for x: (3𝑥 + 1)(𝑥 − 4) < 0
+
1
−3
+
4
✓ Method
1
✓End points
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Simultaneous equations
𝑦 + 7 = 2𝑥 and 𝑥 2 −𝑥𝑦 + 3𝑦 2= 15
𝑦 + 7 = 2𝑥
𝑦 = 2𝑥 − 7 … …
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1 𝒙2−𝒙 − 𝟏𝟐 = 𝟎
(𝑥 − 4)(𝑥 + 3) = 0
𝑥 = 4 𝑜𝑟 𝑥 = −3
1
...
3 𝒙 = 𝒂 2+𝒂 − 𝟐
if 𝒂 = 𝟖𝟖𝟖 𝟖𝟖𝟖 𝟖𝟖𝟖 𝟖𝟖𝟖
𝒂−𝟏
= (𝑎 + 2)(𝑎 − 1)
𝑎−1
=𝑎+2
= 888 888 888 890
𝟏
1
...
𝑦=𝑥+
1
𝑥
𝑥𝑦 = 𝑥 2+1
𝑥 2−𝑥𝑦 + 1 = 0
Since x is real, this equation has real roots
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5 √𝟐 − 𝒙 = 𝒙 + 𝟒
2 − 𝑥 = 𝑥 2+8𝑥 + 16
𝑥 2+9𝑥 + 14 = 0
(𝑥 + 7)(𝑥 + 2) = 0
𝑥 = −7 𝑜𝑟 𝑥 = −2
1
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(1)
𝑦 − 𝑘 − 𝑘𝑥 = 0 … … … (2)
From (2) 𝑦 = 𝑘𝑥 + 𝑘 …