Algebra 2 |
Topics in this section:
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Section 1: Quadratic equations
Solving quadratic equations by factorising |
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Using the quadratic formula |
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Solving a quadratic equation using substitution |
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Solving a quadratic surd equation using substitution |
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2. The nature of quadratic roots
Using the discriminant to find the nature of quadratic roots |
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Problem involving equal roots |
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Proving roots are rational |
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3. Quadratic and linear simultaneous equations
Points of intersection of a line and a quadratic curve |
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Using the substitution method to solve quadratic and linear equations simultaneously |
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4. Quadratic and linear simultaneous equations
Context problem with simultaneous equations |
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5. Sum and product of quadratic roots
6. Vertex form of a quadratic equation
An introduction to completing the square |
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Finding the minimum value of a quadratic expression
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Expressing a quadratic in complete square form:
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7. Surds and surd equations
Simplifying surds |
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Simplifying surd fractions
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8. Solving surd equations
Solving surd equations and verifying solutions |
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Solving an equation with two surd terms and verifying the solutions |
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9. The Factor Theorem
Using the factor theorem to find unknown coefficients |
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Factorising cubic expressions |
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Solving cubic equations |
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11. Cubic graphs
Finding an expression for a cubic function from its graph |
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Finding the expression for a degree 4 polynomial from its graph |
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Revision Questions with Solutions
1. Solve quadratic equations
2. The nature of quadratic roots
3. Quadratic and linear simultaneous equations
4. Sum and product of quadratic roots
5. Vertex form of a quadratic equation
6. Surds and surd equations
7. The Factor Theorem
8. Factorise and solve cubics
9. Cubic graphs