Algebra 2

Topics in this section: 

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

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Section 1: Quadratic equations

Solving quadratic equations by factorising

Using the quadratic formula

Solving a quadratic equation using substitution 

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

Problem involving equal roots

Proving roots are rational

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3. Quadratic and linear simultaneous equations

Points of intersection of a line and a quadratic curve

Using the substitution method to solve quadratic and linear equations simultaneously

4. Quadratic and linear simultaneous equations

Context problem with simultaneous equations

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5. Sum and product of quadratic roots

Forming equations from quadratic roots

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6. Vertex form of a quadratic equation

An introduction to completing the square

Finding the minimum value of a quadratic expression

Expressing a quadratic in complete square form:
- to find the minimum point, and
- to solve 

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7. Surds and surd equations

Simplifying surds

Simplifying surd fractions
Rationalizing the denominator by multiplying the numerator and denominator by the conjugate of the denominator

8. Solving surd equations

Solving surd equations and verifying solutions

Solving an equation with two surd terms and verifying the solutions

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9. The Factor Theorem

Using the factor theorem to show that a given linear expression is a factor

Using the factor theorem to find unknown coefficients

Factorising cubic expressions

Solving cubic equations

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11. Cubic graphs

Finding an expression for a cubic function from its graph

Finding the expression for a degree 4 polynomial from its graph

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Revision Questions with Solutions

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1. Solve quadratic equations

Solution

Solution

Solution

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2. The nature of quadratic roots

Solution

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3. Quadratic and linear simultaneous equations

Solution

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4. Sum and product of quadratic roots

Solution

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5. Vertex form of a quadratic equation

Solution

Solution

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6. Surds and surd equations

Solution

Solution

Solution

Solution

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7. The Factor Theorem

Solution

Solution

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8. Factorise and solve cubics

Solution

Solution

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9. Cubic graphs

Solution

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Printable Revision Workbook and Solutions

Printable Algebra 2 Revsion Questions

Solutions to Revision questions