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Questions and Answers
When factorizing a quadratic expression in the form of x^2 + bx + c, what is the first step?
When factorizing a quadratic expression in the form of x^2 + bx + c, what is the first step?
- List the factor pairs of c (correct)
- Find a common pair
- Find the coefficient of x
- List the numbers that add to make b
When solving a quadratic equation in the form of (x + y)(x + z) = 0, what do you do to find the solutions?
When solving a quadratic equation in the form of (x + y)(x + z) = 0, what do you do to find the solutions?
- Find the sum of y and z
- Find the average of y and z
- Find the opposite of y and z (correct)
- Find the product of y and z
What is the rule to follow when combining like terms in an algebraic expression?
What is the rule to follow when combining like terms in an algebraic expression?
- Combine coefficients first
- Work from left to right (correct)
- Combine variables first
- Work from right to left
What is the purpose of using the FOIL method when multiplying two binomials?
What is the purpose of using the FOIL method when multiplying two binomials?
When solving a quadratic equation with a coefficient greater than 1, what is the first step?
When solving a quadratic equation with a coefficient greater than 1, what is the first step?
What is the rule to follow when solving an inequality in the form of x > a or x < a?
What is the rule to follow when solving an inequality in the form of x > a or x < a?
What is the purpose of using BIDMAS when evaluating an algebraic expression?
What is the purpose of using BIDMAS when evaluating an algebraic expression?
When solving a harder equation with fractions, what is the first step?
When solving a harder equation with fractions, what is the first step?
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Study Notes
Collecting Like-Terms
- Remember BIDMAS rule
- Identify terms to combine
- Combine coefficients working from left to right
- Consider the sign before the number (+ or -)
Expanding Triple Brackets
- Use FOIL method: First, Outer, Inner, Last
- Focus on the first two sets of brackets, then the third
- Always results in at least one x^3 term
Factorising Quadratics
- Use the form: x^2 + bx + c
- List factor pairs of c
- List numbers that add to make b
- Find a common pair and write as (x + y)(x + z)
- Remember the signs in front of the numbers
Solving Quadratics
- Factorise the quadratic equation
- Find the opposite of z and y (e.g. (x + 2)(x + 8) => x = -2 and x = -8)
Solving Harder Quadratics (Coefficient > 1)
- Multiply coefficient and c, then write out factors
- Find a factor pair that makes bx
- Split the equation into two (e.g. (2x^2 + y)(x + z))
- Factorise as much as possible outside of the brackets on both sides
- Move whatever is outside the brackets into the brackets (e.g. (2x^2 + w))
- Move the common y/z in the brackets into another set of brackets with x (e.g. (2x^2 + w)(x + v))
Solving Harder Equations
- If there are fractions, multiply both sides by the denominator to cancel it out
- Remove any normal numbers that don't have x
- Divide x by what is left
Inequalities on a Number Line
- Solid dot means include the number
- Hollow dot means does not include the number
- Inequalities can be shown as x >, <, ≤, or ≥
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