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| Quadratic Formula (For solving quadratic equations) |
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Definition
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| Completing the square steps (for solving quadratic equations) |
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Definition
1. Make sure the constant term (and no others) is on the RHS of the equation.
2. Make sure coefficient of the x^2 term is 1 (divide through each term if needed).
3. Work out the SQUARE OF HALF THE COEFFICIENT OF X and add it to both sides of the equation.
4. Complete the perfect square [either: (x - k)^2 or (x + k)^2]. The term k is half the coefficient of x.
5. Take the square root of of both sides of the equation and solve for x. |
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| Symbol for the discriminant |
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Definition
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| Formula for finding out the discriminant (finding out the nature of the roots) |
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Definition
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NATURE OF ROOTS: (value of discriminant on flip)
Real =
Unreal =
Equal =
Unequal =
Rational =
Irrational = |
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Definition
VALUE OF DISCRIMINANT:
Real - ≥0
Unreal - <0
Equal - =0
Unequal - >0
Rational - Square number
Irrational - Not a square number |
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| Number one rule of factorisation |
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Definition
| Always look for a common factor |
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| Sum of two cubes (a^3 + b^3) |
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Definition
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| Difference of two cubes (a^3 - b^3) |
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Definition
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| Difference of two squares (a^2 - b^2) |
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Definition
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| What do you do if the difference of two squares and the difference of two cubes are both possible? |
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Definition
| Do the difference of two squares first, then the difference of two cubes. |
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| What is the degree of a polynomial? |
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Definition
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P(x) = 2x^3 - 4x^2 + 7x - 3.
What is P(a + 2)? |
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Definition
| P(a + 2) = 2(a + 2)^3 - 4(a + 2)^2 + 7(a + 2) - 3. |
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Definition
The answer to a division question.
eg. 8 ÷ 2 = 4.
4 is the quotient. |
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Definition
The [larger] number that is being "divided by".
eg.8 ÷ 2 = 4
8 is the dividend. |
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Definition
The smaller number that the larger one is being divided by.
eg. 8 ÷ 2 = 4
2 is the divisor. |
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Definition
The amount that is left over from a division.
eg. 8 ÷ 3 = 2 [remainder 2]
2 is the remainder. |
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| If a polynomial P(x) is divided by (x-a) then what is the remainder? |
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Definition
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| If a polynomial P(x) is divided by (ax-b) then what is the remainder? |
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Definition
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| If a polynomial P(x) is divided by (x+b) then what is the remainder? |
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Definition
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| x-a is a factor of P(x), if, and only if, P(a) = |
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Definition
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| ax-b is a factor of P(x), if, and only if, P(b/a) = |
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Definition
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| What is the very first step with finding out the variables in any simultaneous equation? |
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Definition
| Number the two equations (1 and 2). |
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| How do you perform the elimination method for simultaneous equations? |
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Definition
Times one or both of the equations by a number in order to make one of the variables have the same coefficient.
Next, minus or plus one equation from the other (eliminating one of the variables altogether) and solve for the remaining variable.
Finally, substitute in the variable amount and solve for the second variable. |
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| How do you perform the substitution method for simultaneous equations? (Best used when one of the equations is presented as x = **** or y = ****). |
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Definition
Substitute in one of the variables (leaving only one variable).
Solve for the present variable.
Substitute in the found variable and solve for the second variable. |
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| How do you factorise by inspection when (2x+1) is a factor of (2x^3 + 3x^2 - x - 1)? |
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Definition
Match up the first term, then the second. (2x+1)(2x^2 ??? +1)
Next, choose either the x^2 term or the x term from the original polynomial. Find which term will make the term equal to the one in the original polynomial and place it in the middle. |
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