Maths IB EXAM REVIEW with Accurate
Solutions
Quadratic Equations - correct answer-ax² + bx + c = 0
( x = addition)
( c = multiplication)
The solutions to quadratic equations - correct answer-Roots
How do you complete the square? - correct answer-X² + 10x + 10 = 0
(x+5)² + 10 > this number will be half the coefficient.
> Subtract the number in the brackets.
(x+5)² - 25 + 10
>Square root both sides
x+5 = ±√15
X = -5
Deriving the Quadratic Formula - correct answer-Start with ax² + bx + c = 0
(General form. Divide throughout by a)
ax²/a + bx/a + c/a = 0
= x² + bx/a + c/a
(x + b/2a)² - (b/2a)² + c/a = 0
(x + b/2a)² = -c/a + b²/4a²
(get a common denominator for the two constants and make a perfect square)
Quadratic Formula - correct answer-
b - 4ac - correct answer-Tells us that the roots are like. Real, imaginary or repeated.
b - 4ac is called the discriminant.
What is the discriminant? - correct answer-the discriminant tells us whether there are
two solutions, one solution, or no solutions.
Graphed quadratic equations - correct answer-Parabola
, Finding the minimum values of a quadratic - correct answer-Example : x² - 6x - 12
(x-3)² - 9 - 12
(x-3)² - 21
When x = 3, we have a minimum value of -21. (the number outside the bracket is the
minimum)
Vertex equation - correct answer-y = a(x - h)2 + k
Vertex - correct answer-the highest point; the top or apex.
Simultaneous Equations - correct answer-1. Number the equations
2. Balance the coefficient to find the unknown (if not balanced already)
3. Eliminate by subtracting or adding (When the signs are different you add)
4. Using the value of x in equation 1 or 2, find the value of y.
Changing the subject - correct answer-v= 1/3∏r²h
3v/∏r² = h
The difference of two squares is often used when simplifying algebraic fractions -
correct answer-Example :
f²-4 / f+2 → (f-2)(f+2)/ f + 2 = f - 2
Arithmetic Sequences - correct answer-sequence : 2, 5, 8, 11, 14
rule = +3
n = 3n - 1
Quadratic sequence - correct answer-n² + 3n - 2
Integers - correct answer-Whole numbers, positive or negative, eg., 1, 7, -8, -90
Rational Number - correct answer-Written as fractions, eg., 1/3, 4/1
Irrational Number - correct answer-Cannot be written as a fraction, root 2, ∏.
Square Numbers - correct answer-by multiplying any integer by itself.
Factors - correct answer-Divides any number into number exactly, eg., 12 = 1, 2, 3 , 4,
6, 12
Prime numbers - correct answer-A number that has exactly 2 factors, eg., 21= 3, 7.
Proof by contradiction - correct answer-Let's suppose √2 is a rational number. Then we
can write it √2 = a/b where a, b are whole numbers, b not zero.
Solutions
Quadratic Equations - correct answer-ax² + bx + c = 0
( x = addition)
( c = multiplication)
The solutions to quadratic equations - correct answer-Roots
How do you complete the square? - correct answer-X² + 10x + 10 = 0
(x+5)² + 10 > this number will be half the coefficient.
> Subtract the number in the brackets.
(x+5)² - 25 + 10
>Square root both sides
x+5 = ±√15
X = -5
Deriving the Quadratic Formula - correct answer-Start with ax² + bx + c = 0
(General form. Divide throughout by a)
ax²/a + bx/a + c/a = 0
= x² + bx/a + c/a
(x + b/2a)² - (b/2a)² + c/a = 0
(x + b/2a)² = -c/a + b²/4a²
(get a common denominator for the two constants and make a perfect square)
Quadratic Formula - correct answer-
b - 4ac - correct answer-Tells us that the roots are like. Real, imaginary or repeated.
b - 4ac is called the discriminant.
What is the discriminant? - correct answer-the discriminant tells us whether there are
two solutions, one solution, or no solutions.
Graphed quadratic equations - correct answer-Parabola
, Finding the minimum values of a quadratic - correct answer-Example : x² - 6x - 12
(x-3)² - 9 - 12
(x-3)² - 21
When x = 3, we have a minimum value of -21. (the number outside the bracket is the
minimum)
Vertex equation - correct answer-y = a(x - h)2 + k
Vertex - correct answer-the highest point; the top or apex.
Simultaneous Equations - correct answer-1. Number the equations
2. Balance the coefficient to find the unknown (if not balanced already)
3. Eliminate by subtracting or adding (When the signs are different you add)
4. Using the value of x in equation 1 or 2, find the value of y.
Changing the subject - correct answer-v= 1/3∏r²h
3v/∏r² = h
The difference of two squares is often used when simplifying algebraic fractions -
correct answer-Example :
f²-4 / f+2 → (f-2)(f+2)/ f + 2 = f - 2
Arithmetic Sequences - correct answer-sequence : 2, 5, 8, 11, 14
rule = +3
n = 3n - 1
Quadratic sequence - correct answer-n² + 3n - 2
Integers - correct answer-Whole numbers, positive or negative, eg., 1, 7, -8, -90
Rational Number - correct answer-Written as fractions, eg., 1/3, 4/1
Irrational Number - correct answer-Cannot be written as a fraction, root 2, ∏.
Square Numbers - correct answer-by multiplying any integer by itself.
Factors - correct answer-Divides any number into number exactly, eg., 12 = 1, 2, 3 , 4,
6, 12
Prime numbers - correct answer-A number that has exactly 2 factors, eg., 21= 3, 7.
Proof by contradiction - correct answer-Let's suppose √2 is a rational number. Then we
can write it √2 = a/b where a, b are whole numbers, b not zero.
