Equations, Inequalities, Geometric Sequences, Iteration

factorizing

ax² - bx + c

1. find factors of c

2. factors should add up to b, place into brackets

• if co-efficient: a * c

purpose of factorizing + how to solve for x

to find roots (intersection with x-axis)

• i.e. (x-4) // x = +4

completing the square equation

solving completing the square + purpose

find maximum/minimum point of a curve

• (x + a)² + b

• minimum = (-a,b)

how to find ‘x’ from completing the square

1. (x+a)² - b » (x+a)² = b

2. square root whole function

3. add “a” to other side

4. x = -a ±√b

completing the square with an “a” coefficient

separate a and c from the equation

• DON’T INCLUDE SEPARATED COEFFICIENT IN X CO-ORDINATE

quadratic formula

simultaneous equations

1. get rid of one of the letters so the 1st remains

2. substitute value found from the 1st into equation to find 2nd letter

difference between 3y² and (3y)²

• 3y² means only y is squared: 3* y * y

• (3y)² means everything is squared: 3y * 3y

quadratic simultaneous equations

1. substitute the squared value with expanded of other value

• i.e. y² - x², sub y² /w (x+3)(x+3)

• make sure the end result includes the coefficient² if required

linear sequences

• difference between numbers horizontally (1,3) = coefficient

• difference between numbers & og numbers (1,2) = c

2n-1

sequence in fractions

• split up numerators & denominators into diff sequences

• place found sequences back into division format

how to find value of next term in geometric sequence

nth = a * r^n-1

• a = 1st term’s value

• r = multiplier (coefficient, basically)

how to find a geometric sequence

every geometric sequence is written in an² + bn + c

• find difference in between each value twice, then divide by two to get a

• work from the bottom

when is the iterative process used

to find an accurate root of a quadratic equation

what is x_n+1

next term

what is x_n

current term

• i.e. x₀ or x₁

how to rearrange into iterative formula method

1. will be given X₀ (1st) value in q

2. ignore y, rearrange so that x_n+1 = √x_n + a

3. save X₀ as “ans” // sub ans into x

4. press “=” for as many times as required to be iterated in question

how to know if answer is between 2 numbers

change in end value sign