IB Math – Foundations: Linear Equations, Systems & Fractions

What does PEMDAS stand for, and what is it used for?

Parentheses, Exponents, Multiplication/Division, Addition/Subtraction — the order to solve a math expression in

In PEMDAS, do multiplication and division happen in a fixed order relative to each other?

No, whichever comes first left to right (they're equal priority); same rule applies to addition/subtraction

What is the slope-intercept form of a linear equation?

y = mx + c

In y = mx + c, what does m represent?

The slope (gradient) of the line

In y = mx + c, what does c represent?

The y-intercept

What is the standard form of a linear equation?

ax + by + c = 0

What is the point-slope form of a linear equation, and what do the variables mean?

y - y1 = m(x - x1), where m is the slope and (x1, y1) is a known point on the line

In IB math, what term is used interchangeably with "slope"?

Gradient

If two lines are parallel, what is true about their slopes?

They are equal

If two lines are perpendicular, what is true about their slopes?

They are negative reciprocals of each other, so m1 times m2 equals -1

What is a system of equations?

A set of two or more equations that share variables and are solved together

What does the solution to a system of two linear equations represent graphically?

The point where the two lines intersect

What are the two main algebraic methods for solving a system of equations without a calculator?

Substitution and elimination

Briefly, how does the substitution method work?

Solve one equation for one variable, then plug that expression into the other equation

Briefly, how does the elimination method work?

Add or subtract the two equations so one variable cancels out, leaving one variable to solve for

Before adding or subtracting equations in elimination, what must be true about one variable's coefficients?

Same number, opposite sign, so they cancel to zero when combined

If no variable already has matching opposite coefficients, what do you do before eliminating?

Multiply one or both equations by a number so one variable's coefficients become equal and opposite

After solving for one variable in a system, how do you find the other variable?

Substitute that value back into either original equation and solve

What does LCM stand for and mean?

Least Common Multiple, the smallest number that two numbers both divide into evenly

Why is the LCM useful when adding or subtracting fractions?

It gives a common denominator so the fractions can be combined

What are the steps to multiply two fractions?

Multiply the numerators together, then multiply the denominators together

How do you multiply a fraction by a whole number, like 1/3 times 6?

Put the whole number over 1, so 6/1, then multiply straight across: (1x6)/(3x1) = 6/3 = 2

How do you divide by a fraction?

Multiply by its reciprocal instead

What is the reciprocal of a fraction?

The fraction flipped upside down, numerator and denominator swapped