Algebra
1 Pemdas
The correct order of operations when simplifying an expression is: Parenthese-Exponents-
(Multiplication/Divison)-(Addition/Subtraction).
Eerst alles tussen de haakjes oplossen, dan de exponenten, dan delen of keer en dan
aftrekken of optellen.
2 Linear equations
Expressions vs. Equations
The basic difference between expressions and equations is that equations contain an equals
sign, and expressions do not.
An expression represents a value. Even if you don’t know that value, nothing you do to an
expression can change its value.
By equations, any change you make to one side must also be made to the other in order to
maintain the equivalence.
There are 6 operations you can perform to both sides of an equation. Remember to perform
the action on the entire side of the equation. You can:
1. Add the same things to both sides
2. Subtract the same thing from both sides
3. Multiply both sides by the same thing
4. Divide both sides by the same thing
5. Raise both sides to the same power
6. Take the same root of both sides
Simultaneous equations: Solving by substitution
GMAT asks you to solve a system of equations with more than one variable. You might be
given two equations with two variables, or three equations with three variables. There are two
primary ways of solving simultaneous equations:
1. Substitution
X+y = 9
2x = 5y+4
Step 1: x+y=9
x = 9-y
Step 2:: 2x = 5y + 4
2(9-y) = 5y + 4
Step 3: 2(9-y) = 5y + 4
Find Y 18 – 2y = 5y + 4
14 = 7y
2=y
Step 4: x+y=9
Find X x+2=9
x=7
2. Combination
The goal is to make one of two thing happen: either the coefficient in front of one of the
variables is the same in both equations or the coefficient in front of one of the variables is the
same but with opposite signs.
Step 1: X+y = 9
2x = 5y+4
1 Pemdas
The correct order of operations when simplifying an expression is: Parenthese-Exponents-
(Multiplication/Divison)-(Addition/Subtraction).
Eerst alles tussen de haakjes oplossen, dan de exponenten, dan delen of keer en dan
aftrekken of optellen.
2 Linear equations
Expressions vs. Equations
The basic difference between expressions and equations is that equations contain an equals
sign, and expressions do not.
An expression represents a value. Even if you don’t know that value, nothing you do to an
expression can change its value.
By equations, any change you make to one side must also be made to the other in order to
maintain the equivalence.
There are 6 operations you can perform to both sides of an equation. Remember to perform
the action on the entire side of the equation. You can:
1. Add the same things to both sides
2. Subtract the same thing from both sides
3. Multiply both sides by the same thing
4. Divide both sides by the same thing
5. Raise both sides to the same power
6. Take the same root of both sides
Simultaneous equations: Solving by substitution
GMAT asks you to solve a system of equations with more than one variable. You might be
given two equations with two variables, or three equations with three variables. There are two
primary ways of solving simultaneous equations:
1. Substitution
X+y = 9
2x = 5y+4
Step 1: x+y=9
x = 9-y
Step 2:: 2x = 5y + 4
2(9-y) = 5y + 4
Step 3: 2(9-y) = 5y + 4
Find Y 18 – 2y = 5y + 4
14 = 7y
2=y
Step 4: x+y=9
Find X x+2=9
x=7
2. Combination
The goal is to make one of two thing happen: either the coefficient in front of one of the
variables is the same in both equations or the coefficient in front of one of the variables is the
same but with opposite signs.
Step 1: X+y = 9
2x = 5y+4
