SSAT UPPER LEVEL MATH
Parallel lines cut by transversal
...
x^0 =
1
x^4 / x^5 =
1 / x subtract exponents when dividing and leave the variable wherever the bigger exponent was
Inequalities
1) The alligator always eats the bigger number 2) MUST FLIP SIGN whenever multiplying or dividing by a NEGATIVE
Area of a Triangle
1/2 base x height
How many degrees in a straight line?
180 degrees
How many total degrees in a triangle?
180 degrees
Supplementary angles total
180 degrees
Isosceles Triangle
2 equal sides and corresponding angles
x^2 + x^2 =
2x^2 add coefficient
YARDS to FEET
3 feet per yard
How many degrees in a circle?
360 degrees
How many total degrees in a parallelogram? Hint: parallelogram = 2 triangles
360 degrees
Complementary angles total
90 degrees
How many degrees in a right angle?
90 degrees
Equilateral Triangle
All sides and angles are equal (each angle is 60 degrees no matter what the sides equal)
Average / mean
Average = sum / number of things
Area of a Parallelogram
Base x height
Combined average problems
Break into two separate average equations before combining to solve. Ex: The average test score for 5 girls is 90. The average test score for 10 boys is 85. What is the average test score of all the students (boys and girls)? GIRLS 90 = x / 5 (90)(5) = x 450 = x BOYS 85 = x / 10 (85)(10) = x 850 = x Now, combine into one big average problem! Group average = (850 + 450) / 10 + 5 1300 / 15 = 86.7 Group average = 86.7
Two fractions set equal to one another
Cross multiply
SSAT Special Functions (weird symbol problems)
Don't panic! They will define the function for you. All you have to do is plug in the numbers for the variables. Ex: a £ b = a + 5b What is the value of 6 £ 1 ? 6 £ 1 = 6 + (5)(1) 6 £ 1 = 6 + 5 6 £ 1 = 11
Equal angles are across from...
EQUAL SIDES
Angles that are across from each other (aka vertical angles) are...
EQUAL! (aka congruent)
Factor
Ex: factors of 10 are 1,2,5,10
Multiple
Ex: multiples of 10 are
Surface Area
Find the area of each individual side and add up all sides. For cubes, simply multiply side area by 6 (6 sides on cube)
x^2 + x^3 =
IMPOSSIBLE!!! (x^2 + x^3)
Shortcut: The average of any consecutive integers
Is just the middle integer!
Challenging VOLUME problems
Length x width x height Ex: How many cubes with side length 3 can fit into a cube of side length of 6? Small cube volume = (3)(3)(3) = 27 Big cube volume = (6)(6)(6) = 216 216 / 36 = 8 8 small cubes can fit into the larger cube!
Perimeter of weird shapes
Make sure you account for ALL SIDES!
Median
Middle number when numbers are ordered from least to greatest
Scalene triangle
No equal sides or angles
Area of a circle
Pi r squared
Circumference of a Circle
Pi x Diameter
Integer
Positive or negative whole number
Slope
Rise / Run (y2-y1) / (x2-x1) Ex: Find the slope of the line that runs through the points (4,6) and (8,10). (10 - 6) / (8 - 4) = 4 / 4 = 1 The line has a slope of 1 Remember: Positive slope inclines (travels upward) from left to right and negative slope declines (travels downward) from left to right.
Similar Triangles
Sides are in ratio (proportionate to one another).
Percent Change
Step 1: Find the difference in amount Step 2: Look at the original number and ask yourself "What percent of the original number is that amount equal to?"
Graphs / Data Tables
TAKE YOUR TIME. 1) Ignore answer choices 2) Look at x and y axes. What does each measure? 3) What kind of data is being shown? What conclusions can you draw?
Range
The greatest value minus the smallest value
MISSING SIDE OF A TRIANGLE
The length of the third side of any triangle must be between the sum and the difference of the other two sides
MODE
The most frequently occurring number
DON'T MISS THE FINAL STEP OF THE QUESTION!
They're out to trick you. Be smarter than the evil test makers and UNDERLINE what the question is asking.
Percent Short Cut (10% rule!)
Use the 10% shortcut to estimate whenever possible. You can find 10% of any number by moving the decimal one place to the LEFT.
LCD FOR COMPARING FRACTIONS
When adding or subtracting or comparing fractions, always be SURE that you have first established a lowest common denominator across all the fractions
USE YOUR ANSWERS
Whenever you are stuck, let the answers choices help you. Often you can plug them in and see which one works!
Absolute Value Equations
Write out the equation TWICE. One negative answer. One positive answer. Solve for both.
Pythagorean Theorem What is the equation? What is it used for?
a^2 + b^2 = c^2
Percent Strategy
part / whole = percent / 100
x^1 =
x
(x^2)(x^3) =
x^5 add exponents
(x^2)^3 =
x^6 multiply exponents when raising a power to a power