# SHSAT - MATH

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IntegerA whole number (can be positive or negative).PrimeA whole number (integer) that can only be divided by 1 and itself. ***1 IS NOT A PRIME NUMBER.
2,3,5,7,11, 13...Consecutive NumbersNumbers that follow one after another in order without skipping. For example: 1, 2, 3, 4, 5...FactorPositive integer that DIVIDES evenly into a number with no remainder. For example: Factors of 10 = 1, 10, 2, 5MultipleA number that a given number will divide into with no remainder. Think MULTIPLY. For example: Multiples of 10 = 10, 20, 30, 40, 50...PEMDASOrder of Operations: Parentheses, Exponents, Multiplication, Division, Addition, SubtractionAbsolute ValueAbsolute value of a number is ALWAYS positive.x^1 =xx^0 =1x^2 + y^3 =
x^2 - y^3 =IMPOSSIBLE because apples and oranges (must be all x's or all y's - no mixing when adding or subtracting! AND exponents must also be the same!!!)x^2 + x^2 =2x^2(x^2)(x^3) =x^5 Add exponents!(x^2)^3 =x^6 Multiply exponents!Square RootsScientific NotationNumber must be LESS THAN 10 and moving decimal to left = positive exponent. Moving decimal to right = negative exponent.Percent EquationFinal = Original x Percent (in decimal form)
BUT ALWAYS USE THE 10% shortcut if you can.MedianFirst, order least to greatest then it is the middle number.ModeMost frequently occurring number.Ratios and Proportionsa/b or a:b Write out two fractions, set them equal, and cross multiply to solve.Distance FormulaDistance = Rate x TimeProbabilityProbability = Desired Outcome / Total Possible OutcomesSpecial SHSAT EquationsPlug in and follow instructions! Don't panic about weird symbols!Dividing with exponentssubtract exponents!If a question asks, "which number is a multiple" of two other numbers...multiply the two numbers together and look at the last digit of the product. match the answer choice to this digit.a variable in terms of another variable
Example: If 5a = b, what is a in terms of b?isolate a on the left side of the equation. move b to the other side. Answer = a = b/5Inequalities < >The alligator eats the bigger number. REMEMBER: Swap the sign whenever you divide or multiply by a negative number!Negative exponents make fractions!
Example: Re-write m^-4 as a fraction.Answer: 1 / m^4Sneaky Shortcut: What is the average of CONSECUTIVE integers?Just the middle integer! So, don't waste your time finding the average by adding all the numbers up and dividing by how many numbers there are. Instead, if you are asked: What is the average of the following consecutive integers: 5,6,7,8,9, just look and see that 7 is the middle integer, so it's also the average!"of" -->multiply!Right Angle =90 degrees (represented by little box)complementary angles total90supplementary angles total180how many degrees on a straight line?180how many degrees in a circle?360vertical angles are...across from each other
AND THEY ARE ALWAYS EQUALParallel Lines Cut By A Transversal (line running through)...Creates sets of equal angles.Total degrees in a triangle?180The range of possible values for a missing third side of a triangle can be found HOW!?The missing side's value is between the sum and the difference of the other two sides.Area of a triangle= B x H / 2PerimeterSum of all the sides of any shapeSimilar Triangles*All corresponding angles are equal
*Are always in proportion (find the bigger triangle's side. then find the smaller triangle's corresponding side. and ask yourself "what do I multiply the small triangle side by to get the big side?" USE CROSS MULTIPLICATION IF YOU NEED TO! (If the numbers aren't obvious)Isosceles Triangletwo sides are equal. one side is not.Equilateral Triangleall sides are equal!
each of the three angles = 60Right Trianglehas a right angle!Equal sides are across from...EQUAL ANGLES.
Any time you have two or three sides equal in a triangle, then the angles opposite those sides must also be the same.Area of Square or RectangleLength x WidthPythagorean Theorema^2 + b^2 = c^2
*Used to solve for missing side of RIGHT triangle.
c = the side ACROSS from the right angle (draw an arrow from the box across to find c). this side is also called the hypotenuse!Parallelogram AreaBase x Height

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