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SHSAT - MATH
Mean - correct answer Same as Average. Average = (sum / # of things) Strategy: PLUG IN NUMBERS FOR VARIABLES (LETTERS) - correct answer Pick nice, low numbers and plug them in to the question for any variables (letters) that you see. Solve the problem. Then look at the answer choices and plug in the SAME numbers you picked to find the matching solution! AVOID: 0, 1, negatives, fractions and decimals Strategy: BACKSOLVING (using answer choices) - correct answer *Remember that answer choices are ordered least to greatest, so start with C! Always C! REDUCE ALL FRACTIONS TO LOWEST TERMS - correct answer Formulas and definitions are not provided on test (so we must memorize them!) - correct answer DIAGRAMS/SHAPES ARE NOT NECESSARILY DRAWN TO SCALE, BUT GRAPHS ARE. Do not assume any relationship in a diagram unless it is specifically stated or can be figured out from information given. (Remember the poor boy with the ruler!) - correct answer READ THE ENTIRE QUESTION CAREFULLY! No rushing! Re-read until you understand.
- correct answer LEAVE NO BLANKS! Make an educated guess, if you can. - correct answer Integer - correct answer A whole number (can be positive or negative or 0).
Prime - correct answer A 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 Numbers - correct answer Numbers that follow one after another in order without skipping. For example: 1, 2, 3, 4, 5... Factor - correct answer Positive integer that DIVIDES evenly into a number with no remainder. For example: Factors of 10 = 1, 10, 2, 5 Multiple - correct answer A number that a given number will divide into with no remainder. Think MULTIPLY. For example: Multiples of 10 = 10, 20, 30, 40, 50... PEMDAS - correct answer Order of Operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction Absolute Value - correct answer Absolute value of a number is ALWAYS positive. x^1 - correct answer x x^0 = - correct answer 1 x^2 + x^2 = - correct answer 2x^ (x^2)(x^3) = - correct answer x^5 Add exponents! (x^2)^3 = - correct answer x^6 Multiply exponents! Square Roots - correct answer
Negative exponents make fractions! Example: Re-write m^-4 as a fraction. - correct answer Answer: 1 / m^ Sneaky Shortcut: What is the average of CONSECUTIVE integers? - correct answer 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" --> - correct answer multiply! Right Angle = - correct answer 90 degrees (represented by little box) complementary angles total - correct answer 90 supplementary angles total - correct answer 180 how many degrees on a straight line? - correct answer 180 how many degrees in a circle? - correct answer 360 vertical angles are... - correct answer across from each other AND THEY ARE ALWAYS EQUAL Parallel Lines Cut By A Transversal (line running through)... - correct answer Creates sets of equal angles. Total degrees in a triangle? - correct answer 180
The range of possible values for a missing third side of a triangle can be found HOW!? - correct answer The missing side's value is between the sum and the difference of the other two sides. Area of a triangle - correct answer = B x H / 2 Perimeter - correct answer Sum of all the sides of any shape Similar Triangles - correct answer *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 Triangle - correct answer two sides are equal. one side is not. Equilateral Triangle - correct answer all sides are equal! each of the three angles = 60 Right Triangle - correct answer has a right angle! Equal sides are across from... - correct answer 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 Rectangle - correct answer Length x Width Pythagorean Theorem - correct answer a^2 + b^2 = c^ *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!
