SHSAT - MATH questions and answers updated 2022/2023

Midpoint The exact middle point between two other points! Mean Same as Average. Average = (sum / # of things) 01:01 01:24 Strategy: PLUG IN NUMBERS FOR VARIABLES (LETTERS) 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) *Remember that answer choices are ordered least to greatest, so start with C! Always C! REDUCE ALL FRACTIONS TO LOWEST TERMS ... Formulas and definitions are not provided on test (so we must memorize them!) ... 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!) ... READ THE ENTIRE QUESTION CAREFULLY! No rushing! Re-read until you understand. ... LEAVE NO BLANKS! Make an educated guess, if you can. ... No calculators allowed! ... Integer A whole number (can be positive or negative). Prime 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 Numbers that follow one after another in order without skipping. For example: 1, 2, 3, 4, 5... Factor Positive integer that DIVIDES evenly into a number with no remainder. For example: Factors of 10 = 1, 10, 2, 5 Multiple 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 Order of Operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction Absolute Value Absolute value of a number is ALWAYS positive. x^1 = x x^0 = 1 x^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 Roots Scientific Notation Number must be LESS THAN 10 and moving decimal to left = positive exponent. Moving decimal to right = negative exponent. Percent Equation Final = Original x Percent (in decimal form) BUT ALWAYS USE THE 10% shortcut if you can. Median First, order least to greatest then it is the middle number. Mode Most frequently occurring number. Ratios and Proportions a/b or a:b Write out two fractions, set them equal, and cross multiply to solve. Distance Formula Distance = Rate x Time Probability Probability = Desired Outcome / Total Possible Outcomes Special SHSAT Equations Plug in and follow instructions! Don't panic about weird symbols! Dividing with exponents subtract 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/5 Inequalities < > 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^4