SBAC Concept Questions with Correct Answers

What different types of numbers are considered rational? How can you tell if a number is irrational? Rational numbers include integers, fractions, terminating decimals, repeating decimals and perfect square roots. Irrational numbers are typically non-perfect roots, or expressions with pi What technique can be used to approximate the value of non-perfect square roots or cube roots? Finding the perfect roots before and after the number will tell you the numbers that the non-perfect root is in between. You can tell which number it is closer to by seeing which perfect root the non-perfect root is closest to. What are the exponent rules when you have operations with the same base? Give an example of each: a-Multiplication with same base b-Division with same base c-Power to a power d-Negative exponent e-Exponent of zero a-Multiplication: add the exponents: ex: 52 x 53 = 55 b-Division: subtract the exponents: ex: 57/52 = 55 c-Power to a power: multiply the exponents: ex: (53)4 = 512 d-Negative exponent: Take the reciprocal (flip to the opposite side of the fraction): ex: 3-2 = 1/32 or ⅓-2 = 32 e-Exponent of zero: Always equals 1: ex: 50 = 1 If you have an equation x2 = something or x3 = something. How could you test possible values of x to see if they are correct? What should you remember if testing a possible solution that has a number directly next to a square root? Ex: how could you test if x=5√2 is a solution? To test a solution, substitute in values for x and see if they check out. If you have a number next to a square root, using parentheses helps you remember to square or cube everything. For example, (5√2)2 would be 25 X 2 which would be 50. How does scientific notation work for very large numbers (ex: 32,000) and for very small numbers (ex: 0.002)? Scientific notation involves re-writing the number as a multiple of 10. Each time you move the decimal point is another multiple of 10. Large numbers have a positive exponent for 10, while small numbers have a negative exponent. How can exponent rules be applied to problems involving multiplication or division with numbers in scientific notation. Work with the regular number and the powers of 10 separately. Multiple or divide the number in front and then apply the appropriate exponent rule (add or subtract exponents) with the powers of 10.