NYSTCE CST MATH, Exam Preview Questions with accurate answers, rated A+

NYSTCE CST MATH, Exam Preview Questions with accurate answers, rated A+ whole numbers - -numbers that tell how many 0,1,2,3,4,5 infinite cardinal numbers - -tell how many (ex. 9 players) ordinal numbers - -tell what order (ex. 1st, 13th, ect) place value - -value of a digit depends on the place it occupies -millions, hundred thousands, ten thousands, thousands, hundreds, tens, ones positive exponents - -can show repeated multiplication as an exponent, exponent shows how many times the factor appears Rules -7^8x7^6=7^(8+6) 7^8 / 7^6 = 7^(8-6) rules for exponents - --can use rules to multiply or divide exponents with the same base 7^8 x 7^6 = 7^(8+6) 7^8 / 7^6 = 7^(8-6) scientific notation - -uses powers of 10. the power shows how many zeros to use ex. 10^0=1 10^1=10 10^2=100 10^(-1)=0.1 10^(-2)=0.01 write whole numbers and decimals in scientific notation. use a decimal with one number to the left of decimal point 2,345= 2.345x10^3 176.8= 1.768x10^2 0.0034= 3.4x10^(-3) understanding and ordering decimals - -decimals used to represent numbers between 0 and 1 tenths, hundredths, thousandths, ten thousandths, hundred thousandths, ect. rounding - -if next digit is more than 5 round up if next digit is less than 5, round down rational numbers - -numbers that can be written as a fraction, can be written as decimals that terminate or repeat 1=1/1 .25-1/4 .(repeating)=2/3 irrational numbers - -numbers cannot be rewritten as a fraction (most famous is pi) -another famous is square root of 2 (can approx 1.) undefined numbers - -cannot be written? 0 in denominator 1/0? equivalent fractions - -2 fractions that stand for the same number. multiply or divide the numerator and denominator to dins an equivalent fraction mixed numbers and improper fractions - -to change improper fraction to mixed number, divide by denomiator and look of excess (write excess as fraction) to change mixed number to improper fraction multiply denominator and whole number then add to numerator) 3+2/5 = (3x5)+2 /5= 17/5 integers - -negative whole numbers, zero, and positive whole numbers are integers PEMDAS - -(1) parenthesis (2) exponents (3) multiplication and division (4) addition and subtraction key words (addition) - -sum, and, more, increased by, how many in all, the total, key words (subtraction) - -less, difference, decreased by, how many left, how much larger, how many in the rest key words (multiplication) - -of, product, times key words (division) - -per, quotient, shared, ratio key words (equals) - -is, equals factors - -the factors of a number evenly divide the number with no remainder (the number 1 is a factor in every number, each number is a factor of itself) least common multiple (LCM) - -the multiples of a number are all the numbers you get when you count by that number least common is the smallest multiple shared by two numbers ex. 6 and 8 6: 6,12,18,24,30... 8: 8,16,24,32,... 24 is common, Least common= LCM=24 multiples - -are all the numbers you get when you count by that number ex. 3: 3,6,9,12 greatest common factor (GCF) - --largest factor shared between two numbers -ex. 28 and 36 28: 1,2,4,7,14,28 36: 1,2,3,4,6,9,12,18,36 both have 1,2,4, largest is 4 gcf=4 properties of operations - --communicative a+b=b+a or axb=bxa -associative property (a+b)+c=a+(b+c) or (axb)xc=ax(bxc) -identity a+0=a ax1=a -inverse a+(-a)=0 ax(1/a)=1 -distributive property of multiplication over addition a(b+c)= ab+ac or (axb)+(axc) *subtraction and division not communicative or associative (can't rearrange) communicative property - -a+b=b+a -- 2+5=5+2 a x b = b x a -- 2x5=5x2 *cant do with subtraction or division (5-3 does not equal 3-5) (5/3 does not equal 3/5) associative property - -(a+b)+c=a+(b+c) (2+5)+3=2+(5+3) (axb)xc=ax(bxc) (2x5)x3=2x(5x3) *cant do with subtraction or division (3-5)-4 is not same as 3-(5-4) (3/5)/4 is not same as 3/(5/4) identity property - -a+0=a 3+0=3 ax1=a 3x1=3 inverse property - -a+(-a)=0 3+(-3)=0 ax(1/a)=1 3x(1/3)=1 distributive property of multiplication over addition - -a(b+c)= ab+ac or (axb)+(axc) 3(4+5)=(3x4)+(3x5)=12+15=27 multiply decimals - -multiply as whole numbers, then use TOTAL decimals in factors to the product ex. 17.4x1.3=22.62 divide decimals - --make divisor whole number (match that decimal movement in dividend then divide -1.328/0.16 (move decimal 2 places for two in divisor) -132.8/16 (still have one decimal pt now) multiply fractions - -multiply numerators and denominator, then simplify -3/4 x 1/6 =3/24=1/8 multiply mixed numbers - --write mixed numbers as improper fractions -multiply numerators and denominator -then simplify -(3+1/3)x(3/5) = (9/3+1/3)x(3/5)= (10/3)x(3/5)= 30/15 =2 divide fractions - --invert the divisor and multiply (multiply numerators and denominator, then simplify) ex. (3/4) / (2/3)= (3/4) x (3/2)= 9/8 = 1and1/8 divide mixed numbers - --write any mixed numbers as improper fractions -invert the divisor and multiply (multiply numerators and denominator, then simplify) (1+4/5) / (3/8)= (9/5) / (3/8) = (9/5)x(8/3)= 72/15= 4+(4/5) add fractions and mixed numbers - --write fractions with common demoninators then add numerators, then simplify 3/8 +1/4 = 3/8 + 2/8= 5/8 subtract fractions and mixed numbers - --write fractions with common denominators, then subtract numerators, then simplifty 3/8 -1/4 = 3/8- 2/8= 1/8 square roots - --square root of given number, when multiplied by itself equals the given number ex. (square root of 4 x square root