NYSTCE CST MATH EXAM WITH
COMPLETE SOLUTIONS
whole numbers - ANS-numbers that tell how many
0,1,2,3,4,5 infinite
cardinal numbers - ANS-tell how many (ex. 9 players)
ordinal numbers - ANS-tell what order (ex. 1st, 13th, ect)
place value - ANS-value of a digit depends on the place it occupies
-millions, hundred thousands, ten thousands, thousands, hundreds, tens, ones
positive exponents - ANS-can show repeated multiplication as an exponent, exponent
shows how many times the factor appears
Rules
-7^8x7^6=7^(8+6)
7^^6 = 7^(8-6)
rules for exponents - ANS--can use rules to multiply or divide exponents with the same
base
7^8 x 7^6 = 7^(8+6)
7^^6 = 7^(8-6)
scientific notation - ANS-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
*subtraction and division not communicative or associative (can't rearrange)
communicative property - ANS-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 - ANS-(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 - ANS-a+0=a 3+0=3
ax1=a 3x1=3
inverse property - ANS-a+(-a)=0 3+(-3)=0
ax(1/a)=1 3x(1/3)=1
distributive property of multiplication over addition - ANS-a(b+c)= ab+ac or (axb)+(axc)
3(4+5)=(3x4)+(3x5)=12+15=27
multiply decimals - ANS-multiply as whole numbers, then use TOTAL decimals in
factors to the product
ex. 17.4x1.3=22.62
divide decimals - ANS--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 - ANS-multiply numerators and denominator, then simplify
-3/4 x 1/6 =3/24=1/8
multiply mixed numbers - ANS--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 - ANS--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 - ANS--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 - ANS--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 - ANS--write fractions with common
denominators, then subtract numerators, then simplifty
COMPLETE SOLUTIONS
whole numbers - ANS-numbers that tell how many
0,1,2,3,4,5 infinite
cardinal numbers - ANS-tell how many (ex. 9 players)
ordinal numbers - ANS-tell what order (ex. 1st, 13th, ect)
place value - ANS-value of a digit depends on the place it occupies
-millions, hundred thousands, ten thousands, thousands, hundreds, tens, ones
positive exponents - ANS-can show repeated multiplication as an exponent, exponent
shows how many times the factor appears
Rules
-7^8x7^6=7^(8+6)
7^^6 = 7^(8-6)
rules for exponents - ANS--can use rules to multiply or divide exponents with the same
base
7^8 x 7^6 = 7^(8+6)
7^^6 = 7^(8-6)
scientific notation - ANS-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
*subtraction and division not communicative or associative (can't rearrange)
communicative property - ANS-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 - ANS-(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 - ANS-a+0=a 3+0=3
ax1=a 3x1=3
inverse property - ANS-a+(-a)=0 3+(-3)=0
ax(1/a)=1 3x(1/3)=1
distributive property of multiplication over addition - ANS-a(b+c)= ab+ac or (axb)+(axc)
3(4+5)=(3x4)+(3x5)=12+15=27
multiply decimals - ANS-multiply as whole numbers, then use TOTAL decimals in
factors to the product
ex. 17.4x1.3=22.62
divide decimals - ANS--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 - ANS-multiply numerators and denominator, then simplify
-3/4 x 1/6 =3/24=1/8
multiply mixed numbers - ANS--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 - ANS--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 - ANS--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 - ANS--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 - ANS--write fractions with common
denominators, then subtract numerators, then simplifty
