NYSCTE Multi-Subject CST Math Section questions and answers.

Cardinal numbers 1, 2, 3, 4, 5, etc. Ordinal numbers 1st, 2nd, 3rd, 4th, 5th, etc. Place value Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones 3,579,410 (5 = 500,000); (9= 9,000) Exponents 3^5 = 3 x 3 x 3 x 3 x 3 = 243 Multiplying exponents a^n x a^m = a^m+n (7^8 x 7x5 = 7^13) Dividing exponents a^n / a^m = a^m-n (7^8 / 7^5 = 7^3) (a^n)m = a^nxm (3^2)2 = 3^4 = 81 Scientific notation Power shows how many zeros to use: 10^2 = 100; 10^4 = 10,000; 10^-3 - 0.0001 Turn 7,952 into scientific notation 7.952 x 10^3 Rounding Digit to the right; 5 or more = round up; 4 or less = leave. i.e. 859,465 round to the thousands = 859,000 Rational numbers They can be written as a fraction. i.e. 9 = 9/1; 0.25 = 1/4; 0.4 = 410 Irrational numbers Cannot be written as a fraction. i.e. square root of 2 Equivalent fractions You can multiple and divide the fractions by the same number. i.e. 2/5 x 3/3 = 6/15 i.e. 6/8 x 4/4/ = 24/32. Comparing fractions to see which is bigger or smaller Cross-multiply. i.e. Which is bigger: 13/18 or 5/7? Multiple 13 x 7 and 18 x 5. You get 91 and 90. 91 90 so 13/18 5/7 Improper fraction to a mixed number It's the quotient and a fraction of the remainder over the divider. 23/ 8 8 goes into 23 2 with a remainder of 7 2 and 7/8. Mixed number to an improper fraction Multiply whole number by denominator then add numerator. 3 and 2/5 3 x 5 = 15 + 2 = 17 17/5. Order of operations PEMDAS. i.e. 4 + 3 x 7^2 4 + 3 x 49 4 + 147 = 151 Factors Evenly divide the number with no remainder. i.e. factors of 4 = 1, 2, 4; factors of 10 = 1, 2, 5, 10 Multiples All the numbers you get when you count by that number. i.e. multiples of 2 = 2, 4, 6, 8, 10, etc; multiples of 5 = 5, 10, 15, 20, 25, etc. Least Common Multiple (LCM) Smallest multiple shared between two numbers. i.e. LCM of 6 and 8 = 24 Greatest Common Factor (GCF) Largest factor shared by 2 numbers. i.e. GCF of 28 and 36 = 4. Distributive property a(b+c) =(axb) + (axc) Commutative property a+b=b+a and axb=bxa Associative property (a+b) +c= a+ (b+c) and (axb) x c = a x (bxc) Identity property a+ 0 = a and a x 1 = a Inverse property a+ (-a) = 0 and a x 1/a = 1 Adding decimals Line them up at decimal point and add. i.e. 14.9 + 3.108 + 0.16 = 18.168 Subtracting decimals Line them up at decimal point and subtract. i.e. 14.234 - 7.14 Multiplying decimals Multiply as if they are whole numbers (so get rid of decimal). Make sure that for second round of multiplication, you put a 0 at the far right first. Count total number of decimal places and carry that back. i.e. 17.4 x 1.3 = 174 x 13 174 x 3 = 522 174 x 1 = 174 with a 0 at the end so 1740 522 + 1740 = 2262 22.62 Dividing decimals Make divisor whole number and match the movement in the dividend. 1.328 / 0.16 132.8 / 16 (moved decimal over by 2 places because 0.16 had two decimals places). Multiplying fractions Multiply the numerator and denominator. i.e. 3/4 x 1/6 = 3/24 = 1/8. i.e. 3 and 1/3 x 3/5 make 3 and 1/3 an improper fraction 10/3 x 3/5 = 30/15 = 2 Dividing fractions Invert divisor and multiply. 1 and 4/5 divided by 3/8. 1) 1 and 4/5 becomes 9/5 . 2) 3/8 becomes 8/3 and you multiply by that. 3) 9/5 x 8/3 = 72/15 = 4 and 12/15 = 4 and 4/5. Adding fractions Write fractions with common denominators and add. i.e. 3/8 + 1/4 3/8 +2/8 = 5/8. i.e. 7/8 + 5/12 21/24 + 10/24 = 31/24 = 1 and 7/24 Subtracting fractions Writing fractions with common denominators and subtract. i.e. 5/6 - 1/3 5/6 - 2/6 = 3/6 = 1/2. Square roots Square root of = a^1/2. Square root of 1 = 1. Square root of 4 = 2. Square root of 49 = 7. 16^1/2 = 4. Square root of axb = square root of a x square root of b. i.e. square root of 36 x 2 square root of 36 x square root of 2 6 x square root of 2. Decimals to percents Carry over two decimals: 0.34 = 34%, 0.297 = 29.7% Fractions to percents Either make the faction a decimal and then convert or make the fraction out of 100. i.e. 13/25. 13/25 = 52/ 100 = 52% Percents to fractions i.e. 18% = 18/100 = 9/50; 7.5% = 7.5/100 = 75/1000 = 3/40 Finding percent of a number 40% of 90 = 0.4 x 90 = 36 Finding what percent of one number is of another i.e. What % of 5 = 3? n x 5 = 3 n = 3/5 0.6 = 60% Finding a number when a percent of it is known 5% of what number is 2? 0.05 x n = 2 n = 2/0.05 = 40