Mathematical Review

1. Mathematical Review Fractions & Decimals • A fraction represents division, the numerator is divided by the denominator. • 2/3 is read as 2 divided by 3 • Proper fraction: numerator is smaller than denominator. Example: 3/5 • Improper fraction: numerator is larger than the denominator. Example: 5/3 • A decimal is a fraction with the division carried out. • A decimal is a fraction expressed in powers of 10. • 0 . 0 0 1 • ones . Tenths hundredths thousandths

2. Mathematical Review Algebraic Equations • Variables are the symbols used to represent a measurement. • For example; T is the variable for temperature while t is the variable for time. • To isolate one variable of an equation remember to divide if the unwanted variable is on top and to multiply if the variable is on the bottom. An asterisk * represents multiplication. • A = B / C • to isolate C first rearrange the equation to it will read C=? Do this by multiplying both sides by C (since it is on the bottom of a fraction (denominator). • C* A = B *C / C note: C/C = 1 • C * A = B • Now to isolate C we need to divide by A (it is on top of a fraction; A/1 = A) • C * A /A = B /A • Remember: what ever you do to one side you must do it to the other side. • C = B / A

3. Mathematical Review Algebraic Equations • When multiplication & division is mixed with adding & subtracting, try the multiplication or division first. • (A - D) / (C + F) = B • to solve for C, first rearrange the equation to it will read C=? Do this by multiplying both sides by C + F (since it is on the bottom of a fraction (denominator). • (A - D) * (C + F) / (C + F) = B * (C + F) • (A - D) = B * (C + F) • Now to isolate C we need to divide by B • (A - D) / B = B * (C + F) / B • (A - D) / B = C + F • Now you can subtract F from both sides. • [(A - D) / B] - F = C + F - F • [(A - D) / B] - F = C • which is the same as C = [(A-D) / B] -F If A = 8, D = 2, B = 3, & F = 7 then C must = [(8-2) / 3] - 7 =-5

4. Mathematical Review Exponents • An exponent is a number written as a superscript. • X2 is X-squared or “X to the power of 2” • The base (X) is multiplied by itself the number of times represented in the exponent(superscript, 2 in this example). • 23 or two cubed (2 is the base and 3 is the exponent) • 23 is 2 * 2 * 2 = 4 * 2 = 8 • A positive exponent represents a large number (greater than one). • 1 x 103 is 10 *10 *10 = 1000 thousand • A negative exponent represents a small number (less than one). • 1 x 10-3 is (1/10) * (1/10) * (1/10) = 0.001 thousandths • When multiplying numbers written with exponents, add the exponents. If dividing then subtract the exponents. • x4 * x6 = x (4+6) = x10 or (2 x 103)(3 x 106) = 6 x 10(3+6) = 6 x 109 • 2x6/7x3 = 0.2857 x(6-3) = 0.2857 x3

5. Practice Questions 1. 2,533 The five is in the ____ place. a) thousands b) tens c) ten thousands d) hundreds 2. 2.533 The five is in the ___ place. a) tens b) tenths c) oneths d) hundredths 3. Round 0.18948 to the nearest thousandths. a) 0.18 b) 0.189 c) 0.190 d) 0.1895 4. 216/2 = a) 18 b) 108 c) 1008 d) 432 5. Student A scored 45 on the first exam, 67 on the second exam and 51 on the third exam. What was the average score? a) 67.1 b) 81 c) 54.3 d) 49.3 D B B B C

6. Practice Questions 6. 3/8 x 8/5 = a) 5/9 b) 5/7 c) 3/5 d) 15/4 7. 5/3 + 1/9 = a) 3/7 b) 3/12 c) 2/7 d) 16/9 8. 0.006/ 0.0002 = a) 0.03 b) 0.3 c) 3.0 d) 30 9. What is 36% of 19? a) 1.9 b) 6.8 c) 53 d) 684 10. Solve for x: 6x + 4 = 16 a) 2 b) 3 c) 4 d) 5 C D D B A

7. Practice Questions 11. Factor: x2 + 20x + 100 = a) (x + 10)(x + 10) b) (x + 20)(x + 10) c) (x - 10)(x - 20) d) (x + 10)(x - 10) 12. Solve for y: y2 - 6y + 9 = 0 a) -1 b) 3 c) 1 d) -2 13. The correct value for the expression [(1 x 10-21 x 1 x 1035)5] / (1 x 1014)2 a. 1 x 10-58 b. 1 x 1042 c. 1 x 1026 d. 1 x 1012 14. Change the following decimal to a fraction in its lowest term: 0.625 a) 1/8 b) 5/8 c) 1/6 d) 3/4 A B B B