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 (46) x10 or (2 x 103)(3 x 106)
  6 x 10(36) 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 10 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 1047
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