Math Review

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Transcript Math Review

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
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
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
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
Practice Questions
1. 2,533
The five is in the ____ place.
a) thousands b) tens
c) ten thousands
2. 2.533
The five is in the ___ place.
a) tens
Bb) tenths
c) oneths
3. Round 0.18948 to the nearest thousandths.
a) 0.18 B
b) 0.189 c) 0.190
4.
216/2 =
a) 18
Bb)
108
c) 1008
d)
D
hundreds
d) hundredths
d) 0.1895
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?
Cc) 54.3
a) 67.1
b) 81
d) 49.3
Practice Questions
6.
7.
8.
9.
3/8 x 8/5 =
a) 5/9
b) 5/7
c)
C 3/5
d) 15/4
5/3 + 1/9 =
a) 3/7
b) 3/12
c) 2/7
D
d)
16/9
0.006/ 0.0002 =
a) 0.03
b) 0.3
c) 3.0
D
d)
30
What is 36% of 19?
a) 1.9
Bb) 6.8
c) 53
d) 684
c) 4
d) 5
10. Solve for x:
A
a) 2
6x + 4 = 16
b) 3
Practice Questions
11. Factor: x2 + 20x + 100 =
Aa) (x + 10)(x + 10)
b) (x + 20)(x + 10)
c) (x - 10)(x - 20)
d) (x + 10)(x - 10)
12.
Solve for y:
a) -1
y2 - 6y + 9 = 0
c) 1
Bb) 3
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
c. 1 x 1026
Bb. 1 x 1042
d. 1 x 1012
14. Change the following decimal to a fraction in its lowest term: 0.625
a) 1/8
Bb)
5/8
c) 1/6
d) 3/4