Transcript GHSGT Mathematics Review - Mr. White's

GHSGT Number/Comp and
Algebra Review
How to use this review:
Play the PPT from the beginning and try each question.
Press ‘Enter’ to determine the correct answer.
Look for boxes that highlight the main idea of the concept.
Return to the SHS GHSGT Prep page to try more review questions.
Pass the FIRST time!
Number and Computation
17% of test
Percents, Fractions, Decimals
Percent to decimal – decimal point two places to left
50.0 %
becomes
0.50
Decimal to percent – decimal point two places to right
1.37
becomes
137. %
Fraction to decimal – divide numerator by denominator
3
4
becomes
3 ¸ 4 = 0.75
Represent 45% as a fraction.
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A)1/5
B)2/10
C)9/20
D)45/50
Express 0.456 as a percent.
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A).00456%
B)4.56%
C)45.6%
D)456%
Using Percents
Interest = principal × rate × time
I = prt
Mr. Sam borrowed $1000 for 6 months at an
annual interest rate of 27 percent.
How much interest did he pay?
I = prt
I = ($1000)(0.27)(0.5)
I = $135.00
Exponents
5 = 5×5×5×5×5×5 = 15,625
6
Multiply terms with exponents by adding exponents
4 ×4 = 4 ×4 ×4 ×4 ×4 = 4
2
3
2+ 3
= 4
5
Divide terms with exponents by subtracting exponents
3
3 ×3 ×3 3 ×3 ×3
3- 2
=
=
=3 =3
2
3
3 ×3
3 ×3
3
Exponents
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Simplify: p-2p5
A)p-10
B)p-3
C)p3
D)p7
Simplify: (a3 b2)4
A . (ab)20
B . (ab)24
C . a7b6
D. a12b8
Scientific Notation
Huge Numbers
Tiny Numbers
25,000,000 = 2.5´ 107
0.000031= 3.1´ 10- 5
Estimates
• You have a calculator – use it !
• Main idea
• Round the numbers in the problem so you can do
the math in your head…(or on your fingers)
• 12,357 becomes 12,000
• 3.12 becomes 3
Properties of Numbers
• Remember the Names
• Commutative “commute”
3+5=5+3
• Associative “associate at a party
in different groups”
4(2x + 3) = (2x + 3)4
• Distributive
3(5 + 1) = 3 × 5 + 3 × 1
• Identity “mirror #” (Addition)
-3 + 0 = -3
• Identity “mirror #” (Multiplication) 5 × 1 = 5
Rules for Integers
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Adding
2 positives = positive
2 negatives = negative
Subtracting
Subtraction is just adding the opposite sign
3 – -5 = 3 + -(-5) = 3 + 5 = 8
Multiplying and Dividing
2 positives or 2 negative = positive
1 positive and 1 negative = negative
Order of Operations
P
12 - 6 ¸ 2
Parenthesis
= 12 - 3
= 9
E
Exponents
M, D Multiply & divide
3
3
+
4
×
2
(
) ( - 1)
= 7 ×(8 - 1)
= 7 ×7 = 49
A, S Add & subtract
21- 7
3 ×(8 - 4) +
2
14
= 3 ×4 +
2
= 12 + 7
= 19
Simplify: 2 3 + 4 - 62
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A) -26
B) -22
C) -2
D) 10
Simplify Algebraic Expressions
Combine like terms
3x + 2y - 6 x + 3y = 3x + 2y - 6 x + 3y
= 3x - 6 x + 3y + 2y = - 3x + 5y
3ab - b
b(3a - 1) b (3a - 1) 3a - 1
=
=
=
ab
ab
ab
a
Algebra Review
29% of test
Simplify:
2
3
2
(3x + 2x + 7x ) + (10x + 6x + 9)
2
A) 13x + 8x + 16x
3
3
2
B) 7x + 13x + 8x + 9
C)
3
2
7x + 30x + 12x + 9
4
2
3
D) 13x + 8x + 7x + 9
Simplify
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Add: (3t - 3) + (6t2 + 4t + 13) + (-8t2 + 11t - 1)?
A)-2t2 +18t + 9
B) -2t4 + 182 + 9
C)2t4 -18t – 9
D) 25t7
Evaluate Algebraic Expressions
Evaluate an algebraic expression means to substitute
a number for each variable and then carry out the
indicated operations – remember to follow the order
of operations.
(a + b)- 2c when
2b2 + b when b = - 6
a = 2, b = 3, and c = 1
2b2 + b =
(a + b)- 2c =
2
= 2(- 6) + (- 6)
= (2 + 3)- 2 ×1
= 2(36) + (- 6)
= 5- 2
= 72 + (- 6) = 66
= 3
If r = -6, s = -2, t = -3 v = 10, and
w = -1/2 then wv|-t - s| =
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A) -25
B) -5
C) 5
D) 25
Write Algebraic Expressions
Translate word for word into algebraic symbols
The sum of a and b multiplied by two-thirds
2
(a + b)×
3
A number divided by two is equal to two-thirds of
another number
x 2
= y
2 3
Which represents the sentence twenty less
than triple a number is thirty?
A)20 – 3x = 30
B)20 – 3x > 30
C)3x - 20 < 30
D)3x – 20 = 30
Solve Equations
Keep it balanced
x+ 2 = 20
x + 2 - 2 = 20 - 2
x = 18
x
= 36
2
x
2 × = 36 ×2
2
x = 72
Perform the opposite operations
4x- 7 = 13
4x - 7 + 7 =
4x =
4x
=
4
x=
13 + 7
20
20
4
5
Solve the equation for x.
3
2  x  10
4
A.
B.
C.
D.
-16
16
-32/3
32/3
Solve for x
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Solve the quadratic equation: 4x2 - 9 = 0
A) 3/2
B) -3/2
C) 9/4 and -9/4
D) 3/2and -3/2
Linear Equations- intercept
method
y = mx + b
x+ y = 5
y = - x+ 5
y intercept (x = 0)
x intercept (y = 0)
Linear
y2 - y1
m=
Equations
–
Slope
x2 - x1
y = mx + b
positive
undefined
negative
zero
Solve and Graph Inequalities
Same as equations EXCEPT
when multiply or divide by a
a negative number flip the inequality
- 2x + 4 < 10
- 2x + 4 - 4 < 10 - 4
- 2x < 6
- 2x
6
>
- 2 - 2
x> - 3
Open
Closed
>, <
>, <
-3
0
6x - 2(x + 1) > 0
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Solve the inequality.
A) x > 2
B) x < 2
C) x < 1/2
D) x > 1/2
Solve.
• Solve the inequality.
-2x + 5 ≥ 3x + 20
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A) x ≤ 3
• B) x ≥ 3
• C) x ≤ -3
• D) x ≥ -3
Systems of Linear Equations
4
y = - x+ 3
3
Main Idea
The solution to a
system of
equations is the
point where the
2 lines intersect
Solution (3, - 1)
1
5
y = x2
2
Identify the
solution to the
system of
equations
graphed.
A. (0, 1)
B. (1 -1)
C. (0, -3)
D. (-1, 1)
Systems of Equations – Substitution
x - 2y = 5
4 x + 3y = 9
x = 2y + 5
substitute
x = 2(- 1) + 5
x= - 2+ 5
x= 3
4(2y + 5)+ 3y = 9
8y + 20 + 3y = 9
11y + 20 - 20 = 9 - 20
11y = - 11
y= - 1
(3,- 1)
x=y-3
x + 3y = 13
• What is the solution to the system of
equations?
A) (1, 4)
• B) (4, 1)
• C) (2.5, 5.5)
• D) (5.5, 2.5)
Systems of Equations – Elimination
2x + 2y = 10
x- y = 5
eliminate y
2x + 2y = 10
2(x - y = 5) Þ
+ 2x - 2y = 10
add both
equations
4 x = 20
x- y = 5
5- y = 5
- y= 0
y= 0
4 x 20
=
4
4
x= 5
(5,0)
2x - 3y = 16
5x - 3y = 13
What is the solution to the system of equations?
A) (-1, -6)
B) (-6, -1)
C) (5, -2)
D) (5, 4)
Which mapping has EXACTLY the
set of points {(2,6), (3,6), (4,8)}?
A
B
C
D
Note:
This PPT was trimmed from an original document on the web by
Hillgrove HS in Cobb County, GA. I have made particular additions
and subtractions due to our school’s needs.
The original home of the PPT is:
http://www.cobbk12.org/schools/Hillgrove/GHSGT%20REVEIWS/
Math%20GHSGT.htm
Mr. White
3/2009