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 Computation17% of test

Percents, Fractions, DecimalsPercent 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

becomes34

3 4 0.75¸ =

Represent 45% as a fraction.

• A)1/5• B)2/10• C)9/20• D)45/50

Express 0.456 as a percent.

• A).00456%• B)4.56%• C)45.6%• D)456%

Using PercentsInterest = 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?

( )( )( )$1000 0.27 0.5

$135.00

I prt

I

I

=

=

=

Exponents65 5 5 5 5 5 5 15,625= ××××× =

Multiply terms with exponents by adding exponents

Divide terms with exponents by subtracting exponents

2 2 3 534 4 44 4 4 44 4+× =×× = × × =

2

33 3 33 3 3

3 3××=

×=

3×3

3×3×

233 3-= =

Exponents

• 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 NotationHuge Numbers Tiny Numbers

725,000,000 2.5 10= ´ 50.000031 3.1 10-= ´

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

• 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

Use the

calculator!!!

Order of OperationsP Parenthesis

E Exponents

M, D Multiply & divide

A, S Add & subtract

( )21 7

3 8 42-

× - +14

3 42

12 7

19

= × +

= +

=

12 6 2- ¸ 12 3

9

= -

=

( ) ( )33 4 2 1+ × - ( )7 8 1

7 7 49

= × -

= × =

Simplify: 2 3 + 4 - 62

• A) -26• B) -22• C) -2• D) 10

Simplify Algebraic ExpressionsCombine like terms

3 2 6 3x y x y+ - + 3 2 6 3x y x y= + - +

3 6 3 32 5x yx x y y= - + + - +=

3ab bab- ( )3 1b a b

ab-

= =( )3 1aab

- 3 1aa-

=

Algebra Review29% of test

2 3

3 2

3 2

4 2 3

A) 13x + 8x + 16x

B) 7x + 13x + 8x + 9

C) 7x + 30x + 12x + 9

D) 13x + 8x + 7x + 9

2 3 2

Simplify:

(3x + 2x + 7x ) + (10x + 6x + 9)

Simplify

• 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 ExpressionsEvaluate 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.

( ) ( )

( )

( )

2

2

2

2 6 6

2 36 ( 6)

72 6 66

b b+ =

= - + -

= + -

= + - =

22 when 6b b b+ =-( )-2 when

2, 3, and 1

a b c

a b c

+

= = =

( )( )

2

2 3 2 1

5 2

3

a b c+ - =

= + - ×

= -

=

If r = -6, s = -2, t = -3 v = 10, and w = -1/2 then wv|-t - s| =

• A) -25• B) -5• C) 5• D) 25

Write Algebraic ExpressionsTranslate word for word into algebraic symbols

The sum of a and b multiplied by two-thirds2

( )3

a b+ ×

A number divided by two is equal to two-thirds of another number

22 3x

y=

Which represents the sentence twenty less than triple a number is thirty?

A)20 – 3x = 30B)20 – 3x > 30C)3x - 20 < 30D)3x – 20 = 30

Solve EquationsKeep it balanced Perform the opposite operations

2 20x+ =

2 2 20 2

18

x

x

+ - = -

=36

2x

=

2 36 22

72

x

x

× = ×

=

4 7 13x- =

4 7 7 13 7

4 20

4 204 4

5

x

x

x

x

- + = +

=

=

=

Solve the equation for x.3

2 104x

A. -16B. 16C. -32/3D. 32/3

Solve for x

• Solve the quadratic equation: 4x2 - 9 = 0• A) 3/2• B) -3/2• C) 9/4 and -9/4• D) 3/2and -3/2

If you’re clueless, just use your

calculator to plug in all answers for

x! Remember x2 equations have

TWO solutions!

Linear Equations- intercept method5x y+ = y mx b= +

5y x=- +

x intercept (y = 0)

y intercept (x = 0)

Linear Equations – Slope 2 1

2 1

y ym

x x-

=-

positive

negative

undefined

zero

y mx b= +

Solve and Graph Inequalities Same as equations EXCEPT

when multiply or divide by aa negative number flip the inequality

2 4 10x- + <

2 4 4 10 4

2 6

2 62 2

3

x

x

x

x

- + - < -

- <

->

- ->-

0-3

Open Closed

>, < >, <

6x - 2(x + 1) > 0

• 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•

A) x ≤ 3• B) x ≥ 3• C) x ≤ -3• D) x ≥ -3

Systems of Linear Equations

Main Idea

43

3y x=- +

1 52 2

y x= -

( )3, 1-

The solution to asystem of equations is the point where the 2 lines intersect

Solution

When you substitute the

solution, it must make

BOTH equations true !!

Identify the solution to the system of equations graphed.

A. (0, 1)B. (1 -1)C. (0, -3)D. (-1, 1)

Systems of Equations – Substitution2 5

4 3 9

x y

x y

- =

+ =

2 5x y= + ( )4 2 5 3 9

8 20 3 9

11 20 20 9 20

11 11

1

y y

y y

y

y

y

+ + =

+ + =

+ - = -

=-

=-( )2 1 5

2 5

3

x

x

x

= - +

=- +

= ( )3, 1-

substitute

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 – Elimination2 2 10

5

x y

x y

+ =

- =

( )2 2 10

2 5 2 2 10

x y

x y x y

+ =

- = Þ + - =

4 20

4 204 4

5

x

x

x

=

=

=

add both equations

eliminate y

5

5 5

0

0

x y

y

y

y

- =

- =

- =

= (5,0)

What is the solution to the system of equations? A) (-1, -6)B) (-6, -1)C) (5, -2)D) (5, 4)

2x - 3y = 16 5x - 3y = 13

  Which mapping has EXACTLY the set of points {(2,6), (3,6), (4,8)}?

ABCD

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. White3/2009