math midterm study

⁻⁴/¹⁷

What is the value of n? (81³ⁿ⁺²)/(243⁻ⁿ) = 3⁴

-2

What is the value of n? (¹/₁₂₈) = 2⁵ⁿ⁺³

⁴/₃

What is the value of n? (¹/₂₅)ⁿ⁻² = (125)ⁿ÷³

⁻¹/₆

What is the value of n? (¹/₆)³ⁿ⁺² × 216³ⁿ = (¹/₂₁₆)

-6

What is the value of n? (¹/₇)ⁿ⁺⁴ - 8 = 41

all real numbers

What is the value of n? (¹/₈)²ⁿ = 4⁻³ⁿ

½

What is the value of n? 10⁻³ⁿ × 10ⁿ = ¹/₁₀

-5

What is the value of n? 2⁴ⁿ = 32ⁿ⁺¹

12

What is the value of n? 2⁵ⁿ = 8²ⁿ⁻⁴

3

What is the value of n? 36⁻³ⁿ⁺³ = (¹/₂₁₆)ⁿ⁺¹

³/₂

What is the value of n? 3⁶ⁿ⁻³ = 9²ⁿ

⁻²/₃

What is the value of n? 3⁻²ⁿ⁺¹ × 3⁻²ⁿ⁻³ = 3⁻ⁿ

1

What is the value of n? 4ⁿ = (½)ⁿ⁻³

5

What is the value of n? 4ⁿ⁻² - 22 = 42

¹¹/₂

What is the value of n? 4ⁿ⁻³ = 32

2

What is the value of n? 64²ⁿ⁺⁴ = 16⁵ⁿ

¹/₄

What is the value of n? 9²ⁿ⁺³ = 2187

¹¹/₃

What is the value of x?

Integers

Z = {...-3, -2, -1, 0, 1, 2, 3, ...}

Relation

a set of ordered pairs: { (1,4), ( 1,5), (4,5), (3,2)}

Which set shows all the solutions for ³√64? a. 4 only b. -4 and +4 c. 8 only d. -8 and +8

a.

Which set is the solution for x³ = -343? a. ³√7 b. -7 c. 7 d. ±7

b.

Distance Formula (Using Pythagorean Theorem)

finds the length of line segment

proportional

ratios are equivalent

non-proportional

ratios are not equivalent

non-proportional

the line does not pass through the point of origin in the graph

proportional

the line passes through the point of origin in the graph

(10, -1)

x - y = 11 2x + y = 19

Solve for x. x² = 0

x = 0

Solve for x. x³ = 0

x = 0

Solve for x. x³ = 0.0027

x = 0.03

Solve for x. x³ = 1

x = 1

Solve for x. ³√x = 10

x = 1000

Solve for x. ³√x = 5

x = 125

Solve for x. x³ = 8/27

x = 2/3

Solve for x. √x = 5

x = 25

Solve for x. x² = 0.49

x = ±0.7

Solve for x. x² = 1

x = ±1

Solve for x. x² = 2.25

x = ±1.5

Solve for x. x² = 4/36

x = ±1/3

Solve for x. x² = 225

x = ±15

Solve for x. x² = 256

x = ±16

Solve for x. x² = 16/49

x = ±4/7

infinite solutions

y = -4x + 2 4x + y = 2

no solution

y = 2x + 5 y = 2x - 7

(2, 3)

y = 5x - 7 -3x - 2y = -12

(2, 1)

y = 6x - 11 -2x - 3y = -7

Linear functions

y = Mx + b

Quadratic functions

y = a times an unknown number to the second power + bx + c

Exponential functions

y = a times b to the power of x

(5, 10)

y = x + 5 3x + y = 25

non-proportional

y=1/2x-3

proportional

y=1/3x

proportional

y=12x

proportional

y=4x

non-proportional

y=6x+1

non-proportional

y=9x-2

Natural Numbers

{1,2,3...}

22 / 10

2.2

Put in scientific notation: 300,000

3 x 10⁵

Inputs (Domain)

The set of x-values

Put in standard notation: 1.50 x 10⁻⁴

0.000150

4.6 / 1,000

0.0046

Put in standard notation: 6.330 x 10⁻³

0.006330

0.075 / 10

0.0075

0.04 x 10

0.4

43 x 0.01

0.43

0.05 x 10

0.5

941 x 0.001

0.941

³√1

1

1,139.4 / 1,000

1.1394

199 / 100

1.99

proportional

1/11 and 3/33

proportional

1/2 and 4/8

proportional

1/3 and 2/6

proportional

1/5 and 3/15

√121

11

√144

12

12.45 / 1

12.45

1,298 / 10

129.8

√225

15

1,563 / 100

15.63

1.58 x 100

158

√289

17

1.98 x 10

19.8

x = 5

2 (x + 1) = 3x - 3

Put in proper scientific notation: 235 x 10^-4

2.35 x 10^-2

Put in proper scientific notation: 2350 x 10^0

2.35 x 10^3

Put in proper scientific notation: 23.5 x 10^5

2.35 x 10^6

Put in scientific notation: 24,327

2.4327 x 10⁴

Put in scientific notation: 24,327,000

2.4327 x 10⁷

2.91 x 1

2.91

non-proportional

2/10 and 5/20

25.3 x 100

2530

2.95 x 1000

2950

infinite solutions

2x + 8y = 6 -5x - 20y = -15

(4, 3)

2x - 3y = -1 y = x - 1

0.03 x 100

3

Put in scientific notation: 30

3 x 10¹

Put in scientific notation: 3

3 x 10⁰

34 / 10

3.4

341 / 100

3.41

non-proportional

3/4 and 1/10

proportional

3/4 and 6/8

non-proportional

3/9 and 4/16

Put in standard notation: 3 x 10²

300

Put in standard notation: 3 x 10⁵

300,000

329.4 / 10

32.94

Put in standard notation: 3.25 x 10²

325

100 x 3.49

349

Put in proper scientific notation: 400 x 10^-8

4 x 10^-6

Put in proper scientific notation: 0.004 x 10^5

4 x 10^2

Put in proper scientific notation: 40 x 10^6

4 x 10^7

non-proportional

4/12 and 1/2

non-proportional

4/20 and 4/16

³√125

5

Put in proper scientific notation: 0.005 x 10^3

5 x 10^0

Put in proper scientific notation: 500 x 10^-2

5 x 10^0

Put in proper scientific notation: 50 x 10

5 x 10^2

Put in standard notation: 5.72×10⁹

5,720,000,000

5,125 / 1,000

5.125

Put in scientific notation: 0.053

5.3 x 10⁻²

Put in scientific notation: 0.0053

5.3 x 10⁻³

53.7 / 10

5.37

0.001 x 5600

5.6

Put in scientific notation: 572

5.72×10²

Put in scientific notation: 57,200

5.72×10⁴

Put in standard notation: 5.72×10⁴

57,200

592.3 x 0.1

59.23

(-6, 0)

5x + 4y = -30 3x - 9y = -18

621 / 100

6.21

Put in scientific notation: 0.0078

7.8 x 10⁻³

³√512

8

√64

8

83.2 / 10

8.32

894.1 x 0.01

8.941

(-1, -8)

8x + y = -16 -3x + y = -5

Linear

A function that forms a straight line when graphed

Function f(x)

A relation for which each element of the domain corresponds to exactly one element of the range

Function

A relationship that assigns exactly one output value for each input value

Relation

A set of ordered pairs

Vertical Line Test

A test use to determine if a relation is a function. A relation is a function if there are no vertical lines that intersect the graph at more than one point.

dependent variable

A variable (y) that depends on one or more other variables

Standard Form of a Linear Equation

Ax+By=C, where A, B, and C are integers and A is not negative

Negative Slope

Falls from left to right

True or False? √1 is not equal to ³√1.

False. Both statements are equivalent to 1.

Parallel Lines

Have equal slopes (gradients)

Perpendicular Lines

Have opposite reciprocal slopes (gradients)

Nonlinear

Not a straight line when graphed

Rational Numbers

Q : Numbers that can be written as the ratio of two integers; includes decimals that terminate or repeat

Irrational Numbers

Q' ( or I ) : Any number that is not a rational number, includes decimals that neither terminate nor repeat

Positive Slope

Rises from left to right

(⁵/₁₁)x²y⁷

Select the equivalent expression. (10x⁴y⁸)/(22x²y)

32x⁴y⁵

Select the equivalent expression. (2xy)³×(4xy²)

-96x⁷y⁶

Select the equivalent expression. (2xy)⁵(-3x²y)

8x⁴y⁴z⁴

Select the equivalent expression. (2xy²z²)×(4x³y²z²)

16x⁸

Select the equivalent expression. (2x²)⁴

144x¹⁸

Select the equivalent expression. (2x²)⁴×(3x⁵)²

8x⁶y⁹

Select the equivalent expression. (2x²y³)³

z¹⁰/(4x⁴y⁶)

Select the equivalent expression. (2x³y⁻⁵z⁷)/(8x⁷yz⁻³)

(⁻⁴/₅)x⁴

Select the equivalent expression. (2x⁴y)³/(-10x⁸y³)

6x¹⁵y¹⁰

Select the equivalent expression. (3x¹⁰y⁸)×(2x⁵y²)

9x⁸y¹⁶

Select the equivalent expression. (3x⁴y⁸)²

y⁶/(27x¹²)

Select the equivalent expression. (3x⁴y⁻²)⁻³

-y¹⁰/(4x²z)

Select the equivalent expression. (4x³y¹⁰z⁻⁴)/(-16x⁵z⁻³)

8x⁷/y²

Select the equivalent expression. (4x⁴y³)×(2x³y⁻⁵)

2/(5x⁹y⁴)

Select the equivalent expression. (4x⁻⁵y⁻³)(2x²) / (20x⁶y)

15x⁵y³

Select the equivalent expression. (5x³y⁵)×(3x²y⁻²)

4x²

Select the equivalent expression. (8x⁵)/(2x³)

x¹⁰y¹⁵

Select the equivalent expression. (x²y³)⁵

y³/x

Select the equivalent expression. (x³y⁵)/(x⁴y²)

x⁷y¹⁵

Select the equivalent expression. (x³y⁶)×(x⁴y⁹)

1/y³

Select the equivalent expression. (x⁴y)(xy⁷)/(x⁵y¹¹)

x²y³

Select the equivalent expression. (x⁴y⁹)/(x²y⁶)

x²⁴

Select the equivalent expression. (x⁶)⁴

x⁸⁰

Select the equivalent expression. (x⁸)¹⁰

y³/x³

Select the equivalent expression. (y²x)×(yx⁻⁴)

-6x⁸y¹²

Select the equivalent expression. -6(x²y³)⁴

x²²

Select the equivalent expression. x¹⁰ × x¹²

x¹³

Select the equivalent expression. x⁵ × x⁸

x

Select the equivalent expression. x⁵/x⁴

x⁵/y⁴

Select the equivalent expression. x⁵y⁻⁴

x³

Select the equivalent expression. x⁹/x⁶

1/x³

Select the equivalent expression. x⁻³

What is the principal square root of 36 and why?

Six is the principal square root because it is the positive root.

x = 9.6

Solve 0.3x - 4 = 0.8 - 0.2x

x = 0.4

Solve 15 - 3x = x + 13 + x

x = 4

Solve 3 (x +1) = 2x + 7

x = 0.5

Solve 3 - 2(x - 1) = 2 + 4x

x = 1/3

Solve 3(2x + 2) - 4 = 3(x + 1)

x = 4/3

Solve 4(2x - 1) + 5 = 5(x + 1)

x = 1

Solve 4x + 2 = 3 (6 - 4x)

x = 12

Solve 4x - 5 = 3x + 7

x = -8

Solve 6x - 4 (2x + 1) = 12

x = 3

Solve 7x + 3 - 2x = 4x + 6

x = -4

Solve 8x - 3 = 5 (2x + 1)

x = 1.5

Solve 8x - 5 = 4x + 4 - 2x

Parabola

The U shaped curve of a quadratic function and each time you have x squared

Domain

The possible values for the input, or independent variable of the function, the x value

Range

The possible values for the output, or the dependent variable of the function, the y value

Outputs (Range)

The set of y-values

Zero Slope

The slope of a horizontal line m=0

Undefined Slope

The slope of a vertical line

Independent variable

The variable that represents the input and causes the change in the dependent variable; x-axis label

73 x 0.01

0.73

√1

1

Slope-Intercept Form : Gradient-intercept form

(in USA ) y =mx +b (in IB): y =mx +c

³√-1000

-10

no solution

-3x + 3y = 4 -x + y = 3

(6, -6)

-4x - 2y = -12 4x + 8y = -24

³√-8

-2

³√-729

-9