Ms. Cherney's ALGEBRA FINAL EXAM REVIEW 2021-2022

Dress $69 and tax is 5 %. Find the total price

$72.45

Use substitution to solve the system of equations: y = 4x and x + y = 5

(1, 4) Check using desmos.com.

Use elimination to solve the system of equations: x + 4y = 11 and x − 6y = 11

(11, 0) Check using desmos.com.

Factor 4x²− 25

(2x − 5)(2x + 5)

Use substitution to solve the system of equations: 3x − y = 4 and 2x − 3y = −9

(3, 5) Check using desmos.com.

Factor the polynomial 9x² −3xy + 6x − 2y

(3x + 2)(3x− y)

Factor 16p² − 36

(4p − 6)(4p + 6)

Factor n² + 7n + 12

(n + 4)(n + 3)

Factor 2t² + 9t − 5

(t+ 5)(2t −1)

Fator 2x² + 5x + 2

(x + 2)(2x + 1)

Factor y² − 6y +8

(y − 2)(y − 4)

Define slope

(y2 − y1)/(x2 − x1) Other definitions are rise/run and change in y/change in x

Use an augmented matrix to solve the system of equations: x + 4y = 19 and −3x − 2y= −7

(−1 , 5) Check using desmos.com.

Solve the system of equations by graphing . . . . x + 3y = −3 and x − 3y = −3

(−3, 0) Check using desmos.com.

Use elimination to solve the system of equations: 2x − y = −1 and 3x − 2y = 1

(−3,−5) Check using desmos.com.

Solve using elimination: . . . . . . . . . . . . . . . . −3x −4y = −4 and x + 3y = −1

(−4, −2) Check using desmos.com.

Find the slope of the line that passes through (6, 1) and (−6, 1)

0

Solve the equation 2x(x − 3) = 0

0 and 3

Solve (4x + 7)/15 = (6x +2)/10

0.8 Hint: Cross-multiply to start.

Express the number 158 X 10⁻⁷in scientific notation.

1.58 X 10⁻⁵

Express 1,900,000 in scientific notation

1.9 X 10⁶

Find the product (5a − 2)(2a − 3)

10a² − 19a + 6

Find 5m²(2m³ −m)

10m⁵ − 5m³

Write an algebraic expression for the product of ten and x

10x

Find three consecutive integers whose sum is 36

11, 12, 13

Evaluate 30 − 5 ∙ 4 + 2

12

Use the distributive property to factor 24x + 48y = 0

12(x + 2y)

Evaluate if a = 12, b = 9, c = 4 a² + b − c²

137

Simplify the expression. If not possible write simplified 3x + 2(4y + 5x)

13x + 8y

Evaluate if x = −1, y = 3, and z = −4. . . . . . . . |−3y + z| − x

14

Simplify the expression. If not possible write simplified 7(2x + 5)

14x + 35

y = 2x The slope is ____________

2

Find the degree of the polynomial 2x² + 3x + 7

2 (degree = highest exponent)

Evaluate and name the property used in each step 2 + 6(9− 3²) − 2

2 + 6 (9 − 9) − 2 (sub) . . . . . . . . . . . . . . . . . . . . 2 + 6(0) − 2 (sub) . . . . . . . . . . . . . . . . . . . . . . . . 2 + 0 − 2 (Mult prop of zero). . . . . .. . .. . . . .. . 2-2 (add iden). . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 (sub) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Factor the monomial completely 42g²h

2 ∙ 3 ∙ 7 ∙ g ∙ g ∙h

Factor 8m − 6

2(4m − 3)

Look at the graph of the line in problem 2-24 and determine the slope of the line.

2/6, which reduces to 1/3

Write an equation and solve. Twenty decreased by three times a number equals −10.

20 − 3x = −10 When the equation is solved, x = 10

Solve the proportion. . . . . . . . . 9/(y + 1) = 18/54

26

Find the volume of a cube whose length, width, and heighth have a measure of 3x⁵

27x¹⁵

Translate the sentence in to an equation. Twice a increased by the cube of a equals b

2a + a³ = b

f(x) = 2x − 4 Find f(k + 1)

2k − 2

Evaluate 162 ÷ [6(7 − 4)²]

3

In the equation y = 3x + 7, the slope is _______________

3

Two trains leave Chicago, one traveling east at 30 miles per hour and one traveling west at 40 miles per hour. When will the trains be 210 miles apart?

3 hours

Factor completely 3a² + 30a + 63

3(a + 7)(a + 3)

Translate the sentence in to an equation. Three times the sum of g and h is 12.

3(g + h) = 12

Find the solution set if the replacement set is x = {0. 1/2, 1, 3/2, 2} for the equation 120 − 28x = 78

3/2

Find three consecutive odd integers whose sum is 117

37, 39, 41

Write the equation in standard form: y − 11 = 3(x − 2)

3x − y = −5

Simplify the expression. If not possible, write simplified 5x + 4 + 3x² − 3x

3x² + 2x + 4

Write 4 − x + 3x³ − 2x² in standard form and identify the leading coefficient

3x³ − 2x² −x + 4 The leading coefficient is 3

Evaluate 6²+ 3 ∙ 7 − 9

48

Find the GCF 40xy², 56x3y², 124x²y³

4xy²

Find the difference. (3x² − 7x + 5) − (−x² + 4x)

4x² − 11x + 5

Express 0.000000058 in scientific notation

5.8 X 10⁻⁸

Express the number 0.00005816 in scientific notation.

5.816 X 10⁻⁵

Simplify (−4xy)³(−2x²)³

512x⁹y³

Evaluate if x = 2, y = 3, z = 4 2xyz + 5

53

Find two consecutive even integers whose sum is 126.

62, 64

Evaluate the expression 5 raised to the fourth

625

Find the degree of the polynomial 5x²y + 7xy⁶− 3xy

7

Find the solution set if the replacement set is x = {4, 5, 6, 7, 8} for the equation 5x − 9 = 26

7

In the equation y = 3x + 7, the y intercept is _______________

7

Find the degree of the polynomial 10x³y⁵

8

Solve the equation that follows 2(x + 2) =20

8

Write an algebraic expression for the sum of eight and the square of a number x

8 + x²

Find the GCF 88a³d, 40a²d², 32a²d

8a²d

Simplify the expression. If not possible, write simplified 3x + 6x

9x

Find the product (3x − 2)(3x + 2)

9x² − 12x + 4

²Simplify. Assume no denominator is equal to zero. (4x/3x²)−²

9x²/16

Find the product (3x − 1)²

9x²− 6x + 1

Solve 3(x + 1) − 5 = 3x −2

All numbers

Sketch a system of equations that has many solutions.

Check using desmos.com.

Sketch a system of equations that has no solution.

Check using desmos.com.

State whether the percent of change is a percent of increase or percent of decrease. Find the percent of change to the nearest whole percent. Original $25, New $10

Decrease of 60%

List the domain and the range for the following relation {(−2,−1), (3, 3), (4,3)}

Domain = {−2, 3, 4} Range = {−1, 3}

Is the equation y = 5ⁿ linear, quadratic, or exponential?

Exponential

Factor and solve 2x² + 7x + 3 = 0

Factors are (2x + 1)(x + 3) = 0 Using the Zero Product Property, the solutions are −3 and −1/2

Factor and solve 25p² − 16 = 0

Factors are (5x − 4)(5x + 4) = 0 Solutions are 4/5 and −4/5

Factor and solve 5d² − 22d + 8 = 0

Factors are (d − 4)(5d − 2) = 0 Solutions are 4 and 2/5

Factor and solve h²− 17h = −60. Hint, first get the equation equal to zero.

Factors are (h − 12) (h − 5) = 0 Solutions are 5 and 12

Factor and solve p² + 5p − 84 = 0

Factors are (p + 12)(p − 7) = 0 Using ZPP, the Solutions are −12 and 7

Factor and solve x²− 16 = 0

Factors are (x − 4) (x + 4)) Solutions are 4 and −4

Solve the equation x² = 10x

Factors are x(x − 10) = 0 Using ZPP, the Solutions are 0 and 10

Write a verbal expression for the algebraic expression 5(x² +2)

Five times the quantity x squared plus two

Solve the equation 15x −30 = 5x − 50 by graphing and algebraically.

Graph f(x) = 10x + 20 and it crosses the x-axis at − 2. Solve 10x + 20 and x = −2

Is the equation y = 1/2x + 5 linear, quadratic, or exponential?

Linear

Determine whether the lines are parallel, perpendicular, or neither: . . . . . . . . . . . . . . . . . 2x + 5y = 15 and 3x + 5y = 15

Neither

Determine whether each pair of ratios is an equivalent ratio. 5/9, 7/11

No because when you cross multiply, 55 is not equal to 63. Also, 5÷9 is not equal to 7÷11.

Solve 3(x − 6) = 3x

No solution

Solve the system of equations by graphing: . . . y = 2x + 3 and 3y = 6x − 6

No solution Check using desmos.com.

Determine whether the equation is linear or not. If yes, write the equation in standard form y = 3x² + 1

No, because the x is raised to a power greater than one

Determine whether the equation is linear or not. If yes, write the equation in standard form xy = 6

No, because variables are multiplied together

Is the following an arithmetic sequence 1, 4, 9, 16...

No. There is not a common difference.

Determine whether the lines are parallel, perpendicular, or neither: . . . . . . . . . . . . . . . . . y = −2x and 2x + y = 3

Parallel

Determine whether the lines are parallel, perpendicular, or neither: . . . . . . . . . . . . . . . . . 3x + 5y = 10 and 5x − 3y = −6

Perpendicular

Describe how you would graph y = 1/3 x + 2 using the slope and the y interept.

Put a dot on the y-axis on the number 2. Count a slope of 1/3 by going up 1 and right 3 or down 1 and left 3. Count the slope two or three times and then draw the line.

Sketch a graph that has a minimum at the point (4, −2) and has roots (or solutions) at 2 and 6

Put a point on the minimum of (4, −2) Put points on the x-axis on 2 and 6 and connect the parabola Check using desmos.com.

Is the equation y = x² + 2x + 7 linear, quadratic or exponential?

Quadratic

Evaluate. Express in scientific and standard form (4.9 X 10−³)/(4.0 X 10−⁵)

Scientific 1.96 X 10−⁷and standar 0.000000196

Evaluate. Express in scientific and standard form (4.8 X 10⁴)(6 X 10⁶)

Scientific 2.88 X 10¹¹ and standard 288,000,000,000

Write a verbal expression for 6x + 7

Six times x plus seven

In the equation, y = mx + b, the m stands for _____________

Slope

What form should you put lines in to determine if they are parallel, perpendicular, or neither?

Slope intercept form

Solve 2/3 n + 8 = 1/3 n + 2

Solution: n=−18 Hint: Start by multiplying the equation by 3 to clear fractions. Do you know how to check your solution?

Graph y − x = 4 using a table

Solve the equation for y. y = x + 4. Some points on the line are (0, 4), (1, 5), (−1, 3) Check using desmos.com

Graph y = 3ⁿ

Some points are (0, 0), (1, 3), (2, 9), (−1, 1/3), (−2, 1/9) Check using desmos.com.

Graph y = −6x

Some points on the line are (0, 0), (1, −6),(−1, 6) Type the equation into Desmos Graphing Calculator to check your work.

Graph y = 1/3 x + 2 using a table

Some points on the line are (0, 2),(3, 3), (6, 4). Type the equation into Desmos Graphing Calculator to check your work.

Solve x² − 2x − 8 by graphing. What are the domain and range?

The axis of symmetry is 1. The vertex is (1, −9). Some points in the table may be (1, −9), (0, −8), (2, −8), (4, 0), (−2, 0) The solutions are 4 and −2. Domain all real #s and range y ≥ −9

Solve x² + 6x + 8 = 0 by graphing and what are the domain and range.

The axis of symmetry is −3. The vertex is (−3,−1). Some points in the table may be (−3, −1), (−2, 0), (−4, 0), (−1, 3), (−5, 3) The solutions are − 4 and −2. Domain all reals, Range y ≥ −1

Sketch a quadratic equation that has no roots (solutions)

The parabola does not touch the x-axis. Check using desmos.com.

Sketch a quadratic equation that has one root (solution).

The parabola touches the x-axis at one point. Check using desmos.com.

Sketch a quadratic equation that has two roots (solutions).

The parabola touches the x-axis at two points. Check using desmos.com to see if your graph hits the x-axis twice.

What is true about the slopes of perpendicular lines?

The product of slopes of perpendicular lines is −1. (Slopes of perpendicular lines are opposite reciprocals)

What is true about the slopes of parallel lines?

The slopes of parallel lines are the same

Write the equations for two lines that are parallel.

There are many answers. An example would by y = 2x and y = 2x + 7.

Write the equations for two lines that are perpendicular.

There are many answers. An example would by y = 2x and y = −1/2 x + 6. The product of the two slopes has to be −1

What is true about any horizontal line and a vertical line?

They are perpendicular

Translate the equation in to a sentence 2x + 10 = 26

Two times x plus ten equals twenty-six. OR The product of two and x increased by ten is twenty-six.

Find the slope of the line that passes through (5, 2) and (5, −2)

Undefined

Determine whether the equation is linear or not. If yes, write the equation in standard form y = 2 − 3x

Yes. 3x + y = 2

Solve 2(a − 3) = 3(−2a + 6)

a = 3

Solve the equation for the variable a listed . . . 7a − b = 15a for a

a = −b/8

f(x) = x² + 3 Find f(b) + 4

b² + 7

Solve h/3 = −2

h = − 6

Solve −2m = 16

m = −8

Simplify m⁴r²/mr⁴

m³/r²

Find the value for n and name the property used: 7 + n = 7

n = 0 Additive identity

Find the value for n and name the property 5 · n · 2 = 0

n = 0 multiplication property of zero

Find the value for n and name the property used: 11· n = 11

n = 1 Multiplicative identity

Find the value of n and name the property used: 3 · 1/3 = n

n = 1 Multiplicative inverse or reciprocal

Find (n −4)(n − 6)

n² − 10n + 24

Find the value of r so the line that passes through each pair of points has the given slope. (r, 3), (5, 9), m = 2

r = 2

Find the value of r so the line that passes through each pair of points has the given slope. (−4, 3)), (r, 5), m= 1/4

r = 4

Write an equation and solve. X plus 10 is equal to 3 times x.

x + 10 = 3x When the equation is solved, x = 5

Write the equation in standard form: y − 10 = −(x − 2)

x + y = 12

Solve the equation 4x − 1 = 0

x = 1/4

Solve the equation 0 = 4 − 2x

x = 2

Solve 2(4x + 3) + 2 = −4(x + 1)

x = −1

Solve 5(x + 3)+9= 3(x − 2) + 6

x = −12

Solve 3.2x − 4.3 = 12.6x + 14.5

x = −2

Solve 18 − 4x = 42

x = −6

Graph 2x + 4y = 16 using x an y intercepts

x intercept is 8, and the y intercept is 4. Type the equation into Desmos Graphing Calculator to check your work.

Graph 2x + y = −2 using the x and y intercepts

x intercept is −1 and the y intercept is −2 Check using desmos.com

Find the product (x + 9)²

x² + 18x + 81

Find the product (x − 7)(x + 5)

x² − 2x − 35

Simplify (x⁷)⁴

x²⁸

Simplify. Assume no denominator is equal to zero. (3x³y)²/27x²

x⁴y²/3

Simplify x³ ∙ x²

x⁵

Simplify x⁹/x²

x⁷

Solve the equation for the variable indicated. 7x + 3y = m, for y

y = (m − 7x)/3

Given the point (1, 3) and (−3, −5), write the equation in slope intercept form

y = 2x + 1

Write an equation in slope intercept form for the line that passes through (−1, −2) and is parallel to 3x − y = 5.

y = 3x + 1

Write an equation in slope intercept form for the line that passes through (−2, 2) and is perpendicular to y = −1/3 x + 9.

y = 3x + 8

Write an equation in slope intercept form for the line that passes through (10, 5) and is perpendicular to 5x + 4y = 8.

y = 4/5x − 3

Write the equation in slope intercept form:. . . y + 2 = 4(x + 2)

y = 4x + 6

The slope intercept form of a linear equation is ____

y = mx + b

Write an equation in slope intercept form for the line that passes through (3, 2) and is parallel r to y = x + 5.

y = x − 1

Write the equation in slope intercept form: 2x + 4y = 12

y = −1/2x + 3

In the equation, y = mx + b, the b stands for _____________

y-intercept

Solve the equation. Show work. x/5 + 6 = 2

− 20

Factor the monomial completely −38a²b

−1 ∙ 2 ∙ 19 ∙ a ∙ a ∙ b

Solve the equation. Show work. |5y − 2| = 7

−1, 9/5 There are two solutions to absolute value problems. Refer to #3-99 in the ebook for an example of how to solve these.

Find the slope of the line that passes through (10, 0) and (−2, 4)

−1/3

f(x) = 2x − 4 Find the value of f(−5)

−14

In the equation y = −2x − 6, the slope is ________________

−2

Simplify (−3ab⁴)³

−27a³b¹²

Find the difference. (3a − 5)) − (5a + 1)

−2a − 6

Simplify. Assume no denominator is equal to zero. −15 w⁰u−¹/5u³

−3/u⁴

Find the sum (−4p² − p + 9) + (p²+ 3p −1)

−3p²+ 2p + 8

Simplify: (2xy)²(−3x²)(4y⁴)

−48x⁴y⁶

Solve −x/3 − 4 = 13

−51

In the equation, y = −2x − 6, the y intercept is _____________

−6

Solve |x + 1| = 5

−6 and 4 See #3-99 in ebook for example.

Solve by using the quadratic formula. Round to the nearest tenth if necessary x² + 5x = 6

−6, 1

Solve by completing the square. Round to the nearest tenth if necessary x²+ 6x = 7

−7 and 1

Solve the equation by using the quadratic formula. Round to the nearest tenth if necessary x² + 8x + 7 = 0

−7 and −1