MTH 65 No Calculator Portion Practice Midterm Exam 1

Practice Midterm Exam 1

This is a sample test. Your actual test may contain some similar questions, as well as ones that

are not included here. Please do not consider this to be an all-inclusive sample of what might

be contained on your exam. Doing so would be a disservice to your exam preparation.

Calculators are not permitted on this portion of the exam.

1. For the polynomial −2 3 x2 y3 + 4×3 y − 12.5×2, identify the following:

(a) The leading term:

(b) The coefficient of the third term:

(c) The degree of the polynomial:

2. Add/ subtract the following expressions as indicated. Simply the final expression as much as possi-

ble.

(a) (16×2 − 5x)− (x2 + 8x − 1)

(b) (2×2 − 3x − 5) + (−12×2 + 7x − 9)

(c) (x2 + 3x y + 2y2) + (5y2 − 11x y)

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Practice Midterm Exam 1 No Calculator Portion MTH 65

3. Simplify the following expressions. Do not leave negative exponents in your answers.

(a) t−13 · t7 (b) �

4×3 y5 � �

7×2 y−9 �

(c) 9r−10 (d) �

−5m4v−7 �−2

(e) −18p0 (f) 12w(4w)−1

(g) 5y2

10y−5

(h) −82

4. Multiply/expand the following expressions as indicated. Simply the final expression as much as

possible.

(a) −8t(−4t3 + 2) (b) 2×3(x2 − 3x + 10)

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MTH 65 No Calculator Portion Practice Midterm Exam 1

5. Determine if each statement is true or false. If false, give a brief justification for each answer.

(a) True or False: (t − 4)2 = t2 − 16

(b) True or False: (5− q)(5+ q) = 52 − q2

(c) True or False: (x2 + 4x + 5) + (2x + 3) = x2 + 6x + 8

(d) True or False: −2x−3 = 1 −2×3

(e) True or False: −112 = 121

(f) True or False: 5(p− 3)2 = (5p− 15)2

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Practice Midterm Exam 1 No Calculator Portion MTH 65

6. Multiply/expand the following expressions as indicated. Simply the final expression as much as

possible.

(a) (4n− 2)(4n+ 9) (b) (3x + 2y)(2x + y)

(c) (7s+ 5)(7s− 5) (d) (9t − 2)2

(e) (x + 4)3 (f) 2p(5p− 1)(5p+ 1)

7. Evaluate/simplify each of the following expressions. If the number is not real, state this.

(a) p

49 (b) p −25 (c)

s

4 81

(d) p

100− 64 (e) p

0 (f) − p

9

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MTH 65 No Calculator Portion Practice Midterm Exam 1

8. Divide and simplify.

(a) 12t9 − 28t7 + 4t6

−4t6

(b) 20r9 t8 − 16r7 t6 − 12r5 t4 + 8r3 t4

8r2 t4

9. Simplify p

27 using the multiplication properties of square roots.

You should be able to do this without a calculator.

10. Simplify the following.

(a) 6 p

3− 2 p

12 (b) 5 p

4− 11 p

9

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Practice Midterm Exam 1 Calculator-Allowed Portion MTH 65

Calculators are permitted on this portion of the exam.

You may use a calculator (basic, scientific, or graphing), but may not use any other electronic de-

vice. The calculator should only be used at the end of your problem-solving process, to calculate

some decimal value. Where appropriate, round to two decimal places.

11. Simplify each of the following and write your answer using only positive exponents.

(a) 3×5 · 2×4

18×3

(b)

�

k2n−3 �−4

(kn4)−3

(c) a−5 b4c−6

a−2 b−3c4

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MTH 65 Calculator-Allowed Portion Practice Midterm Exam 1

12. Rationalize the denominators.

(a)

p 3

p 15

(b) 6 p

18

13. Find the missing exponents and coefficients.

Rewrite the entire equation with the missing exponents and coefficients filled in.

(a) 25x

e − 50x

e + 3×6 +

e x5

e x

e = e

x3 + 10×2 + e

x e + 8

(b)

e a5 b

e − 9a4 b

e +

e a

e b2

e a

e b

e = 2a e

b− a− 3b

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MTH 65 No Calculator Portion Practice Midterm Exam 2

Practice Midterm Exam 2

This is a sample test. Your actual test may contain some similar questions, as well as ones that

are not included here. Please do not consider this to be an all-inclusive sample of what might

be contained on your exam. Doing so would be a disservice to your exam preparation.

Calculators are not permitted on this portion of the exam.

1. Solve the following using the square root property.

(a) 2y2 = 24 (b) (x − 5)2 = 9

2. Solve x2 − 2x = 15 using the quadratic formula.

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Practice Midterm Exam 2 No Calculator Portion MTH 65

3. Write each expression using a rational (fractional) exponent. (a) 7p6 (b)

8p k5 (c)

p 19

4. Write each expression using radical notation. (a) t3/11 (b) 2−1/4 (c) 7p−3/2

5. Simplify the following. (Stating that these are not real numbers will not earn any credit.)

(a) p −16 (b) 11+

p −45

6. Solve 3pk+ 4+ 9= 7 and formally check your solution(s).

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MTH 65 No Calculator Portion Practice Midterm Exam 2

7. (a) What type of equation is 10− 3(2m− 1) = −23?

(b) Solve 10− 3(2m− 1) = −23.

8. (a) What type of equation is p

x − 15= 3− p

x?

(b) Solve p

x − 15= 3− p

x .

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Practice Midterm Exam 2 No Calculator Portion MTH 65

9. Solve (4y − 7)2 = −20 using the square root property.

10. Solve x2 + 2x + 5= 0 using the quadratic formula.

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MTH 65 No Calculator Portion Practice Midterm Exam 2

11. Solve p = 7

2 p

t − 4 for t. (Note: t > 4.)

12. Solve y = m(x − h) + k for x .

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Practice Midterm Exam 2 No Calculator Portion MTH 65

13. Evaluate the following. If the expression is not a real number, explain why this is so or express the

value as a complex number. (You do not need to do both.)

(a) −491/2

(b) �

1 27

�−1/3

(c) (−25)1/2 (d) 16−1/4

14. Use rational exponents to simplify. Use radical notation in your answers.

Assume that all variables represent positive real numbers.

(a) 18×5/7

3×1/7

(b) r−3/4 · r2/3

(c) t1/3 · t1/4 (d) �

p2/7 �7/6

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MTH 65 Calculator-Allowed Portion Practice Midterm Exam 2

Calculators are permitted on this portion of the exam.

15. The height, in feet, of a water balloon launch from a water balloon sling-shot t seconds after it was

launched is given by h= −16t2 + 48t + 16.

(a) What is the height of the water balloon 1.7 seconds after it was launched?

(b) When will the water balloon reach a height of 20 ft?

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Practice Midterm Exam 2 Calculator-Allowed Portion MTH 65

16. Find the missing side length for the triangle. Do not approximate the length.

h

6 cm

8 cm

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Partial Final Exam Review

A Revisit of Modules 7 – 10

This is just a recompilation of some key concepts from the past four modules. It is meant to be a

summary of some of the key topics, but not an all-inclusive sampling of possible test questions.

In addition to these examples, you should study the module worksheets, WeBWorK assignments, and

the book’s exercises.

It is assumed that all solutions can be real or complex numbers. Do not stop solving an equation because

you have determined that the solutions are not real numbers.

Example 1:

a) Write the following numbers in scientific notation.

(a) 0.00030502 (b) 54, 370,000

b) Write the following numbers in standard notation.

(a) 7.32× 105 (b) 6.1× 10−7

Example 2:

Perform the indicated operation. Write your answers in scientific notation.

a) �

3× 106 � �

5× 10−2 �

b) 56× 108

8× 105

c) �

8× 1015 � �

6× 10−28 �

d) 1.5× 10−7

6× 1018

Modules 7 – 10 Review MTH 65

Example 3:

a) How many quarts are in 3 liters?

b) If gas in somewhere in Europe costs $1.795 per liter, what is the price per gallon?

Example 4:

a) How many yards are in 1.5 miles?

b) If my cousin is 2.05 meters tall, how tall is she in feet and inches?

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MTH 65 Modules 7 – 10 Review

Example 5:

a) How many grams are in one pound?

b) If a kilogram of bell peppers costs $1.50, what is the price per pound?

Example 6:

a) How many square inches are in one square yard?

b) How many cubic feet are in one cubic meter?

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Modules 7 – 10 Review MTH 65

Example 7:

a) You need to measure out 2 cups of water, but only have a measuring cup that measures in milliliters. How

many milliliters of water do you need?

b) You bough a house that sits on a lot that is 7500 square feet. How many acres of land did you buy?

Example 8:

a) Sound travels at the speed of 343 meters per second. What is the speed of sound in miles per hour?

b) You count 7 seconds between a flash of lightening and the sound of the thunder the lightening created. Given

that sound travels at the speed of 343 meters per second, how far away (in miles) was the lightening.

Assume the the lightening is seen the instant it flashes.

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MTH 65 Modules 7 – 10 Review

Example 9:

Complete the following geometric formulas.

a) Perimeter of a Rectangle: P =

b) Area of a Rectangle: A=

c) Circumference of a Circle: C =

d) Area of a Circle: A=

e) Area of a Triangle: A=

f) Volume of a Rectangular Prism: V =

g) Volume of a Cylinder: V =

Example 10:

Give examples of appropriate units for

a) perimeter:

b) circumference:

c) area:

d) volume:

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Modules 7 – 10 Review MTH 65

Example 11:

Find the perimeter and area of a rectangular garden that measures 5 feet by 9 feet.

Example 12:

Find the circumference and area of a circular trampoline that has diameter of 3 meters.

State both the exact and approximate answers.

Example 13:

Find the area of a window that is a triangle, has base length of 8 feet, and height of 5 feet.

Example 14:

Find the volume of a box that 3 inches wide, 4 inches high, and 7 inches deep.

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MTH 65 Modules 7 – 10 Review

Example 15:

Find the volume of a circular cylinder that has a 2-inch radius and is 9 inches tall.

State both the exact and approximate answers.

Example 16:

Find the perimeter and area of the shape below.

15 in

25 in

10 in

8 in

Example 17:

Find the perimeter and area of the shape below.

35 cm

11 cm

27 cm

7 cm

5 cm

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Modules 7 – 10 Review MTH 65

Example 18:

A rectangle has an area of 50 square inches and a width of 5 inches. What are the length and perimeter of the

rectangle?

Example 19:

A circle has an area of 49π square yards. What are the diameter and circumference of the circle?

Example 20:

A triangle has an area of 18 square centimeters and a height of 4 centimeters. What are the length of the base of

the triangle?

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MTH 65 Modules 7 – 10 Review

Example 21:

Consider the following two similar right triangles.

Triangle A

5 p

3 cm

10 cm

30◦

Triangle B 18 cm

30◦

a) Find the length of the base of Triangle B. State both the exact and approximate values.

b) Find the height Triangle A.

c) Find the height of Triangle B.

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Modules 7 – 10 Review MTH 65

Example 22:

To have a flock of 20 chickens designated as free range, you need to have at least 48 square feet of space for the

entire flock. If you have exactly 15 feet between your house and your garage and this will be the width of the

chickens’ yard, how wide does their yard need to be?

Example 23:

a) Determine the x-intercept(s) and y-intercept for the equation −4x + 5y = 30.

b) Determine the x-intercept(s) and y-intercept for the equation y = 2×2 − 8x − 10.

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MTH 65 Modules 7 – 10 Review

Example 24:

A toy rocket is shot into the air and its height (in feet) t seconds after launch is modeled by the equation h =

−16t2 + 56t + 4.

a) What is its height 1 second after launch?

b) When does the rocket reach its greatest height?

c) What is its greatest height?

d) When does it hit the ground?

e) When does it reach a height of 28 feet?

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Modules 7 – 10 Review MTH 65

Example 25:

For y = −3×2 − 12x + 63, identify the following.

a) opens upward/downward:

b) vertex:

c) axis of symmetry:

d) vertical intercept:

e) horizontal intercept(s):

For y = 2×2 − x − 15, identify the following.

a) opens upward/downward:

b) vertex:

c) axis of symmetry:

d) vertical intercept:

e) horizontal intercept(s):

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MTH 65 Modules 7 – 10 Review

Example 26:

For the equation y = −x2 − 2x + 8, complete the following: a) Determine the vertex of this parabola.

b) Algebraically determine the vertical intercept.

c) Algebraically determine any horizontal

intercepts.

d) Graph y = x2 − 2x − 8.

Example 27:

The height of a baseball (in feet) t seconds after being hit is modeled by the equation

h= −16t2 + 75t + 4.7, while t ≥ 0 and h≥ 0.

a) When will the ball reach it’s greatest height?

b) When will the ball hit the ground?

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Modules 7 – 10 Review MTH 65

Example 28:

Given are the graphs of y1 = 1 3

x− 8 3

and y2 = − 1 2

x+ 3 2

.

a) What are the points of intersection?

b) Use the graph to solve 1 3

x − 8 3 = −

1 2

x + 3 2

.

−5 −4 −3 −2 −1 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

y1 = 1 3 x −

8 3

y2 = − 1 2 x + 3

2

x

y

c) Use the graph to solve 1 3

x − 8 3 ≤ −

1 2

x + 3 2

.

State the solution set in both interval and set-

builder notations.

d) Use the graph to solve 1 3

x − 8 3 > −

1 2

x + 3 2

.

State the solution set in both interval and set-

builder notations.

Example 29:

Given are the graphs of y1 = x2 − 3x − 2 and y2 = 2.

a) What are the points of intersection?

b) Use the graph to solve x2 − 3x − 2= 2.

−5 −4 −3 −2 −1 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

y 1 =

x 2 −

3x −

2

y2 = 2

x

y

c) Use the graph to solve x2 − 3x − 2< 2.

State the solution set in both interval and set-

builder notations.

d) Use the graph to solve x2 − 3x − 2≥ 2.

State the solution set in both interval and set-

builder notations.

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MTH 65 Modules 7 – 10 Review

Example 30:

Given are the graphs of y1 = − p

x + 5 + 3 and

y2 = 9

20 x2 −

31 20

x − 1.

a) What are the points of intersection?

b) Use the graph to solve − p

x + 5+3= 9

20 x2−

31 20

x−1.

−5 −4 −3 −2 −1 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

y1 = − px + 5+ 3 y 2 =

9 20

x 2 −

31 20 x −

1

x

y

c) Use the graph to solve

− p

x + 5+ 3> 9

20 x2 −

31 20

x − 1.

State the solution set in both interval and set-

builder notations.

d) Use the graph to solve

− p

x + 5+ 3≤ 9

20 x2 −

31 20

x − 1.

State the solution set in both interval and set-

builder notations.

Updated 201904 Page 15

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