Math Practice Questions

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) 18x5/7

3x1/7

(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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