Math Practice Questions
theestargirl
MTH65Midterm1Review.pdf
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 + 4x3 y − 12.5x2, 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) (16x2 − 5x)− (x2 + 8x − 1)
(b) (2x2 − 3x − 5) + (−12x2 + 7x − 9)
(c) (x2 + 3x y + 2y2) + (5y2 − 11x y)
Page 1
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) �
4x3 y5 � �
7x2 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) 2x3(x2 − 3x + 10)
Page 2
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 −2x3
(e) True or False: −112 = 121
(f) True or False: 5(p− 3)2 = (5p− 15)2
Page 3
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
Page 4
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
Page 5
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) 3x5 · 2x4
18x3
(b)
�
k2n−3 �−4
(kn4)−3
(c) a−5 b4c−6
a−2 b−3c4
Page 6
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 + 3x6 +
e x5
e x
e = e
x3 + 10x2 + 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
Page 7
