QMS 110 Review questions Test 1
Review exercises
1. Round the following money value to the nearest cents.
$750 [
1−(1+0.035)−6
]
0.035
2. Evaluate
6
(a) −3(−8) + −2 − (−14)
21(−12) −20(−18)
36−|−36|
5−1
25−0.5
+
1
−2
4 +2
4 2 +6
(b) (b)
(c)
3. Evaluate the following expressions when 𝑎 = 2 and 𝑏 = −1
4
(a) √
−𝑏
2𝑎 2
+ 2𝑏 −2 𝑎−1
3
3
(b) √𝑎−3 𝑏−1 + √8𝑎−2 𝑏2
1
(c)
(d)
5𝑎 2 1
(6 ∗ 5 ) ( )
6
𝑎
3−1 𝑎 0.5
271⁄3 𝑏 1⁄3
÷
51⁄2 𝑏2
−2𝑎𝑏−1⁄4
−𝑎
4. Write in the simplest form and rationalize the denominator wherever possible.
(a) √1 + 4𝑥 + 4𝑥 2
(b) √28 + √36 + 27 − √73
2√12−3
6−√3
+
√12+4
√3−4
√3−2
(d)
√3+2
2𝑥−4
𝑥+11
Solve 7 = 9
(c)
5.
6. If 15 gold bars cost 60,000 dollars, how much do six bars cost?
7. Percentages
(a) Calculate 150 percent of 150.
(b) What is 12 percent of 120?
8. Reduce the simplest form
(a)
(b)
𝑎𝑏−𝑏2 𝑎 2 +2𝑎𝑏+𝑏2
∗
𝑎−𝑏
𝑎 2 −𝑏 2
2
√4𝑥 −12𝑥𝑦+9𝑦 2
9𝑥 2 −𝑦 2
×
2
2
2
12𝑥 −14𝑥𝑦−6𝑦
4𝑥 −4𝑥𝑦+𝑦 2
9. Multiply the polynomials and determine the degree 𝑓(𝑥, 𝑦) = (2𝑥 2 + 𝑦)(𝑥 3 + 𝑦 2 ).
10. Factor the expressions below
(a) 𝑏 2 − 13𝑏𝑐 + 36𝑐 2
(b) 15𝑥 2 − 95𝑥 + 100
(c) 16𝑥 2 + 24𝑥 + 9
(d) 12𝑚4 + 8𝑚2 − 15
(e) 𝑎2 + 6𝑎𝑏 + 9𝑏 2 − 16
11. Text book Exercise 2.2 question (B) 12.
12. Factor completely
(a) 32𝑥 5 + 8𝑥 3 𝑦 2 + 108𝑦 3 𝑥 2 − 27𝑦 5
(b) 6𝑥 5 − 30𝑥 4 − 162𝑥 2 − 324𝑥
(c) 64𝑥 6 − 1
1
QMS 110 Review questions Test 1
(d) 𝑦 6 − 𝑥 6
13. A midterm test has twenty multiple choice questions. If a student scores 72%, how many questions
were correctly answered?
14. The table below shows the number first year students at unknown college. Find the percent increase
or decrease for between years.
Year
Number of students
2017
26201
2018
27532
2019
29010
2020
25783
2021
26809
15. A balloon is inflated with a gas to 15 cubic meters. After its volume is increased by 12 %, by how
much factor does the radius increased? Assume the balloon has spherical shape. The formula for
4
the volume of sphere is 𝜋𝑟 3 , where r is the radius.
3
16. I purchased an old painting for $2000. It is expected that two years later the price of the painting
will be up by 61%. If I sale the painting what is the profit? How much will be the price at after two
years?
17. Joe bought a pizza and ate 3/8th of it. The pizza cost $16.95. Estimate the price of the pizza slices
Joe ate.
18. Compute the value of the expression
(a)
(b)
6𝑦 2 −6𝑥𝑦 2 +2𝑥𝑦
𝑥 2 −2𝑥𝑦
×
2
2
2𝑥 −4𝑥𝑦
9𝑥 −6𝑥𝑦+𝑦 2
𝑥 2 −6
𝑥 2 +4𝑥−5
2𝑥−4
( 2
∗
)∗
𝑥 −3𝑥+2 𝑥 2 +4𝑥+4
𝑥+√3
when x=1 and y=2
, x=3
19. Helen made a liter of juice. She used 315ml of pineapple, 295 ml of orange and mangos. What
percent of the juice does mango make up?
20. Three men sale a property that earned them 2.836 million. They wanted to share the amount in the
4/5:2/5:3/5 proportion. Calculate the exact amount each man receives.
21. A rectangular sheet of metal has an area of 54 cm sq. If a carpenter cuts a rectangular piece of 22%
of the sheet, what is the area of the remaining sheet?
22. Classify the following numbers into counting numbers, integers, rational, irrational numbers and
imaginary numbers.
⃛,
0.124
22 3
1
𝜋 2 13 3
56
√3
2
4
, √2.01, , 0. ⃛
1, , , √−28, , −5, −10101, 0.00, √2 − 1, √16, −52 , √−16 , 3. ⃛
7,
7
9
4 19
28
2
23. From the numbers listed in Question 22 identify repeating decimal numbers. Can you write the
𝑎
rational number in the form 𝑏 ?
𝑏
𝑐
24. For the numbers listed below write each of them in the form 𝑎 .
4 19 5 27 22 49
67 112 49 88 101
, ,− , ,− , ,−
,−
, , ,−
3 6
2 7
7 12
32
35 42 17
19
25. Perform the division shown below. Get the values of x for which the denominator is not zero.
4𝑥 4 − 35𝑥 2 + 69
𝑥2 − 3
26. Add the following.
6
7
4
+
− 2
3𝑥 − 2 6𝑥 3𝑥 − 2𝑥
27. The sum of two rational numbers is 11. The larger number is five more than 1.5 times the smaller
number. Find the difference of the squares of the numbers.
2