Elec 231 Electronics Applied Mathematics
Name: ___________________________________
Practice Final Exam
(Attach all scratch paper to this exam before turning it in. For full credit, be sure to clearly indicate which question is
associated with all work on your scratch paper.)
1. Write each of the following as a decimal fraction:
a) 0.082 = ____________
(0.5 pt ea)
b) 0.00314 = ______________
2. Convert to a decimal fraction then into a decimal number:
Decimal Fraction:
4 tenths =
(0.5 pt ea)
Decimal number:
______________
__________________
3. Convert the following into decimal numbers:
(0.5 pt ea)
28
465
a). 14 100 = ___________________
4. Round to the nearest: Ten
367.472 = __________
b). 9 10,000 = _____________________
Hundred
Tenths
Hundredths
(0.5 pt ea)
___________
___________
_____________
5. Perform the indicated operations. Show ALL WORK for max credit. Circle final answer.
3[ 32 ÷ (-10 +2)] + 2 x 6 =
(3 pts)
6. Convert the following numbers into scientific notation rounded to three places:
a) 0.2819 = __________
b) 783,192 = ______________
(0.5 pt ea)
7. Convert the following powers of ten numbers to a decimal fraction then a decimal number:
Decimal Fraction:
10-2 = ______________
Decimal number:
_____________________
(0.5 pt ea)
Elec 231 Electronics Applied Mathematics
Name: ___________________________________
8. Perform the indicated operations. Express your answers in powers of ten form. Show ALL WORK for
max credit. Circle final answer.
105 𝑥 10−4 𝑥 107
102 𝑥 103
=
(3 pts)
9. Using the indicated prefixes, change the following metric prefix quantities:
(0.5 pt ea)
9031 Ω = __________________ kΩ = ___________________________ MΩ
10. Perform the indicated operations. Round your final answer to three places. Show ALL WORK for max
credit. Write final answer in space provided.
(a) 652 µA + 8.44 mA =
(b)
1
1
1
+
4 𝑘Ω 5 𝑘Ω
=
____________mA = ____________uA
(4 pts)
____________ Ω = ____________kΩ
(4 pts)
11. Solve the following problems. Round to three places:
(a) 5.53 = _______________
(0.5 pt ea)
(b) 231/2 = ________________
Elec 231 Electronics Applied Mathematics
12. Solve the following problems, where x = 5,
y = 2, z = 3. Round to three places.
Circle final answer.
(a) xy3z – x2y =
(3 pts)
(b) √𝑥𝑧 − 𝑦 =
(3 pts)
Name: ___________________________________
13. In the following problems, round to three
places. Circle final answer. (4 pts)
E = IR. Find E when I = 50 µA, R = 10 kΩ.
Your final answer will be in volts (V).
14. Find the prime factors of the following:
a) 15a3b = ____________________________
(1 pt ea)
b) 3a2b3 = _______________________________
15. Find the lowest common multiple (LCM) of 15a3b and 3a2b3 .
(2 pts)
LCM = _____________________________
16. Perform the following operations.
a) (15𝑎3 b) x (3𝑎2 𝑏 3 ) =
b)
15𝑎3 b
3𝑎2 𝑏3
=
(2 pts)
(2 pts)
Elec 231 Electronics Applied Mathematics
Name: ___________________________________
17. Perform the following operations. Reduce answer to lowest terms. Circle final answer.
a)
b)
4𝑥 2 𝑦
3𝑥
6𝑥𝑦
5𝑥 2
×
÷
9𝑥 3 𝑦4
2𝑥𝑦 2
3𝑦 2
10𝑥𝑦 3
=
(3 pts)
=
(3 pts)
18. Perform the indicated operations. You can leave variables in the denominator for your final answer.
Circle final answer.
a)
b)
2y
3x
+
4
3𝑎2 𝑏3
7y
3x
−
=
2
15𝑎3 b
(3 pts)
=
(3 pts)
19. RT = R1 + R2. Find R1 if RT = 10.2 kΩ and
20. P = I2R. Find I when P = 200 mW and
R2 = 5.7 kΩ. Round to three places and enter it
R = 3.5 kΩ. Round to three places and enter it
in the blank space provided.
in the blank space provided.
R1 = ___________________Ω (5 pts)
I = ___________________mA (5 pts)
Elec 231 Electronics Applied Mathematics
21. P =
𝐸2
𝑅
. Find R if P = 250mW and E = 150 mV.
Name: ___________________________________
22. 𝑓𝑟 =
1
2𝜋√𝐿𝐶
. Find C if 𝑓𝑟 = 100 𝐻𝑧 𝑎𝑛𝑑 𝐿 =
100 𝑚𝐻.
R =____________Ω (5 pts)
23. Solve for the unknown in the following
problems. Express your answers as proper
fractions or as mixed numbers. CIRCLE final
answer. (3 pts)
4
𝐼+2
+2=5
C = ____________µF (5 pts)
24. Given V1 =
𝐸𝑅1
𝑅1 +𝑅2
.
Solve for R1 when E = 15 V, V1 = 11.1 V, and R2
= 12 kΩ. Round to three places. CIRCLE final
answer. (5 pts)
Elec 231 Electronics Applied Mathematics
Name: ___________________________________
25. Perform the indicated operation. Combine like terms. CIRCLE final answer.
(a) 2(z+8)
2pts
(c) (𝑥 + 4)(𝑥 + 2)
𝑥2
(c) 6𝑥(2𝑥 + 12𝑥 )
(b) 2b(2c+3b)
2pts
2pts
(d) (𝑎 + 2)2
2pts
3pts
(d) 4x (
1
6
−
3
4𝑥
− 3)
3pts
Elec 231 Electronics Applied Mathematics
Name: ___________________________________
26. Perform the indicated operation. Combine
like terms. CIRCLE final answer. (3 pts)
27. Perform the indicated operation. Combine
like terms. CIRCLE final answer. (4 pts)
(𝑥 5 + 6𝑥 4 + 2𝑥 3 ) ÷ 𝑥 3
(𝑎2 + 3𝑎 − 54) ÷ (𝑎 + 9)
28. Factor the following. CIRCLE final answer.
7𝑥 3 𝑦 2 − 21𝑥 2 𝑦 2
(3 pts)
29. Factor the following. CIRCLE final answer.
12𝑥𝑦 2 − 8𝑥 3 𝑦 2 + 24𝑥 2 𝑦
(3 pts)
30. Factor the following (split the middle term). CIRCLE final answer. (3 pts)
a2 +15a +56
Elec 231 Electronics Applied Mathematics
Name: ___________________________________
31. Given x2 + 16x + 9 = 0, solve for x. In other words, use the quadratic formula to find the roots. (5 pts)
32. Answer the questions below about the following
equation: 2y + 4 = x
a) What is the x-intercept? ________ (3 pts)
b) What is the y-intercept? ________ (3 pts)
c) Plot this equation on the graph (right). (4 pts)
d) What is the slope of this line? _______ (4pts)
Elec 231 Electronics Applied Mathematics
Name: ___________________________________
33. Answer the questions below about the following
equation: x + 3y = 3
a) Convert the equation into slope-intercept form.
Circle your answer. (4 pts)
b) What is the y-intercept? _________ (2 pts)
c) What is the slope of this line? _______ (2pts)
d) Plot this equation on the graph (right). (4 pts)
34. Using the following image, answer the questions below. Round answer to three places:
a) What is the length of k? _______________ ohms (3 pts)
b) What is the length of J? _______________ ohms (3 pts)
c) What is ф? __________(3 pts)
Elec 231 Electronics Applied Mathematics
Name: ___________________________________
35. Using the following image, answer the questions below. Round answer to three places:
a) What is the length of the hypotenuse? ___________________(3 pts)
b) What is ф? _______________ (3 pts)
c) What is Ѳ? ________________(3 pts)