MATH 1203 Saint Marys University Mathematics Question

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Answer Key
NAME ______________
MATH 1203.2
QUIZ #5 (WINTER 2021)
ID ____________
13 pts
1. Evaluate each of the following, if possible. If not possible, give the reasons.
a). If
S11 
a1  7 and r  2, find S11 .
7  211  1
 7  2047 
2 1
 14329
c)
1
a1  729 and r  , find S8 .
3
8
 1 
729 1     729 1  1 
 3 


6561  729  3  6560 3280





S8 

1
2
2

6561
3
1
3
3
b) If
512  256  128  . . .
S 
d)
5  15  45  135  . . .
Series Diverges
 No Sum
512
512 1024


3
3
 1
1   
2
 2
10 pts
2. Evaluate each of the following.
 3 2 
12
(i).
n 1

 3  6  12  . . .
(ii)
n 1
3  2  1
12
S12 
2 1
a  r  1
n
Sn 
r 1
 3 4096  1  12285
 1
16   

 2
n1
n1
 16  8  4  2  . .
16
a
S 
1 r
 1
1   
 2
16
16 32

 
1 3
3
1
2 2
S 
13 pts
3. (i) Represent each repeating decimal as a series. (ii) Express each as a quotient (fraction) of two integers. Show
clearly.
(a).
0.45
(b)
(i) 0.45  .45  .0045  .000045  . . .
a  0.45, r 
 ii 
S 
0.0045
 0.01
0.45
a
0.45
.45


1  r 1  0.01 .99
5

11
2.063
i  2.063  2  .063  .00063  .0000063  . . .
 ii  2.063  2  S
S 
.063
1  .01
r
.00063
 .01
.063
.063 63
7


.99 990 110
7
227
 2.063  2 

110 110

Answer Key
NAME ______________
MATH 1203.2
QUIZ #6 (WINTER 20210)
ID ____________
5 pts
1. Evaluate each of the following.
150
(i).
  70 
i1
 150  70 
96
(ii)
 10500
13 p
k 7
2
 90 13 p 2 
 1170 p 2
5 pts
2. Insert
5 AMs
between
7 and 31. Show clearly.
Sequence has 7 terms a1  7, a7  a1  6d  31 7  6d  31  6d  24
 d  4
 the 5 AMs are  11,  15,  19,  23,  27
6 pts
3. Insert
3 GMs
between
5 and 80. Clearly show your work.
4
4
Sequence has five terms  a1  5, a5  a1r 4  80  5r  80  r  16
 r  2
 the 3 GMs are  10, 20,  40
3pts
S  24 and a1  36, find r. Show your work clearly.
a
36
S  1 
 24
 36  24  24r  12  24r
1 r 1 r
1
  r
2
4. If
3pts
1
S  27 and r  , find a1 . Show your work clearly.
3a
3a
a1
a
S 
 27  1  27  1  27  1  54  3a1
1
2
2  18  a
1 r
1
1
3
3
5. If
6 pts
6. Evaluate
  2   2 
8
k

k 1
1
k
 

. Clearly show your work.
 


 2   2   22   2   23   2   . . .  28   2 
1
2
3
  2  2   4  4   8  8  . . .   256  256 
8

 0  8  0  32  . . .  512  8  32  128  512
 8 1  4  16  64   8 85  680
6 pts
7. Evaluate
1
 1




n
n2  n  1
100
. Clearly show your work.
1 
 1 1 1 1 1
 1
 1            . . .   

 2  2 3  3 4
 99 100 
1  99

 1 

 100  100
1
MATHEMATICS AND COMPUTING SCIENCE
Saint Mary’s University
MATH 1203.2 MID-TERM EXAM MAY 4, 2021
NAME ______________________
ID _______________
INSTRUCTIONS:
*READ QUESTIONS CAREFULLY
*ANSWER ALL QUESTIONS. GIVE SIMPLIFIED ANSWERS
*OBEY ALL INSTRUCTIONS
*NO DECIMAL ANSWERS
*CLEARLY SHOW YOUR WORK
12 pts
1. Provide the simplified answer to each of the following.
a). State the
b) Simplify
4
nthterm of the sequence
4 7 10 13
, , , ,. . .
5 9 13 17
80t 3c7  4 81t 5c2
b) _______________
76 and 88.
d) Give the Geometric Mean (GM) of 16 and 25.
c) Give the Arithmetic Mean (AM) of
e) Express
4 x3 y 2 7 xy
as a single radical.
f) Express as a single radical
a a
2
5
(rationalize denominator)

5
2
th
h) State the n term of the sequence 3, 15, 75, . . .
g) Simplify
i) A triangle has base
48 cm and height 18 cm. , its area in simplest form is
j) Express as a single radical
3 4
a) _______________
m.
k) Insert two Arithmetic Means (AMs) between 13
and 25.
l) Insert two Geometric Means (GMs) between 6 and 48.
c) _______________
d) _______________
e) _______________
f) ________________
g) ________________
h) ________________
i) ________________
j) ________________
k) _______________
l) _______________
2
19 pts
2. (i) If
a1  2, a2  2 and ak  ak 1  ak 2 , Write the first six terms of the sequence. Be Clear.
(ii) Find the sum of all integers from
(iii) Express
(iv) Simplify
5 x 4 y 7 3 3x 2 y 2
42 to 352 that are multiples of 7.
as a single radical.
16
21  13
(v) Express as a single radical
p p p p p
Show clearly.
3
10 pts
3
18 9
27
3
3. (a). The volume of a cube is given by 512a x w cm . (i) Determine the length of an edge of the cube,
as a single radicand. (ii) Give the length in its simplest radical form.
(b) The parallel sides of a trapezoid have lengths
sides is
3 98 cm, and 3 32 cm, and the distance between the
26 cm. What is the area of the trapezoid?
Give your answer in simplest radical form.
8 pts
4. Find the value of the variable in each of the following. Clearly show your work.
(a).
(c)
3
3x  4  8
(b)
2 x  1  5
(d)
3
5x  1  4
7 x  2  9
4
9 pts
5. (i) Insert
(ii) Insert
4 AMs between 25 and 60.
Show clearly.
3 GMs between 12 and 972.
Show clearly.
10 pts
6. Evaluate each of the following. Show clearly.
72
(i).
  7k  2 
k 3
1
16  

2
i 1
10
(ii)
i 1
10 pts
7. (i) Determine the sum of the first
82 terms of the series 40  35  30  . . . . Show clearly.
5
(ii). Find the sum of the first 12
terms of the series 12  6  3  . . . .
Show clearly.
8 pts
8. Evaluate each of the following. Show clearly.
(a).
8  4  2 1  . . .

 1
(c)  27   
 3
k 1
(b) 10  30  90  . . .
k 1
12 pts
9. (i) Represent each repeating decimal as a series and (ii) write each as a quotient (fraction). Show Clearly.
(a).
0.36
(b)
2.123
a)
b)
c)
d)
e)
1. Provide the simplified answer to each of the following.
4 7 10 13
a). State the n” term of the sequence
5’9’13’17
b) Simplify 180tc • 1811°C
c) Give the Arithmetic Mean (AM) of 76 and 88.
d) Give the Geometric Mean (GM) of 16 and 25.
e) Express 4x’y? J7xy as a single radical.
f) Express as a single radical Vata
2 15
g) Simplify
(rationalize denominator)
15 12
h) State the n” term of the sequence 3, 15, 75, …
i) A triangle has base 148 cm and height V18 cm., its area in simplest form is
Express as a single radical
เปm .
k) Insert two Arithmetic Means (AMS) between 13 and 25.
1) Insert two Geometric Means (GMs) between 6 and 48.
f)
g)
h)
i)
–
j)
k)
1)
5. (i) Insert 4 AMs between 25 and 60. Show clearly.
(ii) Insert 3 GMs between 12 and 972. Show clearly.
10 pts
6. Evaluate each of the following. Show clearly.
72
10
(0) (7k-2)
(του Σ16
()”
10 pts
7. (i) Determine the sum of the first 82 terms of the series 40+35+30+…. Show clearly.
(ii). Find the sum of the first 12 terms of the series 12 +6+3+…. Show clearly.
8pts
8. Evaluate each of the following. Show clearly.
(a). 8-4+2-1+…
(b) 10+30+90+…
(c)
2
12 pts
9. (i) Represent each repeating decimal as a series and (ii) write each as a quotient (fraction). Show Clearly
(b) 2.123
(a). 0.36
3. (a). The volume of a cuhe is given by V5122′ x’w??cm. (1) determine the length of an edge of the cube,
as a single radicand. (ii) Give the length in its simplest radical form.
(b) The parallel sides of a trapezoid have lengths 3198 cm, and 31/32 cm, and the distance between the
sides is 1/26 cm. What is the area of the trapezoid? Give your answer in simplest radical form.
8 pts
4. Find the value of the variable in each of the following. Clearly show your work
13x+4=8
(b) 5x-1=4
(a). V
(12x+1 =-5
(d) V7x+2 =-9
2. (i) if a, = 2, a, = 2 and a, = 0x2 +0-2, Write the first six terms of the sequence. Be Clear.
(ii) Find the sum of all integers from 42 to 352 that are multiples of 7. Show clearly.
(i) Express 5x*y?3x’y? as a single radical.
(iv) Simplify
16
V21 – V13
(v) Express as a single radical
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