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Page 1 of 8
ASSIGNMENT MEMORANDUM SUBJECT
:
BUSINESS NUMERACY 101 (BN101)
ASSIGNMENT
: 1ST SEMESTER 2012
The prescribed textbooks are: Wegner, T. 2004. Basic Mathematics. 1st edn. Cape Town: Juta Zidel, D. 2010. Basic Business Calculations. Cape Town: Penguin Books Learner Guide: Units 1 to 4 Answer ALL the questions QUESTION 1
[20]
1.1 a
16 ÷ 2[8 – 3(4 – 2)] + 1 = 16 ÷ 2[8 – 3(2)] + 1 = 16 ÷ 2[8 – 6] + 1 = 16 ÷ 2[2] + 1 = 16 ÷ 4 + 1 =4+1 =5
b
4 – 3[4 –2(6 – 3)] ÷ 2 = 4 – 3[4 – 2(3)] ÷ 2 = 4 – 3[4 – 6] ÷ 2 = 4 – 3[–2] ÷ 2 =4+6÷2 =4+3 =7
Marking Memorandum: 1st Semester 2012
© IMM Graduate School of Marketing BN 101
Page 2 of 8
c
16 – 3(8 – 3)2 ÷ 5 = 16 – 3(5)2 ÷ 5 = 16 – 3(25) ÷ 5 = 16 – 75 ÷ 5 = 16 – 15 =1
d
(3+4-6/2+2) + ((9/3+6*5)/11)*((4+5-6) + (18-3*4)) (3+4-6/2+2) + ((3+6*5)/11*((4+5-6) + (18-3*4)) (3+4-6/2+2) + ((3+30)/11*((4+5-6) + (18-3*4)) (3+4-6/2+2) + (33/11*((4+5-6) + (18-3*4)) (3+4-6/2+2) + (33/11*((9-6) + (18-3*4)) (3+4-6/2+2) + (33/11*(3 + (18-3*4)) (3+4-6/2+2) + (33/11*(3 + (18-12)) (3+4-6/2+2) + (33/11*(3+6)) (3+4-6/2+2) + (33/11*9) (3+4-3+2) + (33/11*9) (7-3+2) + (33/11*9) (4+2) + (33/11*9) 6 + (33/11*9) 6 + (3*9) 6+27 =33
1.2 a
56 = 2 x 28 = 2 x 2 x 14 =2x2x2x7 =
b
270 = 2 x 135 = 2 x 3 x 45 = 2 x 3 x 3 x 15 =2x3x3x3x5 =2x
X5
Marking Memorandum: 1st Semester 2012
© IMM Graduate School of Marketing BN 101
Page 3 of 8
1.3 a
16 = 2 x 2 x 2 x 2
b
81 = 3 x 3 x 3 x 3 =
1.4 a = = = = = =
b = = = = =
=2
Marking Memorandum: 1st Semester 2012
© IMM Graduate School of Marketing BN 101
Page 4 of 8
QUESTION 2 2.1
[20]
I:S:P 63 : 52 : 45 Ian = 63/160 x 100 = 39.4% Sue = 52/160 x 100 = 32.5% Peter = 45/160 x 100 = 28.1%
2.2
(70 x R30) x 5/100 + (80 x R30) x 15/100 = 2 100 x 0.05 + 2 400 x 0.15 = 105 + 360 = R365
2.3
(1 300 – 1 024)/1 024 X 100 = 276/1024 x 100 = 26.9%
2.4
150/(1+ 0.2) = R125
2.5
(800 – 650)/800 x 100 = 150/800 x 100 = 18.8%
2.6
Girls : Boys 9:5 If X is number of boys at the zoo Then 45 : X 9:5 45 : X Cross product: 9X = 225 Therefore X = 25 boys.
Marking Memorandum: 1st Semester 2012
© IMM Graduate School of Marketing BN 101
Page 5 of 8
QUESTION 3
[40]
3.1 1.68 1.70 1.74 1.78 1.80 1.81 1.85 1.90 1.95 1.98 2.00 2.02
a. Mean = (1.68+1.70+1.74+1.78+1.80+1.81+ .85+1.90+1.95+1.98+2.00+2.02)/12 = 1.85 b. Median = (1.81 + 1.85)/2 = 1.83 c. Q1 = (1.74 + 1.78)/2 = 1.76 d Q3 = (1.98 + 1.95)/2 =1.97 e. IQR = 1.97 – 1.76 = 0.21
=
f. S =
= 0.10
Height (x)
(x -
)
(x -
)
1.68
-0.17
0.03
1.70
-0.15
0.02
1.74
-0.11
0.01
1.78
-0.07
0.00
1.8
-0.05
0.00
1.81
-0.04
0.00
1.85
0
0.00
1.90
0.05
0.00
1.95
0.1
0.01
1.98
0.13
0.02
2.00
0.15
0.02
2.02
0.17
0.03
22.21
Marking Memorandum: 1st Semester 2012
2
0.15
© IMM Graduate School of Marketing BN 101
Page 6 of 8
3.2
Rainfall (mm)
Tally
Frequency
30< to 35
6
35< to 40
13
40< to 45
10
45< to 50
7
50< to 56
4
Marking Memorandum: 1st Semester 2012
© IMM Graduate School of Marketing BN 101
Page 7 of 8
3.3 a
b.
m = 2 (change in y/change in x)
c
c = 1 (read of graph – where line intercepts y-axis)
d
y = 2x + 1
QUESTION 4
[20]
Students can use tables or calculators 4.1 Standard Bank: FV = PV
= 100 000
= 100 000 X 1.2321
= R123 210 FNB = FV = PV
= 100 000
= 100 000 x 1.2184
= R121 840 Select Standard Bank. Marking Memorandum: 1st Semester 2012
© IMM Graduate School of Marketing BN 101
Page 8 of 8
4.2 PV = PMT X Factor for annuity due Therefore PMT = PV/Factor = 150 000/8.160725 = R18 380.72 pa 4.3 FV = PV Therefore PV = FV/
= 200 000/2.158925 = R92 638.70
4.4 Option A: R200 000 Option B: PV = FV/
= R251 942.50/ 1.259712 = R200 000
Option C: PV = FV/
= R242 000/ 1.166400 = R207 476
Select option c.
Marking Memorandum: 1st Semester 2012
© IMM Graduate School of Marketing BN 101
ASSIGNMENT MEMORANDUM SUBJECT
:
BUSINESS NUMERACY 101 (BN101)
ASSIGNMENT
: 1ST SEMESTER 2012
The prescribed textbooks are: Wegner, T. 2004. Basic Mathematics. 1st edn. Cape Town: Juta Zidel, D. 2010. Basic Business Calculations. Cape Town: Penguin Books Learner Guide: Units 1 to 4 Answer ALL the questions QUESTION 1
[20]
1.1 a
16 ÷ 2[8 – 3(4 – 2)] + 1 = 16 ÷ 2[8 – 3(2)] + 1 = 16 ÷ 2[8 – 6] + 1 = 16 ÷ 2[2] + 1 = 16 ÷ 4 + 1 =4+1 =5
b
4 – 3[4 –2(6 – 3)] ÷ 2 = 4 – 3[4 – 2(3)] ÷ 2 = 4 – 3[4 – 6] ÷ 2 = 4 – 3[–2] ÷ 2 =4+6÷2 =4+3 =7
Marking Memorandum: 1st Semester 2012
© IMM Graduate School of Marketing BN 101
Page 2 of 8
c
16 – 3(8 – 3)2 ÷ 5 = 16 – 3(5)2 ÷ 5 = 16 – 3(25) ÷ 5 = 16 – 75 ÷ 5 = 16 – 15 =1
d
(3+4-6/2+2) + ((9/3+6*5)/11)*((4+5-6) + (18-3*4)) (3+4-6/2+2) + ((3+6*5)/11*((4+5-6) + (18-3*4)) (3+4-6/2+2) + ((3+30)/11*((4+5-6) + (18-3*4)) (3+4-6/2+2) + (33/11*((4+5-6) + (18-3*4)) (3+4-6/2+2) + (33/11*((9-6) + (18-3*4)) (3+4-6/2+2) + (33/11*(3 + (18-3*4)) (3+4-6/2+2) + (33/11*(3 + (18-12)) (3+4-6/2+2) + (33/11*(3+6)) (3+4-6/2+2) + (33/11*9) (3+4-3+2) + (33/11*9) (7-3+2) + (33/11*9) (4+2) + (33/11*9) 6 + (33/11*9) 6 + (3*9) 6+27 =33
1.2 a
56 = 2 x 28 = 2 x 2 x 14 =2x2x2x7 =
b
270 = 2 x 135 = 2 x 3 x 45 = 2 x 3 x 3 x 15 =2x3x3x3x5 =2x
X5
Marking Memorandum: 1st Semester 2012
© IMM Graduate School of Marketing BN 101
Page 3 of 8
1.3 a
16 = 2 x 2 x 2 x 2
b
81 = 3 x 3 x 3 x 3 =
1.4 a = = = = = =
b = = = = =
=2
Marking Memorandum: 1st Semester 2012
© IMM Graduate School of Marketing BN 101
Page 4 of 8
QUESTION 2 2.1
[20]
I:S:P 63 : 52 : 45 Ian = 63/160 x 100 = 39.4% Sue = 52/160 x 100 = 32.5% Peter = 45/160 x 100 = 28.1%
2.2
(70 x R30) x 5/100 + (80 x R30) x 15/100 = 2 100 x 0.05 + 2 400 x 0.15 = 105 + 360 = R365
2.3
(1 300 – 1 024)/1 024 X 100 = 276/1024 x 100 = 26.9%
2.4
150/(1+ 0.2) = R125
2.5
(800 – 650)/800 x 100 = 150/800 x 100 = 18.8%
2.6
Girls : Boys 9:5 If X is number of boys at the zoo Then 45 : X 9:5 45 : X Cross product: 9X = 225 Therefore X = 25 boys.
Marking Memorandum: 1st Semester 2012
© IMM Graduate School of Marketing BN 101
Page 5 of 8
QUESTION 3
[40]
3.1 1.68 1.70 1.74 1.78 1.80 1.81 1.85 1.90 1.95 1.98 2.00 2.02
a. Mean = (1.68+1.70+1.74+1.78+1.80+1.81+ .85+1.90+1.95+1.98+2.00+2.02)/12 = 1.85 b. Median = (1.81 + 1.85)/2 = 1.83 c. Q1 = (1.74 + 1.78)/2 = 1.76 d Q3 = (1.98 + 1.95)/2 =1.97 e. IQR = 1.97 – 1.76 = 0.21
=
f. S =
= 0.10
Height (x)
(x -
)
(x -
)
1.68
-0.17
0.03
1.70
-0.15
0.02
1.74
-0.11
0.01
1.78
-0.07
0.00
1.8
-0.05
0.00
1.81
-0.04
0.00
1.85
0
0.00
1.90
0.05
0.00
1.95
0.1
0.01
1.98
0.13
0.02
2.00
0.15
0.02
2.02
0.17
0.03
22.21
Marking Memorandum: 1st Semester 2012
2
0.15
© IMM Graduate School of Marketing BN 101
Page 6 of 8
3.2
Rainfall (mm)
Tally
Frequency
30< to 35
6
35< to 40
13
40< to 45
10
45< to 50
7
50< to 56
4
Marking Memorandum: 1st Semester 2012
© IMM Graduate School of Marketing BN 101
Page 7 of 8
3.3 a
b.
m = 2 (change in y/change in x)
c
c = 1 (read of graph – where line intercepts y-axis)
d
y = 2x + 1
QUESTION 4
[20]
Students can use tables or calculators 4.1 Standard Bank: FV = PV
= 100 000
= 100 000 X 1.2321
= R123 210 FNB = FV = PV
= 100 000
= 100 000 x 1.2184
= R121 840 Select Standard Bank. Marking Memorandum: 1st Semester 2012
© IMM Graduate School of Marketing BN 101
Page 8 of 8
4.2 PV = PMT X Factor for annuity due Therefore PMT = PV/Factor = 150 000/8.160725 = R18 380.72 pa 4.3 FV = PV Therefore PV = FV/
= 200 000/2.158925 = R92 638.70
4.4 Option A: R200 000 Option B: PV = FV/
= R251 942.50/ 1.259712 = R200 000
Option C: PV = FV/
= R242 000/ 1.166400 = R207 476
Select option c.
Marking Memorandum: 1st Semester 2012
© IMM Graduate School of Marketing BN 101
