QME5015 Microeconomics – SEMINAR 1 SOLLUTIONS
Basic Arithmetic 1
Calculate the following:
1. 16 + 8 ÷ 2.5 19.2
2. (16 + 8) ÷ 2.5 9.6
3 7 3 7 9−49 −40
3. − − = = =−1.90476 …
7 3 7 3 21 21
4. (7 x 11 x 13 x 27 x 37 + 2) ÷ 101 9901
5. 17.5% of 229 40.075
35.4
6. Express as a percentage to two decimal places. =0.446969
79.2
=44.70%
7. 8 x (7 + 6) x (5 x 4 – 3 + 2 x 1) = 8 x 13 x 19 = 1976
1 1 1 1
8. 2+ + + + = 2.71666…
2 3 ×2 4 ×3 ×2 5× 4 × 3 ×2
Basic Arithmetic 2
Calculate the following:
1. 60 x (1.0212)3 60 x (1.0212)3=122.3932
2. √6 1.34 =1.0341/6 = + or -1.049988 [lose 1 mark if only one
given]
3. (83 – 73)0.5 =√(512 – 343) = √169 = + or -13 [lose 1 mark if
only one given]
10,000
1
4. [1+ ] =2.7181459..
10,000
5. −¿ = – (1/0.25^0.25 ) = - .707107 = + or -1.41421..
[lose 1 mark if only one given]
6. √3 −39.304 = -3.4 (negative numbers do have real cube roots!)
7. (21972/3 – 17282/3)3/2 =(169 – 144)3/2 = 253/2 = + or - 53 = + or -125
[lose 1 mark if only one given]
180,000 ×0.048/12
180,000× 0.004
8. 0.048
−30× 12
= −360
=¿ 944.3976..
1−(1+ ) 1−( 1.004)
12
, Algebra and Linear equations.
1. Solve for x in the equation: 2+x = 4 : x=2
2. Solve for x in the equation: 4+x = 7 : x=3
3. Solve for x in the equation: 3x +4 = 19 : x=5
4. Solve for x in the equation: x/5 = 3 : x=15
5. Solve for x in the equation: x2 = 16 : x=4 or -4
6. Rewrite the following equation making A0 the subject:
A0r [ 1−( 1+r )−t ]
P= −t A = P
o
1−( 1+r ) r
Assuming r ≠0. Note 1 – (1+r)-t is unchanged
7. Evaluate the following expression when x=9 and y=8:
24 x2 y 24 ×81 ×8 24 ×81 81
= = =11.571428. .
7 x1 /2 y 2 7× 3 ×64 7 × 3× 8 7
Note cancelling
8. Determine the value of x in the following equation:
x 2 x−1
= 3 x=8 x−4; 5 x−4=0; x=0.8
4 3
9. Determine the value of x in the following equation:
3 3
=5 1+0.05 x= =0.6 ∴0.05 x=0.6−1=−0.4
1+ 0.05 x 5
−0.4
x= =−8
0.05
Graphs.
Q1 carries 15 marks. Q2-3 carry 3 marks each. Q4 carries 4 marks. Total 25 marks.
Basic Arithmetic 1
Calculate the following:
1. 16 + 8 ÷ 2.5 19.2
2. (16 + 8) ÷ 2.5 9.6
3 7 3 7 9−49 −40
3. − − = = =−1.90476 …
7 3 7 3 21 21
4. (7 x 11 x 13 x 27 x 37 + 2) ÷ 101 9901
5. 17.5% of 229 40.075
35.4
6. Express as a percentage to two decimal places. =0.446969
79.2
=44.70%
7. 8 x (7 + 6) x (5 x 4 – 3 + 2 x 1) = 8 x 13 x 19 = 1976
1 1 1 1
8. 2+ + + + = 2.71666…
2 3 ×2 4 ×3 ×2 5× 4 × 3 ×2
Basic Arithmetic 2
Calculate the following:
1. 60 x (1.0212)3 60 x (1.0212)3=122.3932
2. √6 1.34 =1.0341/6 = + or -1.049988 [lose 1 mark if only one
given]
3. (83 – 73)0.5 =√(512 – 343) = √169 = + or -13 [lose 1 mark if
only one given]
10,000
1
4. [1+ ] =2.7181459..
10,000
5. −¿ = – (1/0.25^0.25 ) = - .707107 = + or -1.41421..
[lose 1 mark if only one given]
6. √3 −39.304 = -3.4 (negative numbers do have real cube roots!)
7. (21972/3 – 17282/3)3/2 =(169 – 144)3/2 = 253/2 = + or - 53 = + or -125
[lose 1 mark if only one given]
180,000 ×0.048/12
180,000× 0.004
8. 0.048
−30× 12
= −360
=¿ 944.3976..
1−(1+ ) 1−( 1.004)
12
, Algebra and Linear equations.
1. Solve for x in the equation: 2+x = 4 : x=2
2. Solve for x in the equation: 4+x = 7 : x=3
3. Solve for x in the equation: 3x +4 = 19 : x=5
4. Solve for x in the equation: x/5 = 3 : x=15
5. Solve for x in the equation: x2 = 16 : x=4 or -4
6. Rewrite the following equation making A0 the subject:
A0r [ 1−( 1+r )−t ]
P= −t A = P
o
1−( 1+r ) r
Assuming r ≠0. Note 1 – (1+r)-t is unchanged
7. Evaluate the following expression when x=9 and y=8:
24 x2 y 24 ×81 ×8 24 ×81 81
= = =11.571428. .
7 x1 /2 y 2 7× 3 ×64 7 × 3× 8 7
Note cancelling
8. Determine the value of x in the following equation:
x 2 x−1
= 3 x=8 x−4; 5 x−4=0; x=0.8
4 3
9. Determine the value of x in the following equation:
3 3
=5 1+0.05 x= =0.6 ∴0.05 x=0.6−1=−0.4
1+ 0.05 x 5
−0.4
x= =−8
0.05
Graphs.
Q1 carries 15 marks. Q2-3 carry 3 marks each. Q4 carries 4 marks. Total 25 marks.
