Mathematics Multiple Questions

There are 10 questions in total each worth one mark. This includes Question 6 (part (i) - part (iii)).

Question 1: Solve the following equation:

9 + 3 e ^{2 x + 1} = 12 − e ^{2 x + 1}

1. approximately x = 1.305
   B. approximately x = -0.644
   C. approximately x = 1.674
   D. approximately x = -0.562
2. none of the above

Choose the correct answer (A - E):

Question 2: Solve the following equation:

6 + log ⁡ ( 16 x 2 − 64 ) = log ⁡ ( 4 x + 8 ) + 8

A . x = 5.456

B . x = 3.859

C . x = 3.847

D . x = 27

1. none of the above

Choose the correct answer (A - E):

Question 3: Simplify the following to a single term

4 log ⁡ x + log ⁡ ( 1000 x ) − 3 log ⁡ ( 100 x ) ⁡

1. -3
2. -6.91
3. log(10x)
4. -2
5. none of the above

Choose the correct answer (A - E):

Question 4: Given the supply and demand functions,

P S = Q S 2 + 22 Q s + 40 and P D = − Q D 2 − 10 Q D + 200

calculate the economically meaningful equilibrium quantity

1. Q =-20 and Q = 4
2. Q = 20 and Q = -4
3. Q = 9
4. Q = 4
5. none of the above

Choose the correct answer (A - E):<

Question 5: The demand and supply functions for a good are

P d = 320 − 2 Q d and P s = 140 + 3 Q S , respectively. If the government provides a subsidy of $40 per unit sold. Outline the distribution of the subsidy, that is, calculate how much of the subsidy is received by the consumer and producer:

A: The consumer now pays $232, a decrease of $16 on the equilibrium price with no subsidy ($248) and the producer receives $272, an increase of $24 on the equilibrium price with no subsidy

1. The consumer now pays $272, an increase of $24 on the equilibrium price with no subsidy ($248) and the producer receives $232, a decrease of $16 on the equilibrium price with no subsidy
2. The consumer now pays $228, a decrease of $20 on the equilibrium price with no subsidy ($248) and the producer receives $268, an increase of $20 on the equilibrium price with no subsidy
3. The consumer now pays $264, an increase of $16 on the equilibrium price with no subsidy ($248) and the producer receives $224, a decrease of $24 on the equilibrium price with no subsidy
4. none of the above

Choose the correct answer (A - E):

Question 6

A TV manufacturer plans to increase its output by 8% each month. If it is now producing 400 TV’s per month.

(i) Calculate its monthly output for the 16th month

1. 
   approximately 722
   B. approximately 459
   C. approximately 1269
   D. approximately 1370
2. none of the above

Choose the correct answer (A - E):

(ii) Calculate the month in which its output reaches 3200

1. approximately 12th month
   B. approximately 28th month
   C. approximately 9th month
   D. approximately 27th month
2. none of the above

Choose the correct answer (A - E):

(iii) Suppose the TV manufacturer now plans to increase its output by 100 each month. If it is now producing 250 TV’s per month, calculate the month in which its total production reaches 3000

1. 6th month
2. 3rd month
3. -6th month or 10th month
4. -10th month or 6th month
5. none of the above

Choose the correct answer (A-E):

Question 7

Given the demand and supply functions for a good,

P_d = 120 – 3Q and P_s = 2Q + 25, respectively.

If a tax of $15 per unit is imposed, outline the distribution of the tax, that is, calculate the tax paid by the consumer and the producer.

1. The consumer now pays $69, an increase of $6 on the original equilibrium price with no tax ($63) while the producer now receives $54, a reduction of $9 on the original equilibrium price with no tax
2. The consumer now pays $72, an increase of $9 on the original equilibrium price with no tax ($63) while the producer now receives $57, a reduction of $6 on the original equilibrium price with no tax

C: The consumer now pays $70.50, an increase of $7.5 on the original equilibrium price with no tax ( $63) while the producer now receives $55.50, a reduction of $7.5 on the original equilibrium price with no tax

D: The consumer now pays $54, a decrease of $9 on the original equilibrium price with no tax ($63) while the producer now receives $69, an increase of $6 on the original equilibrium price with no tax

1. none of the above

Choose the correct answer (A-E):

Question 8

The sum of the first 20 terms of an arithmetic series is 280, the sum of the first 6 terms is 42. Write down the first 3 terms of the series.

1. 2, 4, 6
2. 3, 5, 8
3. 10, 8, 6
4. 4.5, 5.5, 6.5
5. none of the above

Choose the correct answer (A - E):