Mathematics Grade 12th 2018 Unit One

A person is scheduled to get a raise of Birr 250 every 6 months during his/her first 5 years on the job.If their starting salary is Birr 25,250 per year what will his/her annual salary be at the end of the 3rd year?

• 26750 ETB

• 25250ETB

• 2400ETB

• 18370ETB

Answer explanation

After 3 years, there are 6 raises (one every 6 months). Each raise is Birr 250, totaling 1500 Birr. Adding this to the starting salary of 25,250 Birr gives an annual salary of 26,750 Birr at the end of the 3rd year.

Find the 12th term of the Fibonacci's sequence {1,1,2,3,5,8,...}.

• 89

• 144

• 55

• 554

Answer explanation

The Fibonacci sequence starts with 1, 1, and each subsequent term is the sum of the two preceding ones. The 12th term is calculated as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. Thus, the 12th term is 144.

What is the 6th term of the following {3,5,7,9,11,...}

• 7

• 3

• 13

• 9

Answer explanation

The sequence {3, 5, 7, 9, 11,...} increases by 2 each time. The 6th term is 11 + 2 = 13. Therefore, the correct answer is 13.

What is the 31st term of the sequence 1,4,7,10,...?

• 91

• 3n-2

• 89

• 4n-2

Answer explanation

The sequence is an arithmetic sequence with a first term of 1 and a common difference of 3. The nth term can be calculated using the formula: a_n = 1 + (n-1) * 3. For n=31, a_31 = 1 + 90 = 91.

If the geometric progression S∞=7+7/10+7/100+7/1000+...

• 1/10

• 70/9

• 70/99

• 70/999

Answer explanation

The series is a geometric progression with first term a = 7 and common ratio r = 1/10. The sum S∞ = a / (1 - r) = 7 / (1 - 1/10) = 7 / (9/10) = 70/9. Thus, the correct answer is 70/9.

A person is scheduled to get a raise of birr 250 every 6 months during his/her first 5 years on the job. If their starting salary is birr 25,250 per year Whst will his/her annual salary be at the end of the third year?

• 26750

• 26250

• 26150

• 25250

Answer explanation

In 3 years, there are 6 raises (1 every 6 months). Each raise is birr 250, totaling birr 1,500. Adding this to the starting salary of birr 25,250 gives an annual salary of birr 26,750 at the end of the third year.

The sum of the first three terms of geometric progression is 39/10 and their the product is 1. Find the common ratio and the three terms.

• 5/2,1,3/5

• 5/2,1,2/5

• 3/5,1,5/2

• 5/7

Answer explanation

Let the terms be a, ar, ar^2. From the equations a + ar + ar^2 = 39/10 and a * ar * ar^2 = 1, we find a = 1 and r = 5/2. Thus, the terms are 5/2, 1, and 2/5, matching the correct choice.

If the nth partial sum of an arithmetic sequence {An} is 4n^2, fi d An=?

• 6n-4

• 8n-4

• 5n-6

• 8n+4

Answer explanation

The nth partial sum S_n = 4n^2. The nth term An can be found using An = S_n - S_(n-1). Calculating gives An = 4n^2 - 4(n-1)^2 = 8n - 4. Thus, the correct answer is 8n - 4.

If the nth partial sum of an arithmetic sequence {An} is 4n^2, fi d A10=?

• 66

• 88

• 76

• 77

Answer explanation

The nth partial sum S_n = 4n^2. The nth term A_n = S_n - S_{n-1}. Calculating A_{10} gives A_{10} = S_{10} - S_9 = 400 - 324 = 76. Thus, A_{10} = 76.

Convert this mixed recurring decimal 0.3171717...to fraction

• 157/495

• 17/45

• 3

• 56/45

Answer explanation

To convert 0.3171717... to a fraction, let x = 0.3171717... . Then, 1000x = 317.1717... and 10x = 3.1717... . Subtracting these gives 990x = 314, leading to x = 314/990, which simplifies to 157/495.