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Introduction to Basic Mathematics Part2
Midterm tests
1.
1. (10 points) Give the exact value of
.
2. (10 points) Perform the indicated operations and express the final result in the simplest form:
.
3. (10 points) Simplify the following expression:
.
4. (10 points) Let x+y+z=0. Prove that the following equality holds for all non-zero values of x, y and z:
.
5. (10 points) Solve the following equation:
.
2.
1. (10 points) Give the exact value of
.
2. (10 points) Perform the indicated operations and express the final result in the simplest form:
.
3. (10 points) Simplify: .
4. (10 points) Graph the following function and give its inverse function where
, x ˃ -7 .
5. (10 points) Give the domain and the zeros of the following function:
.
3.
1. (10 points)=?
2. (10 points) Express the final result in the simplest form:
.
3. (10 points) Simplify: .
4. (10 points) Graph the following function and give the inverse function where
, x ˃ 3 .
5. (10 points) Give the domain and zeros of the following function:
.
4.
1. (10 points)
2. (10 points) Simplify: .
3. (10 points) Express the final result in the simplest form:
.
4. (10 points) Let and . Find , and .
5. (10 points) Give the domain and zeros of .
5.
1. (10 points) =?
2. (10 points) Simplify: .
3. (10 points) Simplify: .
4. (10 points) Find the domain and zeros of .
5. (10 points) Strawberries go bad quickly, hence the local grocery discounts them first by 30%, then again 20%. What would have been the original prices of a kilogram of strawberries, if we got it for 700 forints after two discounts?
6.
1. (10 points) Solve the equation over the set of real numbers:
.
2. (10 points) Solve the inequality over the set of real numbers:
.
3. (10 points) Solve the equation over the set of real numbers:
.
4. (10 points) Solve the equation over the set of real numbers:
.
5. (10 points) Three numbers form a geometric sequence. The product of the numbers is -8 and the sum of the numbers is 3. Find the sequence.
7.
1. (10 points) Solve the equation over the set of real numbers:
.
2. (10 points) Solve the inequality over the set of real numbers:
.
3. (10 points) Solve the equation over the set of real numbers:
.
4. (10 points) Solve the equation over the set of real numbers:
.
5. (10 points) Three numbers form a geometric sequence. The product of the numbers is -27 and the sum of the numbers is 7. Find the sequence.
8.
1. (10 points) Solve the inequality over the set of real numbers:
.
2. (10 points) Solve the equation over the set of real numbers:
.
3. (10 points) Solve the equation over the set of real numbers:
.
4. (10 points) Solve the equation over the set of real numbers:
.
5. (10 points) The sum of the first three terms of e geometric sequence is -7, the product of the first term and the third term is 9. Give the first three terms of the sequence.
9.
1. (10 points) Solve the inequality over the set of real numbers:
.
2. (10 points) Solve the equation over the set of real numbers:
.
3. (10 points) Solve the equation over the set of real numbers:
.
4. (10 points) Solve the equation over the set of real numbers:
.
5. (10 points) The sum of the first five terms of an arithmetic sequence is 10. The first term, the third term and the fourth term form the first three terms of a geometric sequence. Find the first term, the difference and the ratio.
10.
1. (10 points) Solve the inequality over the set of real numbers:
.
2. (10 points) Solve the equation over the set of real numbers:
.
3. (10 points) Solve the equation over the set of real numbers:
.
4. (10 points) Solve the equation over the set of real numbers:
.
5. (10 points) The sum of the first three terms of a geometric sequence is 21. If we add 5 to the first one and subtract 14 from the third one, then we get three consecutive terms of an arithmetic sequence. What is the geometric sequence?