Tutorial of College Algebra
Tutorial 1: Review of Basic Concepts
1. Let[pic]. List the elements of A that belong to the given set.
i. Nature numbers ii. Integers iii. Rational numbers
2. Let set M =[pic]. List the elements of M that belong to the given set. i. Whole numbers ii. Integers iii. Rational numbers
3. Multiply out the brackets: a) 7(x + 2y) – 2(3y – 5x) (b) 2x2 + y – z2 – 2(3x2 + 2y – z)
(c) (2x – 5)(5 + 2x) (d) (9y - 8)(3y - 3)
4. Evaluate the following without using a calculator. (a) [pic]=
(b) [pic]=
(c) 8[pic]+[pic] = (d) 1[pic] = (e) 4[pic] =
5. Find expressions for the following algebraic functions, simplify the answers as far as possible. a) [pic] = b) [pic] = (c) [pic] = (d) [pic] =
6. Factor completely: x2 + 3xy – 154y2 =
7. Factor out the greatest common factor: 36x9y9 – 27x7y7 + 90x4y3
8. Simplify the complex function.
a). [pic] =
b). [pic]
c) [pic]=
d) [pic]=
9. A manufacturer's cost is given by C = 400 [pic] + 200, where C is the cost and n is the number of parts produced. Find the cost when 512 parts are produced.
10. Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 9 mi, the distance between the cars was 3 mi more than the distance traveled by the car heading east. How far had the eastbound car traveled?
Tutorial 2: Equations and Inequalities
1. Solve the following inequalities: a) [pic] > [pic] b) [pic] (c) [pic]
2. One solution is 30% acid and another is 10% acid. How many cubic centimetres of each should be mixed to obtain 100cc of a solution that is 18% acid?
3. Kelly fisher has a total of $30,000 invested in two municipal bonds that have yields of 8% and 10% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $2640, how much does she have invested in each bond?
4. Kafka Inc. imports hard drives and sells them on
1. Let[pic]. List the elements of A that belong to the given set.
i. Nature numbers ii. Integers iii. Rational numbers
2. Let set M =[pic]. List the elements of M that belong to the given set. i. Whole numbers ii. Integers iii. Rational numbers
3. Multiply out the brackets: a) 7(x + 2y) – 2(3y – 5x) (b) 2x2 + y – z2 – 2(3x2 + 2y – z)
(c) (2x – 5)(5 + 2x) (d) (9y - 8)(3y - 3)
4. Evaluate the following without using a calculator. (a) [pic]=
(b) [pic]=
(c) 8[pic]+[pic] = (d) 1[pic] = (e) 4[pic] =
5. Find expressions for the following algebraic functions, simplify the answers as far as possible. a) [pic] = b) [pic] = (c) [pic] = (d) [pic] =
6. Factor completely: x2 + 3xy – 154y2 =
7. Factor out the greatest common factor: 36x9y9 – 27x7y7 + 90x4y3
8. Simplify the complex function.
a). [pic] =
b). [pic]
c) [pic]=
d) [pic]=
9. A manufacturer's cost is given by C = 400 [pic] + 200, where C is the cost and n is the number of parts produced. Find the cost when 512 parts are produced.
10. Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 9 mi, the distance between the cars was 3 mi more than the distance traveled by the car heading east. How far had the eastbound car traveled?
Tutorial 2: Equations and Inequalities
1. Solve the following inequalities: a) [pic] > [pic] b) [pic] (c) [pic]
2. One solution is 30% acid and another is 10% acid. How many cubic centimetres of each should be mixed to obtain 100cc of a solution that is 18% acid?
3. Kelly fisher has a total of $30,000 invested in two municipal bonds that have yields of 8% and 10% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $2640, how much does she have invested in each bond?
4. Kafka Inc. imports hard drives and sells them on