Download Math 76 : Test 1 ( September 27, 1999 ) Name :

1
1
Math 70 : Intermediate Algebra
Test 1
Please show your work. Total 100 points.
Circle your answer.
1
Assigned Points Your score
5
2
8
3
15
4
9
5
4
6
4
7
4
8
10
9
5
10
5
11
5
12
7
13
7
14
6
15
6
Name : _______________________
Comments
Total 100
Your test score = __________________
Your course grade = ________________
Suggestion 1: We should practice more problems from the textbook.
Suggestion 2: Go to MSC to study so that you can perform better in the future exams.
1
Fall 2010
2
1. [5] A = { 12, 10, 8, 6, ...... } , B = { 4, 2, 0, 2, ..... }.
Use the set-builder notation to write A  B.
2.
Simplify [4] (i) 3x  2[ y  2( x  3[2 x  3 y ])]
[4] (ii)
1
[8 x  2( x  12)  3]
3
( Write step by step.)
3. [15]Translate the following statements into variable expressions. Then simplify if you can.
(i) The total of four times a number and twice the difference between the number and four.
(ii) Ten times the quotient of three less than a number and two more than a number.
(iii) Thirteen decreased by the product of three less than twice a number and 9.
3
(iv) The sum of two numbers is 20. Using x to represent the smaller number. Translate: the quotient of
five times the larger number and three less than the smaller number.
(v) Translate “ the square root of the quotient of the spring constant (k) and the mass (m) “ into a variable
expression.
4. [4] (a) Solve 2y  4  8y  7y  8  3y .
[5] (b) Solve
5. [4] Graph and present your answer in interval notation.
4[( x  3)  2(1  x)]
 x 1.
5
{x x  1} {x x  4}
6. [4] Write  12,  in set-builder notation.
7. [4] Graph {x x  1}  {x x  1} and write it in interval notation.
4
8.
[5] (i) Solve 6 x  1   x  3(1  x) . Write your solution in interval notation and graph it.
[5] (ii) Solve
9.
5
3
x  2   3 or 2  x   7 . Write your solution in interval notation.
8
5
[5] Solve 4x  3  2  5 .
10. [5] Solve 3x  5  11 .
Use an interval notation to present your answer.
5
11. [5] Solve 3x  2  8 use set-builder notation to present your answer.
12. [7] An investment of $12,000 is deposited into two simple interest accounts. On one account, the annual
simple interest rate is 7.8%. On the other account, the annual simple interest rate is 9%. The total interest earned
for one year is $1,020. How much was invested in each account?
Principal
@7.8%
@9%
Equation:
Present your answer:
Interest rate
Interest
6
13. [7] Company A rents cars for $15 a day and 5 cents for every mile driven. Company B rents cars for $14
per day and 6 cents for every mile driven. You want to rent a car for one week. How many miles can you drive a
company A car if it is to cost you less than a Company B car?
Let's assume the miles driven in one week is x miles.
(i) Write an expression in x for the cost of renting a Company A car : ___________________________
(ii) Write an expression in x for the cost of renting a company B car : ___________________________
(iii) Write the inequality to solve this problem and present your answer.
14. [6] The length of a rectangle is 5 cm less than twice the width. Express as an integer the maximum width of
the rectangle when the perimeter is less than 60 cm.
● First write the length in terms of the width.
● Use the width to express the perimeter.
● Setup an inequality and solve the problem.
7
15. [6] How many pounds of a 12% aluminum alloy must be mixed with 400 pounds of a 30% aluminum alloy
to make a 20% aluminum alloy?
Amount
12% alloy
30% alloy
Percent
Quantity