Math 1051, Exam 1
|1. You earned ____ points out of 10.||Ans: Area ≈24.28ft2|
| Calculate the area of the shape shown.
Round your answer to two decimal places .
We have three shapes: A half circle, a rectangle, and a triangle.
Calculate the area of each and add them up.
The diameter is 4 feet so the radius is 2 feet.
The total area is the sum:
|2. You earned ____ points out of 10.||Ans: Quotient = 2x2+ 6x +16|
|Find the quotient and the remainder of||Ans: Remainder = 52|
2x3 -2x + 4 divided by x - 3
|3. You earned ____ points out of 10.||Ans:4(2x -1)(3x + 2)|
|Factor: 24x2+ 4x - 8
First, factor out the greatest common factor, which is 4:
Now, find two integers whose product is 6 • (-2) = !12 and whose sum is 1.Whole number pairs whose product is 12 are 1 • 12, 2 • 6, and 3 • 4. The pair that adds or
subtracts to give 1 is 3 and 4. Adjusting for the signs (the product is negative and the sum is
positive) we will replace the middle term, x, with –3x + 4x and then factor by grouping.
|4.You earned ____ points out of 10.||Ans:|
|Perform the indicated operations and simplify:
Factor each denominator and form the LCD:
Now, convert each given fraction into an equivalent fraction but with the LCD in the denominator:
We need to see if the numerator can be factored.
If it can, we may be able to reduce.
|5. You earned ____ points out of 10.||Ans: x = 10|
Clear the fractions by multiplying each term by the LCD of all the terms. Then, solve as usual.
|6. You earned ____ points out of 10.||Ans: 6|
Follow the order of operations for simplifying
|7. You earned ____ points out of 10.||Ans: 35 pounds|
|A store sells peanuts for $1.20 per pound and
cashews for $3.40 per pound. How many pounds of
peanuts should be mixed with 20 pounds of cashews so that the mixture should sell for $2.00 per
pound? Be sure to define your variables, clearly write the equation, and be careful solving it! Using
our 9 step process would be a really good idea.
1. Read the problem several times carefully until you fully understand it.
2. Draw a diagram if appropriate.
3. Identify any formulas you might need (e.g., area, perimeter, simple interest).
4. Assign a variable to represent what you are looking for.
x = number of pounds of peanuts
5. Express any other unknown quantities in terms of your variable .
20 + x = # pounds of mix
6. Write an equation that models a relationship between your expressions.
We have a relationship between the values of the nuts:
Value of peanuts +Value of cashews =Value of nuts
7. Solve the equation.
8. Write the final answer, including units.
|8. You earned ____ points out of 10.||Ans:|
Write your final answer using
positive exponents only.
Use the laws of exponents to combine the common factors: