Math 1051
Math 1051, Exam 1
1. You earned ____ points out of 10.  Ans: Area ≈24.28ft^{2} 
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. Circle: The diameter is 4 feet so the radius is 2 feet.
Rectangle: Triangle:
The total area is the sum: 

2. You earned ____ points out of 10.  Ans: Quotient = 2x^{2}+ 6x +16 
Find the quotient and the remainder of  Ans: Remainder = 52 
2x^{3} 2x + 4 divided by x  3 

3. You earned ____ points out of 10.  Ans:4(2x 1)(3x + 2) 
Factor: 24x^{2}+ 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 orsubtracts 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 
Solve: 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 
Simplify completely:
Follow the order of operations for simplifying
arithmetic expressions: 

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: 
Simplify completely:
Write your final answer using
positive exponents only. Use the laws of exponents to combine the common factors:

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