Practice Test 1

1.) $8-15/3+1=?$

2.) In Atlanta, GA the record low temperature is $-9^{\circ}\text{F}\;$ and the record high is $105^{\circ}\text{F}$. What is the temperature difference between these records?

3.) $\frac{1}{2}+\frac{2}{3}-\frac{3}{4}=?$

4.) Mikkel bakes a pie. He then eats $\frac{1}{3}\;$ of the pie and puts the rest in the fridge. The next day he and his friends eat $\frac{3}{4}\;$ of what is left of the pie. What amount of the original pie is still leftover?

5.) $\frac{4}{5}\div\frac{2}{3}-\frac{7}{10}=?$

6.) Alan works for 4.6 hours at $4.75/hour. During this time he also makes$82.63 in tips. How much money has Alan earned?

7.) In April 2010, the population of India was estimated at 1.18 billion. Express this number in scientific notation.

8.) Simplify: $\sqrt{3^{4}}$.

9.) What value of $x\;$ solves the proportion $\frac{x}{9}=\frac{5}{15}\;?$

10.) If 9 sweet potatoes costs \$6.75, how much do 5 sweet potatoes cost?

11.) 22,000 people voted in an election where the winning candidate won with 54% of the votes. How many votes did the winning candidate receive?

12.) 60% of the students in a college class are over 25 years old. Of the remain students, 50% are younger than 21. What percentage of the students are between 21 and 25?

13.) Four people are in a room. If you add up all of their ages and divide this number by 10 you get 14.8. What is the average age of the people in the room?

14.) A total of 40 math and physics majors were given a test. The average score of the 15 physics majors was 66. The average score of the 25 math majors was 62. What was the average score of the entire group?

15.) If $x=4$, what is the value of $\frac{x^{3}+1}{x+1}$?

16.) If $a=1,\;b=-2,\;\text{and}\;c=5$, what is the value of $\frac{(c-a)^{2}-b}{bc-2a}\;?$

17.) In a certain ecosystem the population of sheep (s) is 15% greater than 500 minus the population of wolves (w). Express s in terms of w.

18.) One student scored 1 on a test, two scored 2, three scored 3, four scored 4, and x scored 5. If the average score was 3.75, what is x?

19.) What is the sum of the polynomials $4a^{2}b^{2}-3a^{2}b+ab\;$ and $ab+a^{2}b+5ab^{2}-3a^{2}b^{2}\;?$

20.) If $5x+1=2(x-4)$, then $x=?$

21.) Factor the polynomial $x^{2}-6x+8$.

22.) If $\frac{1}{3}x-\frac{1}{2}=\frac{1}{4}$. then $x=?$

23.) For nonzero values of x, y, and z, $\frac{-2x^{3}y^{2}z}{6x(yz)^{6}}=?$

24.) For all $x\neq-1$, simplify the expression $\frac{x^{2}+6x+5}{x+1}$.

25.) For $x,y\;> 0$, rationalize the denominator of $\frac{-\sqrt{x}}{2\sqrt{x}-\sqrt{y}}$.

26.) For all x values in the domain, simplify the expression $\frac{16-x^{2}}{x^{2}+9x+20}$.

27.) What is the y-intercept of the line with the equation $3x+2y+6=0\;?$

28.) Carlos has worked at a company five years longer than Katie. Katie has worked at the company half the time of Carlos. How long have the both worked at the company for?

29.) At what point do the lines $y=2x-1\;$ and $x+y=5\;$ intersect?

30.) What is equation of the line parallel to $y=\frac{1}{2}x\;$ that passes through the point $(2,2)\;?$