# Practice Test 2

1.) $18-(-5)+2\cdot(-6)$

2.) If $\frac{3}{5}+\frac{1}{6}-\frac{1}{2}\;$ is simplified and reduced to the lowest terms, what is the denominator of the resulting fraction?

3.) $(\frac{3}{2}\div\frac{3}{5})-(\frac{5}{6}\cdot\frac{1}{3})=?$

4.) Half of a class got A’s on a test. Of the students that got A’s of the test, $\frac{3}{5}\;$ of them have A’s in the class. What percent of the class got an A on the test and has an A in the class?

5.) A man buys $3.45\;$ pounds of apples, $2.74\;$ pounds of bananas, and $\frac{11}{5}\;$ pounds of oranges. How many pounds of fruit has he bought?

6.) Jessica earns $22.50/hour, but she earns 1.5 times that for any overtime hours she works. This week Jessica worked 40 regular hours and 15 overtime hours. How much money did she earn? 7.) Convert the product $3,500\cdot10,000\;$ into scientific notation. 8.) Convert $4<\sqrt{x}<7\;$ into an equivalent expression without the radical. 9.) What value of x solves the proportion $\frac{10}{x}=\frac{5}{4}\;?$ 10.) It takes a man 27 minutes to jog x miles. At the same speed the man jogs 7 miles in 63 minutes. Find x. 11.) What is 25% of 80% of 200? 12.) A group of 12 sits down at a restaurant. Four people order soda, five order water, and three order wine. What percentage of the group ordered non-alcoholic beverages? 13.) The mean grade point average (GPA) in a class of 24 is 3.10. By how much will the average GPA of the class increase if one student with a GPA of 3.60 is added? 14.) A data set consists of the numbers 8,13,9, and x. If the average is 10, what is the median? 15.) If $x=-2$, what is the value of $(x^{2}-1)(x-3)\;?$ 16.) A person’s maximum heart rate (MHR) is equal to 220 minus their age in years. Different people have different resting heart rates (RHR), which depend on many factors. Weekly exercise that elevates your heart rate to is recommended to maintain cardiovascular health. One suggested training heart rate (THR) is given by the formula: $THR=RHR+0.75(MHR-RHR)$ Based on this formula, at what THR should a 36 year old with a resting heart rate of 60 beats per minute exercise? 17.) Your expected outcome (E) from a bet is represented by the equation: $E=p_{w}\cdot w-p_{l}\cdot l$ Where $p_{w}\;$ is the probability of winning, $p_{l}\;$ is the probability of losing, $w\;$ is the payout for a win, and $l\;$ is the payment for a loss. You enter into a bet where you must pay$50 if you lose, but you get \$100 if you win. The probability of winning is 25%, and the probability of losing is 75%. What is your expected outcome from this bet?

18.) A rocket travelled for 2 hours at a speed of 1200 mph and then for x hours at a speed of 900 mph. If the average speed of the flight was 1140 mph, then what is x?

19.) Expand the factored polynomial: $(2a+b)(a-3b)$.

20.) Add and combine like terms: $3x^{2}y^{2}+x^{2}y-4xy^{2}-2xy + 2(x^{2}y^{2}-3x^{2}y-xy^{2}+4xy)$.

21.) Factor the polynomial $x^{2}-14x+49$.

22.) If $x-5=-3(1-x)$, then $x=?$

23.) Factor the polynomial $x(x+3)+2$.

24.) Solve for x: $\frac{5}{3}+\frac{1}{2}=x+\frac{5}{6}$.

25.) For non-zero values of a,b, and c, simplify the expression:

$\frac{(2a)^{3}b^{7}c^{5}}{(2a^{4}bc^{2})^{2}}$

26.) For non-zero values of x, y, and z simplify the expression:

$\sqrt[3]{27x^{6}y^{2}z^{3}}$

27.) For all x>0 and y>0, rationalize the denominator of the expression:

$\frac{4\sqrt{x}}{3\sqrt{x}+3\sqrt{y}}$

28.) For all $x\neq4$, simplify the expression:

$\frac{x^{2}-10x+24}{x-4}$

29.) What is the slope of the line perpendicular to $2x-3y+4=0\;?$

30.) What is the equation of the line that passes through the points $(0,1)\;\text{and}\;(2,7)\;?$