• A useful relation in many CS contexts is that, for $$n \ge 0$$, \[\sum_{i=0}^n i = \frac{n(n+1)}{2}.\] \[a=b+c\]

  111

• This is another test problem \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

  118

• \(x\),\(y\) are real numbers. \[4x+\left(3y+4\right)i=21+7i\] Evaluate \(y\).

  121

• if \(x\) and \(y\) are real numbers, and \[3x+y+\left(2x+2y\right)i=13+10i\], what is \(z\) if \(z=x-4y\) ?

  126

• Solve for \(x\) if \(x=4\left(i^2+3\right)\) .

  137

• Evaluate and simplify \[\left(i+3\right)^2\]

  142

• Solve for \(z\ \) \[\left(6+3i\right)^2=4i-30z\]

  147

• An anthropologist studies a woman's femur that was uncovered in Madagascar. To estimate the woman's height, he uses the equation \(h=60+2.5f\) where \(h\) represents height in centimeters and \(f\) epresents length of the femur in centimeters. Which inequality best represents the lengths of the femur that would suggest the woman had a height greater than 160 cm.

  156

• As Marta built a square fence around her garden, she wondered how much she would have to pay if she increased the length of each side of the fence by the same number of meters. Each meter of fence costs 3 dollars. Which of the following functions best describes the additional amount of money Marta will have to spend, in dollars, if she increases each side of the fence by \(m\) meters?

  161

• Deniz had a full gallon of milk. She poured out 4 cups of milk. There are 16 cups in 1 gallon. About what percent of the original volume is left?

  166

• Joelle plans to sell two types of balloons at her charity event: 17-inch latex balloons that require 2 cubic feet \(\left(ft^3\right)\) of helium and 18-inch mylar balloons that require only \(0.5ft^3\). She only has access to \(1,000ft^3\) of helium, \(15\%\) of which will be unused due to pressure loss in the tanks. She wants to have at least 500 balloons for sale in total. For the number of latex balloons, \(L\), and number of mylar balloons, \(M\), which of the following systems of inequalities best represents this situation?

  172

• \[11i^{11}\] Which of the following is equivalent to the complex number shown above? Note: \(i=\sqrt{-1}\)

  177

• Square \(ABCD\) shown to the left is composed of several triangles. What is the value of \(t^{\circ}\) ?

  182

• The sector of a circle shown to the left has its center at point \(O\). The arc \(XYZ\) has length 10.8, and the central angle\(XOZ\) has measure 1.8 radians. What is the radius length,\(r\), of the sector?

  188

• Which of the following is the value of \(\cos\left(180^{\circ}\right)\)?

  194

• \[P=45,000 - 1,000m\] People start to leave the stadium at the end of a football game. The number of people, \(P\), that are left in the stadium \(m\) minutes after the end of the game is given by the equation above. How many people were present when the game ended but before people started to leave?

  199

• If the equation \(y=\frac{1}{6}\left(x+12\right)\) were graphed in the \(xy\)-plane. which of the following statements would be true of the graphed line?

  204

• The angle \(\theta\) is located in Quadrant III, and \(\cos\left(\theta\right)=-\frac{5}{8}\). Which of the following is most close to the values of \(\sin\left(\theta\right)\)?

  217

• The angle \(\theta\) is located in Quadrant II, and \(\cos\left(\theta\right)=-\frac{2}{11}\). Which of the following is most close to the values of \(\sin\left(\theta\right)\)?

  222

• \[3\frac{1}{5}+5\frac{1}{3}=\]

  229

• It takes Julia \(\frac{1}{2}\) hour to wash, comb her hair and put on her clothes, and \(\frac{1}{4}\) hour to have her breakfast. How much time does it take Julia to be ready for school?

  234

• Billy ate \(1\frac{1}{4}\) pizzas and John ate \(1\frac{2}{3}\) pizzas. How much more pizza did John eat than Billy?

  239

• Tina works 15 hours a week (Monday to Friday). Last week she worked \(3\frac{1}{2}\) hours on Monday, 4 hours on Tuesday, \(2\frac{1}{6}\) hours on Wednesday and \(1\frac{1}{2}\) on Thursday. How many hours did she work on Friday?

  244

• Order from least to greatest the fractions \(\frac{3}{5}\) , \(\frac{7}{6}\), \(\frac{1}{3}\), \(\frac{4}{9}\).

  249