In the circle shown below, C is the center and lies on segments \(\overline{AE}\) and \(\overline{BF}\). Which of the following statements is NOT true?

Solution
The statement that CF is congruent to EF is not true because CEF is an isosceles triangle in which CE and CF are equal. Since the triangle is isosceles, ∠CFE is congruent to ∠CEF, and they have measure 70◦. In a triangle, the length of a side is proportional to the measure of the angle opposite it. Since the measure of the angle opposite EF is only 40◦ while the measure of the angle opposite CF is 70◦, EF must be shorter than CF.
What are the values for a that satisfy the equation (a + y)(a + z) = 0?

Solution
In order for the expression (a + y)(a + z) to equal zero, either a + y = 0 or a + z = 0. Thus either a = −y or a = −z.

Solution
The absolute value of any number is nonnegative. Since  − 3 = 3, the value of \(\frac{6}{\left  3 \right }=\frac{6}{3}\), or −2.
A system of linear equations is shown below.
4y = 3x + 12
−4y = −3x − 8
Which of the following describes the graph of this system of linear equations in the standard (x, y) coordinate plane?

Solution
To see the properties of each linear equation more clearly, convert each to slopeintercept form (y = mx + b, where m is the slope and b is the yintercept). The equation 4y = 3x + 12 becomes y = \(\frac{3x}{4}\) + 3 after you divide by 4. The equation −4y = −3x−8 becomes y = \(\frac{3x}{4}\) + 2 after you divide by −4. It is now clear that the equations are lines with slope ^{3}⁄_{4}, making them parallel lines with positive slope. However,since they have different yintercepts, they are two distinct lines.
If x^{2} = 36 and y^{2} = 81, which of the following CANNOT be the value of x + y?

Solution
If x^{2} = 36 and y^{2} = 81, then x = ±6 and y = ±9. There are then 4 possible combinations of x + y: 6 + 9, −6 + 9, 6 + (−9), and −6 + (−9), which have values 15, 3, −3, and −15, respectively. Therefore, the value of x + y
cannot be 0.
A survey is conducted among 700 highschool students to see who their favorite college basketball teams are. If 250 students like the Hawks, 200 students like the Vikings, 50 students like the Bears, and the remaining students like the Warriors, approximately what percentage of the 700 high school students answered that the Warriors were their favorite team? (round to the nearest tenth of a percentage point)

Solution
Which of the following is a value of n that satisfies log_{n}64 = 2?

Solution
Logarithms are used to indicate exponents of certain numbers called bases. By definition, log_{a}b = c, if a^{c} = b. Therefore, log_{n} 64 = 2 implies that 64 = n^{2}. Thus n = 8.
Reduce\(\frac{x^{8}y^{12}}{x^{4}y^{3}z^{2}}\)to its simplest terms.

Solution
In the standard (x, y) coordinate plane, if a square has the vertices (−2,−3), (2,−3), and (2,1), what is the set of coordinates for the final vertex?

Solution
To solve this problem it might be helpful to draw a picture like the one below.
Since the figure is a square, the placement of the missing point becomes clear: the upper left corner. The point will share the same xcoordinate as (−2,−2) and the same ycoordinate as (2,1), making its coordinates (−2,1).
Which of the following is the product of (3x^{2} − 1)(x^{2} − 4)?

Solution
To solve this problem, distribute using the FOIL method, as follows:
(3x^{2} − 1)(x^{2} − 4)
First: 3x^{4}
Outside: −12x^{2}
Inside: −x^{2}
Last: 4
Combine like terms and simplify to get 3x^{4} − 13x^{2} + 4.