Math Quiz

For all nonzero values of w, which of the following expressions is equivalent to (4/w) + (2/w^2)?

• (2w + 1)/w^2

• (4w + 2)/w^2

• 6/w

• 6/w^2

• 6/w^3

Let A, B, and C represent the digits in the hundreds, tens, and ones places, respectively, of a certain 3-digit whole number. Let D, E, and F represent the digits in the hundreds, tens, and ones places, respectively, of a different 3-digit whole number. The positive difference between the 2 numbers is greater than 100. Which of the following inequalities must be true?

• |A - D| >= 1

• |B - E| >= 1

• |C - F| >= 1

• A - D >= 1

• B - E >= 1

A number line graph includes the points at real numbers a and b, as shown below. Which of the following inequalities expresses an interval that must include the product ab?

• -1 < ab < a

• a < ab < 0

• 0 < ab < b

• b < ab < 1

• 1 < ab < 2

Sani's course grade in his chemistry class is based on 3 tests and 1 final exam. Each of the 3 test scores is weighted as 20% of the course grade, and the final exam score is weighted as 40% of the course grade. Sani's 3 test scores are 78, 86, and 82, respectively. What is the minimum score that Sani will have to earn on the final exam in order to receive a course grade of at least 86?

• 82

• 84

• 90

• 92

• 98

The triangle below has vertices A(-1,-2), B(2,2), and C(-1,4). What is the area of ΔABC, in square coordinate units?

• 9

• 15

• 18

• \(\frac{1}{2} \sqrt{13}\)

• 3\(\sqrt{13}\)

For some real number x, \(\sqrt{x} \neq x\). Therefore x is:

• zero

• greater than π

• irrational

• negative

• undefined

In the standard (x,y) coordinate plane below, point A has coordinates (2,-4), and point B(8,-1) divides AC so that the ratio AB:BC is 1:3. What are the coordinates of point C?

• (-16,-13)

• (10,0)

• (14,2)

• (26,8)

• (32,11)

A wire binds 4 identical posts together as shown below. Each post has a 3-inch radius. What is the length, to the nearest inch, of the shortest wire that will go around the 4 posts without overlap?

• 21

• 31

• 33

• 43

• 52

Given that b is rational and i = √-1, the product of the expression (3 + bi) and which of the following expressions must be a rational number?

• i

• bi

• 3bi

• 3 + bi

• 3 - bi

For positive integers x and y where x < 8, logx 8 = y. What is the value of y?

• 1

• 2

• 3

• 4

• 8