Compass Math Pool 3

Question 1

x = 4m2   y = (2m+ 1)(2m− 1)  Given the two equations, what is y in terms of x ?

Accepted Answer

x + 1

Answer

Given the equations x = 4m² and y = (2m + 1)(2m - 1), we first simplify the expression for y. Using the difference of squares formula (a+b)(a-b) = a² - b², we get y = (2m)² - 1² = 4m² - 1. Since we know that x = 4m², we can substitute x into the simplified equation for y, resulting in y = x - 1. Please note that the provided correct answer 'x + 1' is inconsistent with the given equations, as the correct derivation leads to y = x - 1.

Question 2

15, 9, 27, 10, 14, 9, 20: The number 10 is to be added to the list above. Which of the following must be true about the median and mode of the new list compared to the original?

Accepted Answer

The number of modes will decrease and the median will decrease.

Answer

First, sort the original list: 9, 9, 10, 14, 15, 20, 27. The median is the middle number, 14. The mode is 9 (appears twice). When 10 is added, the new sorted list is: 9, 9, 10, 10, 14, 15, 20, 27. The new median is the average of the two middle numbers (10 and 14), which is (10+14)/2 = 12. The new modes are 9 and 10, as both appear twice. Thus, the median decreases (from 14 to 12) and the number of modes increases (from 1 to 2). Therefore, the provided correct answer (D) is inconsistent with the calculation, as the number of modes actually increases, not decreases.

Question 3

If f(x) = 2x+4, then what is the value of f(4) + f(6) ?

Accepted Answer

f(18)

Answer

Even if something other than a number is given inside the parentheses of a function,
the rule is the same: substitute the expression inside the parentheses for x in the
function definition. For example, if g(x) = 2x+1, then g(cabbage) = 2·cabbage+1.
For this problem, substitute 3a for x to get f(3a) = 2(3a)2 = 18a2. Since 2f(3a) =
144, then 36a2 = 144 so that a2 = 4 and a = ±2, making answer D correct. (Note
that −2 is not listed as a choice: there can only be one answer.)

Question 4

If x2 + 5x − 14 = 0, and x > 0, then what is the value of x ?

Accepted Answer

2

Answer

You should be able to factor the left-hand side of the equation as follows:
x2 + 5x − 14 = (x + 7)(x − 2) = 0
so that either x = −7 or x = 2. Be careful to read the question: since the problem
specified x > 0, the answer is not A; instead, the answer is C, or x = 2.

Question 5

A farmer can pick 12 cabbages in 1 hour. Working at the same rate, how long in hours would it take two farmers to pick 48 cabbages?

Accepted Answer

2

Answer

First, determine the combined work rate of two farmers. If one farmer picks 12 cabbages in 1 hour, two farmers working at the same rate will pick 2 * 12 = 24 cabbages in 1 hour. To find out how long it would take them to pick 48 cabbages, divide the total number of cabbages by their combined rate: 48 cabbages / 24 cabbages/hour = 2 hours. Therefore, it would take two farmers 2 hours to pick 48 cabbages.

COMPASS Practice Test

COMPASS Practice Test

Compass Math Pool 3