Math Evaluation Test

Please select the correct answers for all the questions below. Each question may have one or more correct options. Fill in your Name and Email and submit the test using the button at the bottom.

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Question No. 1

If $\frac{\left(x-1\right)}{3}=k$ and $k=3$, what is the value of x?

Question No. 2

For $i=$$\sqrt{-1}$ what is the sum below ?
$\left(7+3i\right)+\left(-8+9i\right)$

$-1+12i$

$-1-6i$

$15+12i$

$15-6i$

Question No. 3

On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?

$9mp$

$20mp$

$5m+4p$

$4m+5p$

Question No. 4

Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation below , where $P$ is the number of phones left and $d$ is the number of days she has worked that week. What is the meaning of the value 108 in this equation?
$P=108-3d$

Kathy will complete the repairs within 108days.

Kathy starts each week with 108 phones to fix.

Kathy repairs phones at a rate of 108 per hour.

Kathy repairs phones at a rate of 108 per day.

Question No. 5

Which of the following is equivalent to the expression below?
$\left(x^2y-3y^2+5xy^2\right)-\left(-x^2y+3xy^2-3y^2\right)$

$4x^2y^2$

$8xy^2-6y^2$

$2x^2y+2xy^2$

$2x^2y+8xy^2-6y^2$

Question No. 6

A pediatrician uses the model below to estimate the height h of a boy, in inches, in terms of the boy’s age a, in years, between the ages of 2 and 5.Based on the model, what is the estimated increase, in inches, of a boy’s height each year?
$h=3a+28.6$

5.7

9.5

14.3

Question No. 7

The formula below gives the monthly payment m needed to pay off a loan of P dollars at r percent annual interest over N months .Which of the following gives P in terms of m, r, and N?
$m=\frac{\left(\frac{r}{1200}\right)\left(1+\frac{r}{1200}\right)^N}{\left(1+\frac{r}{1200}\right)^N-1}P$

$P=\frac{\left(\frac{r}{1200}\right)\left(1+\frac{r}{1200}\right)^N}{\left(1+\frac{r}{1200}\right)^N-1}m$

$P=\frac{\left(1+\frac{r}{1200}\right)^N-1}{\left(\frac{r}{1200}\right)\left(1+\frac{r}{1200}\right)^N}m$

$P=\left(\frac{r}{1200}\right)m$

$P=\left(\frac{1200}{r}\right)m$

Question No. 8

If $\frac{a}{b}=2$, what is the value of $\frac{4b}{a}$

Question No. 9

What is solution (x,y) for the below equations?
$3x+4y=-23,2y-x=-19$

(-5,-2)

(3,-8)

(4,-6)

(9,-6)

Question No. 10

For the function defined below, a is a constant. What is $g\left(-4\right)$ ?
$g\left(x\right)=ax^2+24$
$g\left(4\right)=8$

-1

-8

Question No. 11

In the equations below, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?
$b=2.35+0.25x$
$c=1.75+0.4x$

$2.60

$2.85

$2.95

$3.35

Question No. 12

A line in the xy-plane passes through the origin and has a slope of $\frac{1}{7}$. Which of the following points lies on the line?

(0,7)

(1,7)

(7,7)

(14,2)

Question No. 13

If x>3, which of the following is equivalent to the below fraction
$\frac{1}{\frac{1}{x+2}+\frac{1}{x+3}}$

$\frac{2x+5}{x^2+5x+6}$

$\frac{x^2+5x+6}{2x+5}$

$2x+5$

$x^2+5x+6$

Question No. 14

If $3x-y=12$ what is the value of below fraction
$\frac{8^x}{2^y}$

$2^{12}$

$4^4$

$8^2$

The value cannot be determined from the information given

Question No. 15

If the equations below are true for all values of x, find the 2 possible values of c.
$\left(ax+2\right)\left(bx+7\right)=15x^2+cx+14$
a+b=8

3 and 5

6 and 35

10 and 21

31 and 41

Question No. 16

If $t>0$ and $t^2-4=0$, find t.

1.5

-2

Question No. 17

A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. The lengths represented by AB, EB ,BD ,and CD on the sketch were determined to be 1800 feet,1400 feet,700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and ∠AEB and ∠CDB have the same measure. What is the value of x?
Figure 1:

1600

1700

1800

1900

Question No. 18

In a right triangle, one angle measures $x^o$ , where $\sin x^o=\frac{4}{5}$

What is $\cos\left(90-x\right)^o$?

$\frac{1}{2}$

$\frac{1}{5}$

$\frac{2}{5}$

$\frac{4}{5}$

Question No. 19

According to the system of equations below what is x?
$x+y=-9$
$x+2y=-25$

-7

Question No. 20

If the following is true, what is x?
$a=5\sqrt{2}$
$2a=\sqrt{2x}$

100

-25