OG Test 3 - Reading 5

Question 1

If 5x + 6 = 10, what is the value of 10x + 3 ?

• A 4

• B 9

• C 11

• D 20

Question 2

x+y=0
3x−2y=10

Which of the following ordered pairs (x, y) satisfies the system of equations above?

• A (3, −2)

• B (2, −2)

• C (−2, 2)

• D (−2, −2)

Question 3

A landscaping company estimates the price of a job, in dollars, using the expression 60 + 12nh, where n is the number of landscapers who will be working and h is the total number of hours the job will take using n landscapers. Which of the following is the best interpretation of the number 12 in the expression?

• A The company charges $12 per hour for each landscaper. • B A minimum of 12 landscapers will work on each job. • C The price of every job increases by$12 every hour.

• D Each landscaper works 12 hours a day.

Question 4

$9a^4+12a^2b^2+4b^4$

Which of the following is equivalent to the expression shown above?

• A $(3a^2+2b^2)^2$

• B $(3a+2b)^4$

• C $(9a^2+4b^2)^2$

• D $(9a+4b)^4$

Question 5

$\sqrt{2k^2+17}-x=0$

If k > 0 and x = 7 in the equation above, what is the value of k ?

• A 2

• B 3

• C 4

• D 5

Question 6

In the xy-plane above, line $\ell$ is parallel to line $k$. What is the value of $p$?

• A 4

• B 5

• C 8

• D 10

Question 7

If $\frac{x^{a^2}}{x^{b^2}}=x^{16}$, $x>1$, and $a+b=2$, what is the value of $a−b$ ?

• A 8

• B 14

• C 16

• D 18

Question 8

nA = 360
The measure A, in degrees, of an exterior angle of a regular polygon is related to the number of sides, n, of the polygon by the formula above. If the measure of an exterior angle of a regular polygon is greater than 50°, what is the greatest number of sides it can have?

• A 5

• B 6

• C 7

• D 8

Question 9

The graph of a line in the xy-plane has slope 2 and contains the point (1, 8). The graph of a second line passes through the points (1, 2) and (2, 1). If the two lines intersect at the point (a, b), what is the value of a + b ?

• A 4

• B 3

• C -1

• D -4

Question 10

Which of the following equations has a graph in the xy-plane for which y is always greater than or equal to −1 ?

• A $y = x − 2$

• B $y = x^2 − 2$

• C $y = (x − 2)^2$

• D $y = x^3 − 2$

Question 11

Which of the following complex numbers is equivalent to $\frac{3-5i}{8+2i}$?(Note: $i=\sqrt{-1}$)

• A $\frac{3}{8}-\frac{5i}{2}$

• B $\frac{3}{8}+\frac{5i}{2}$

• C $\frac{7}{34}-\frac{23i}{34}$

• D $\frac{7}{34}+\frac{23i}{34}$

Question 12

$R=\frac{F}{N+F}$

A website uses the formula above to calculate a seller`s rating, R, based on the number of favorable reviews, F, and unfavorable reviews, N. Which of the following expresses the number of favorable reviews in terms of the other variables?

• A $F=\frac{RN}{R-1}$

• B $F=\frac{RN}{1-R}$

• C $F=\frac{N}{1-R}$

• D $F=\frac{N}{R-1}$

Question 13

What is the sum of all values of $m$ that satisfy $2m^2−16m+8=0$?

• A $−8$

• B $-4\sqrt{3}$

• C $4\sqrt{3}$

• D $8$

Question 14

A radioactive substance decays at an annual rate of 13 percent. If the initial amount of the substance is 325 grams, which of the following functions $f$ models the remaining amount of the substance, in grams, $t$ years later?

• A $f(t) = 325(0.87)^t$

• B $f(t) = 325(0.13)^t$

• C $f(t) = 0.87(325)^t$

• D $f(t) = 0.13(325)^t$

Question 15

The expression $\frac{5x-2}{x+3}$ is equivalent to which of the following?

• A $\frac{5-2}{3}$

• B $5-\frac{2}{3}$

• C $5-\frac{2}{x+3}$

• D $5-\frac{17}{x+3}$

Question 16

The sales manager of a company awarded a total of $3000 in bonuses to the most productive salespeople. The bonuses were awarded in amounts of$250 or $750. If at least one$250 bonus and at least one $750 bonus were awarded, what is one possible number of$250 bonuses awarded?

Question 17

$2x(3x+5)+3(3x+5)=ax^2+bx+c$

In the equation above, a, b, and c are constants. If the equation is true for all values of x, what is the value of b ?

Question 18

In the figure above, $\overline{AE}\parallel\overline{CD}$ and segment AD intersects segment CE at B. What is the length of segment CE?

Question 19

In the xy-plane above, O is the center of the circle, and the measure of ∠AOB is $\frac{\pi}{a}$ radians. What is the value of a ?

Question 20

ax+by=12
2x+8y=60

In the system of equations above, a and b are constants. If the system has infinitely many solutions, what is the value of $\frac{a}{b}$?

Reference

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