 ## Full Length PSAT Math Practice Test

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PSAT Math
Practice Test 2

Section 1

(No Calculator)

17 questions

Total time for this section: 25 Minutes

You May NOT use a calculator on this Section.

1- If $$5 \ x \ - \ 8=4.5$$, what is the value of $$3 \ x \ + \ 3$$?
(A) $$10.5$$
(B) $$12.5$$
(C) $$15.5$$
(D) $$25$$
2- If the function $$ƒ$$ is defined by $$f(x)=x^2 \ + \ 2 \ x \ - \ 5$$, which of the following is equivalent to $$f(3 \ t^2)$$?
(A) $$3 \ 𝑡^4 \ + \ 6 \ 𝑡^2 \ − \ 5$$
(B) $$9 \ 𝑡^4 \ + \ 6 \ 𝑡^2 \ − \ 5$$
(C) $$3 \ 𝑡^4 \ + \ 3 \ 𝑡^2 \ − \ 5$$
(D) $$3 \ 𝑡^4 \ + \ 6 \ 𝑡^2 \ + \ 5$$
3- If $$x \ p \ + \ 2 \ y \ q=26$$ and $$x \ p \ + \ y \ q=17$$, what is the value of $$y \ q$$?
(A) $$6$$
(B) $$7$$
(C) $$8$$
(D) $$9$$
4- The circle graph below shows all Mr. Green’s expenses for last month. If he spent $$660$$ on his car, how much did he spend for his rent? (A) $$700$$
(B) $$740$$
(C) $$780$$
(D) $$810$$
5- If $$x^2 \ + \ 3$$ and $$x^2 \ - \ 3$$ are two factors of the polynomial $$12 \ x^4 \ + \ n$$ and $$n$$ is $$a$$ constant, what is the value of $$n$$?
(A) $$− \ 108$$
(B) $$− \ 24$$
(C) $$24$$
(D) $$108$$
6- $$0.$$ABC      $$0.0$$D
The letters represent two decimals listed above. One of the decimals is equivalent to $$\frac{1}{8}$$ and the other is equivalent to $$\frac{1}{20}$$. What is the product of C and D?
(A) $$0$$
(B) $$5$$
(C) $$25$$
(D) $$20$$
7- In the diagram below, circle A represents the set of all odd numbers, circle B represents the set of all negative numbers, and circle C represents the set of all multiples of $$5$$. Which number could be replaced with $$y$$? (A) $$5$$
(B) $$0$$
(C) $$- \ 5$$
(D) $$- \ 10$$
8- There are only red and blue cards in a box. The probability of choosing a red card in the box at random is one third. If there are $$246$$ blue cards, how many cards are in the box?
(A) $$123$$
(B) $$308$$
(C) $$328$$
(D) $$369$$
9- Both $$(x= \ - \ 2)$$ and $$(x=3)$$ are solutions for which of the following equations?
I. $$x^2 \ - \ x \ + \ 6=0$$
II. $$2 \ x^2 \ - \ 2 \ x=12$$
III. $$5 \ x^2 \ - \ 5 \ x \ - \ 30=0$$
(A) II only
(B) I and II
(C) II and III
(D) I, II and III
10- The radius of circle A is three times the radius of circle B. If the circumference of circle A is $$18 \ π$$, what is the area of circle B?
(A) $$3 \ 𝜋$$
(B) $$6 \ 𝜋$$
(C) $$9 \ 𝜋$$
(D) $$12 \ 𝜋$$
11- In a certain bookshelf of a library, there are $$35$$ biology books, $$95$$ history books, and $$80$$ language books. What is the ratio of the number of biology books to the total number of books in this bookshelf?
(A) $$\frac{1}{4}$$
(B) $$\frac{1}{6}$$
(C) $$\frac{2}{7}$$
(D) $$\frac{3}{8}$$
12- In the figure below, what is the value of $$x$$? (A) $$43^\circ$$
(B) $$67^\circ$$
(C) $$77^\circ$$
(D) $$90^\circ$$
13- The following table represents the value of $$x$$ and function $$f(x)$$. Which of the following could be the equation of the function $$f(x)$$? (A) $$𝑓(x)=x^2 \ − \ 5$$
(B) $$𝑓(x)=x^2 \ − \ 1$$
(C) $$𝑓(x)=\sqrt{x \ + \ 2 }$$
(D) $$𝑓(x)=\sqrt{x } \ + \ 4$$
14- Michelle and Alec can finish a job together in $$100$$ minutes. If Michelle can do the job by herself in $$5$$ hours, how many minutes does it take Alec to finish the job?
(A) 150
(B) 150.0
(C) 150
15-  In the following figure, point O is the center of the circle and the equilateral triangle has perimeter $$33$$. What is the circumference of the circle? $$(π=3)$$ (A) 66
(B) 66.0
(C) 66
16- If $$12\%$$ of $$x$$ is $$72$$ and $$\frac{1}{8}$$ of $$y$$ is $$16$$, what is the value of $$x \ - \ y$$?
(A) 472
(B) 472.0
(C) 472
17- Angle a is $$630$$ degrees and can be written $$x \ π$$ in radian. What is the value of $$x$$?
(A) 3.5
(B) 3.5
(C) 3 (1/2)
(D) 3(1/2)
(E) 3+(1/2)
(F) 3 + (1/2)
(G) 3 +(1/2)
(H) 3+0.5
(I) 3 +0.5
(J) 3 + 0.5
18-

PSAT Math
Practice Test 2

Section 2

(Calculator)

31 questions

Total time for this section: 45 Minutes

You can use a scientific calculator on this Section.

19- What is the value of $$\frac{3 \ a \ - \ 2}{2}$$, if $$- \ 3 \ a \ + \ 5 \ a \ + \ 7 \ a=45$$ ?
(A) $$6.5$$
(B) $$6$$
(C) $$5.5$$
(D) $$5$$
20- What is the average (arithmetic mean) of all integers from $$11$$ to $$19$$?
(A) $$14$$
(B) $$14.5$$
(C) $$15$$
(D) $$15.5$$
21- What is the value of $$|- \ 12 \ - \ 5| \ - \ |- \ 8 \ + \ 2|$$?
(A) $$11$$
(B) $$- \ 11$$
(C) $$23$$
(D) $$- \ 23$$
22- The table represents different values of function $$g(x)$$. What is the value of
$$3 \ g(- \ 2) \ - \ 2 \ g(3)$$? (A) $$- \ 12$$
(B) $$- \ 2$$
(C) $$3$$
(D) $$13$$
23- A container holds $$3.5$$ gallons of water when it is $$\frac{7}{24}$$ full. How many gallons of water does the container hold when it’s full?
(A) $$8$$
(B) $$12$$
(C) $$16$$
(D) $$20$$
24- On the following figure, what is the area of the quadrilateral ABCD? (A) $$27$$
(B) $$30$$
(C) $$33$$
(D) $$36$$
25- If $$a$$ is an odd integer divisible by $$5$$. Which of the following must be divisible by $$4$$?
(A) $$𝑎 \ − \ 1$$
(B) $$𝑎 \ + \ 1$$
(C) $$2 \ a$$
(D) $$2 \ a \ - \ 2$$
26- If $$(3^a)^b=81$$, then what is the value of $$a \ b$$?
(A) $$2$$
(B) $$3$$
(C) $$4$$
(D) $$5$$
27- Between which two of the months shown was there a twenty percent decreased in the number of pants sold? (A) January and February
(B) February and March
(C) March and April
(D) April and May
28- During the six-month period shown, what is the median number of shirts and mean number of shoes per month? (A) $$146.5, 30$$
(B) $$147.5, 29$$
(C) $$146.5, 31$$
(D) $$147.5, 30$$
29- How many shoes need to be added in April until the ratio of number of pants to number of shoes in April equals to five-seventeenth of this ratio in May? (A) $$90$$
(B) $$80$$
(C) $$60$$
(D) $$50$$

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30- What is the $$x-$$intercept of the line with equation $$2 \ x \ - \ 2 \ y=5$$?
(A) $$− \ 5$$
(B) $$− \ 2$$
(C) $$\frac{5}{2}$$
(D) $$\frac{5}{4}$$
31- The perimeter of a triangle is $$10$$ cm and the lengths of its sides are different integers. What is the greatest possible value of the biggest side?
(A) $$4$$ cm
(B) $$5$$ cm
(C) $$6$$ cm
(D) $$7$$ cm
32- If $$(x \ - \ 2)^3=27$$ which of the following could be the value of $$(x \ -\ 4) \ (x \ - \ 3)$$?
(A) $$1$$
(B) $$2$$
(C) $$- \ 1$$
(D) $$- \ 2$$
33- A library has $$840$$ books that include Mathematics, Physics, Chemistry, English and History
What is the product of the number of Mathematics and number of English books? (A) $$21,168$$
(B) $$31,752$$
(C) $$26,460$$
(D) $$17,640$$
34- A library has $$840$$ books that include Mathematics, Physics, Chemistry, English and History
What are the values of angle $$α$$ and $$β$$ respectively? (A) $$90^\circ, 54^\circ$$
(B) $$120^\circ, 36^\circ$$
(C) $$120^\circ, 45^\circ$$
(D) $$108^\circ, 45^\circ$$
35- A library has $$840$$ books that include Mathematics, Physics, Chemistry, English and History
The librarians decided to move some of the books in the Mathematics section to Chemistry section. How many books are in the Chemistry section if now $$\gamma=\frac{2}{5 } \ α$$? (A) $$80$$
(B) $$120$$
(C) $$150$$
(D) $$180$$
36- In $$1999$$, the average worker's income increased $$2,000$$ per year starting from $$24,000$$ annual salary.  Which equation represents income greater than average? ($$I =$$ income, $$x =$$ number of years after $$1999$$)
(A) $$𝐼 \ > \ 2000 \ x \ + \ 24000$$
(B) $$𝐼 \ > \ - \ 2000 \ x \ + \ 24000$$
(C) $$𝐼 \ < \ - \ 2000 \ x \ + \ 24000$$
(D) $$𝐼 \ < \ 2000 \ x \ – \ 24000$$
37- The Jackson Library is ordering some bookshelves. If $$x$$ is the number of bookshelf the library wants to order, which each costs $$100$$ and there is a one-time delivery charge of $$800$$, which of the following represents the total cost, in dollar, per bookshelf?
(A) $$100 \ x \ + \ 800$$
(B) $$100 \ + \ 800 \ x$$
(C) $$\frac{100 \ x \ + \ 800}{x}$$
(D) $$\frac{100 \ x \ + \ 800}{100}$$
38- What is the sum of $$\sqrt{x \ - \ 7}$$ and $$\sqrt{x} \ - \ 7$$ when $$\sqrt{x}=4$$?
(A) $$− \ 3$$
(B) $$− \ 1$$
(C) $$0$$
(D) $$3$$
39- In the following figure, point Q lies on line n, what is the value of $$y$$ if $$x = 35$$? (A) $$15$$
(B) $$25$$
(C) $$35$$
(D) $$45$$
40- In the following figure, AB is the diameter of the circle. What is the circumference of the circle? (A) $$5 \ π$$
(B) $$10 \ π$$
(C) $$15 \ π$$
(D) $$20 \ π$$
41- What is the smallest integer whose square root is greater than $$6$$?
(A) $$16$$
(B) $$25$$
(C) $$37$$
(D) $$49$$
42- If the area of trapezoid is $$126$$ cm, what is the perimeter of the trapezoid? (A) $$12$$ cm
(B) $$32$$ cm
(C) $$46$$ cm
(D) $$55$$ cm
43- What is the solution of the following inequality?
$$|x \ - \ 2| \ ≥ \ 3$$
(A) $$x \ ≥ \ 5 \ ∪ \ x \ ≤ \ − \ 1$$
(B) $$− \ 1 \ ≤ \ x \ ≤ \ 5$$
(C) $$x \ ≥ \ 5$$
(D) $$x \ ≤ \ − \ 1$$
44- If the area of the following rectangular ABCD is $$100$$, and E is the midpoint of AB, what is the area of the shaded part? (A) $$25$$
(B) $$50$$
(C) $$75$$
(D) $$80$$
45- Which of the following is equivalent to $$13 \ < \ - \ 3 \ x \ - \ 2 \ < \ 22$$?
(A) $$− \ 8 \ < \ x \ < \ − \ 5$$
(B) $$5 \ < \ x \ < \ 8$$
(C) $$\frac{11}{3} \ < \ x \ < \ \frac{20}{3}$$
(D) $$\frac{- \ 20}{3} \ < \ x \ < \ \frac{- \ 11}{3}$$
46- In the following figure, ABCD is a rectangle. If $$a=\sqrt{3}$$, and $$b=2 \ a$$, find the area of the shaded region? (the shaded region is a trapezoid) (Round your answer to the nearest hundredths place) (A) 6.93
(B) 6.93
(C) 6+0.93
47- If sin $$A = \frac{ 1}{3}$$ in a right triangle and the angle $$A$$ is an acute angle, then what is cos $$A$$? (Round your answer to the nearest hundredths place)
(A) 0.94
(B) 0.94
48- $$6$$ liters of water are poured into an aquarium that's $$15$$ cm long, $$5$$ cm wide, and $$60$$ cm high. How many cm will the water level in the aquarium rise due to this added water? ($$1$$ liter of water $$= 1000$$ cm$$^3$$)?
(A) 80
(B) 80
(C) 80.0
49- If $$x \ \begin{bmatrix}2 & 0 \\0 & 4 \end{bmatrix} = \begin{bmatrix}x \ + \ 3 \ y \ - 5 & 0 \\0 & 2 \ y \ + \ 10 \end{bmatrix}$$, what is the product of $$x$$ and $$y$$?
(A) 12
(B) 12
(C) 12.0
 1- Choice A is correct The correct answer is $$10.5$$$$5 \ x \ - \ 8=4.5→5 \ x=4.5 \ + \ 8=12.5→x=\frac{12.5}{3}=2.5$$Then; $$3 \ x \ + \ 3=3 \ (2.5) \ + \ 3=7.5 \ + \ 3=10.5$$ 2- Choice B is correct The correct answer is $$9 \ 𝑡^4 \ + \ 6 \ 𝑡^2 \ − \ 5$$$$f(x)=x^2 \ + \ 2 \ x \ - \ 5$$$$f(3 \ t^2 )=(3 \ t^2 )^2 \ + \ 2 \ (3 \ t^2 ) \ - \ 5=9 \ t^4 \ + \ 6 \ t^2 \ - \ 5$$ 3- Choice D is correct The correct answer is $$9$$$$x \ p \ + \ 2 \ y \ q=26→x \ p=26 \ - \ 2 \ y \ q$$ $$(1)$$ $$x \ p \ + \ y \ q=17$$ $$(2)$$$$(1)$$ in $$(2) \ \ →26 \ - \ 2 \ y \ q \ + \ y \ q=17→26 \ - \ y \ q=17→y \ q=26 \ - \ 17=9$$ 4- Choice D is correct The correct answer is $$810$$Let $$x$$ be all expenses, then $$\frac{22}{100} \ x=660 →x=\frac{100 \ × \ 660}{22}=3,000$$He spent for his rent: $$\frac{27}{100} \ × \ 3,000=810$$ 5- Choice A is correct The correct answer is $$− \ 108$$$$12 \ x^2 \ + \ n=a \ (x^2 \ + \ 3) \ (x^2 \ - \ 3)=a \ x^4 \ - \ 9 \ a→a=12$$ And $$n=- \ 9 \ a=- \ 9 \ × \ 12=- \ 108$$ 6- Choice C is correct The correct answer is $$25$$$$\frac{1}{8}=0.125→C=5$$$$\frac{1}{20}=0.05→D=5→C \ × \ D=5 \ ×\ 5=25$$ 7- Choice C is correct The correct answer is $$- \ 5$$$$y$$ is the intersection of the three circles?Therefore, it must be odd (from circle A), negative (from circle B), and multiple of $$5$$ (from circle C).From the options, only $$- \ 5$$ is odd, negative and multiple of $$5$$. 8- Choice D is correct The correct answer is $$369$$let $$x$$ be total number of cards in the box, then number of red cards is: $$x \ - \ 246$$The probability of choosing a red card is one third. Then:probability $$=\frac{1}{3}=\frac{x \ - \ 132}{x}$$Use cross multiplication to solve for $$x$$. $$x \ × \ 1=3 \ (x \ - \ 246)→x=3 \ x \ - \ 738→2 \ x=738→x=369$$ 9- Choice C is correct The correct answer is II and IIIPlug in the values of $$x$$ in each equation and check.I. $$(- \ 2)^2 \ - \ 2 \ + \ 6=4 \ - \ 2 \ + \ 6=8≠0$$   $$(3)^2 \ - \ 3 \ + \ 6=3 \ - \ 3 \ + \ 6=12≠0$$II. $$2 \ (- \ 2)^2 \ - \ 2 \ (- \ 2)=8 \ + \ 4=12→12=12$$   $$2 \ (3)^2 \ - \ 2 \ (3)=18 \ - \ 6=12→12=12$$III. $$5 \ (- \ 2)^2 \ - \ 5 \ (- \ 2) \ - \ 30=20 \ + \ 10 \ - \ 30=0$$   $$5 \ (3)^2 \ - \ 5 \ (3) \ - \ 30=45 \ - \ 15 \ - \ 30=0$$Equations II and III are correct. 10- Choice C is correct The correct answer is $$9 \ 𝜋$$Let P be circumference of circle A, then; $$2 \ π \ r_{A}=18 \ π→r_{A}=9$$$$r_{A}=3 \ r_{B}→r_{B}=\frac{9}{3}=3→$$ Area of circle B is; $$π \ r_{B}^2=9 \ π$$ 11- Choice B is correct The correct answer is $$\frac{1}{6}$$Number of biology book: $$35$$Total number of books; $$35 \ + \ 95 \ + \ 80=210$$the ratio of the number of biology books to the total number of books is: $$\frac{35}{210}=\frac{1}{6}$$ 12- Choice B is correct The correct answer is $$67^\circ$$$$α=180^\circ \ - \ 112^\circ=68^\circ$$$$β=180^\circ \ - \ 135^\circ=45^\circ$$$$x \ + \ α \ + \ β=180^\circ→x=180^\circ \ - \ 68^\circ \ - \ 45^\circ=67^\circ$$ 13- Choice D is correct The correct answer is $$𝑓(x)=\sqrt{x } \ + \ 4$$A. $$f(x)=x^2 \ - \ 5$$       if $$x=1→f(1)=(1)^2 \ - \ 5=1 \ - \ 5=- \ 4≠5$$ B. $$f(x)=x^2 \ - \ 1$$       if $$x=1→f(1)=(1)^2 \ - \ 1=1 \ - \ 1=0≠5$$C. $$f(x)=\sqrt{x \ + \ 2}$$     if $$x=1→f(1)=\sqrt{1 \ + \ 2}=\sqrt{3}≠5$$D. $$f(x)=\sqrt{x} \ + \ 4$$     if $$x=1→f(1)=\sqrt{1} \ + \ 4=5$$Choice D is correct. 14- Choice C is correct The correct answer is $$150$$Let $$b$$ be the amount of time Alec can do the job, then, $$\frac{1}{a} \ + \ \frac{1}{b}=\frac{1}{100}→\frac{1}{300} \ + \ \frac{1}{b}=\frac{1}{100}→\frac{1}{b}=\frac{1}{100} \ - \ \frac{1}{300}=\frac{2}{300}=\frac{1}{150}$$Then: $$b=150$$ minutes 15- Choice C is correct The correct answer is $$66$$In the equilateral triangle if $$x$$ is length of one side of triangle, then the perimeter of the triangle is $$3 \ x$$.Then $$3 \ x=33→x=11$$ and radius of the circle is: $$x=11$$Then, the perimeter of the circle is: $$2 \ π \ r=2 \ π \ (11)=22 \ π$$ $$π=3→22 \ π=22 \ × \ 3=66$$ 16- Choice C is correct The correct answer is $$472$$$$\frac{12}{100} \ x=72→x=\frac{72 \ × \ 100}{12}=600$$$$\frac{1}{8} \ y=16→y=8 \ × \ 16=128$$$$→x \ - \ y=600 \ - \ 128=472$$ 17- Choice J is correct The correct answer is $$3 \ \frac{1}{2}$$One degree equals $$\frac{π}{180 }$$. The angle $$α$$ in radians is equal to the angle α in degrees times $$π$$ constant divided by $$180$$ degrees. Then:$$1$$ degree $$= \frac{π}{180}→630$$ degrees $$=\frac{630 \ π}{180}=3.5 \ π$$$$3.5 \ π=x \ π→x=3.5$$ 17- Choice J is correct The correct answer is $$3 \ \frac{1}{2}$$One degree equals $$\frac{π}{180 }$$. The angle $$α$$ in radians is equal to the angle α in degrees times $$π$$ constant divided by $$180$$ degrees. Then:$$1$$ degree $$= \frac{π}{180}→630$$ degrees $$=\frac{630 \ π}{180}=3.5 \ π$$$$3.5 \ π=x \ π→x=3.5$$ 19- Choice A is correct The correct answer is $$6.5$$$$- \ 3 \ a \ + \ 5 \ a \ + \ 7 \ a=45→9 \ a=45→a=\frac{45}{9}=5$$Then; $$\frac{3 \ a \ - \ 2}{2}=\frac{3 \ (5) \ - \ 2}{2}=\frac{15 \ - \ 2}{2}=6.5$$ 20- Choice C is correct The correct answer is $$15$$All integers from $$11$$ to $$19$$ are: $$11, 12, 13, 14, 15, 16, 17, 18, 19$$The mean of these integers is:$$\frac{11 \ + \ 12 \ + \ 13 \ + \ 14 \ + \ 15 \ + \ 16 \ + \ 17 \ + \ 18 \ + \ 19}{9}=\frac{135}{9}=15$$ 21- Choice A is correct The correct answer is $$11$$$$|- \ 12 \ - \ 5| \ - \ |- \ 8 \ + \ 2|=|- \ 17| \ - \ |- \ 6|=17 \ - \ 6=11$$ 22- Choice D is correct The correct answer is $$13$$Based on the table provided:$$g(- \ 2)=g(x=- \ 2)=3$$$$g(3)=g(x=3)=- \ 2$$$$3 \ g(- \ 2) \ - \ 2 \ g(3)=3 \ (3) \ - \ 2 \ (- \ 2)=9 \ + \ 4=13$$ 23- Choice B is correct The correct answer is $$12$$let $$x$$ be the number of gallons of water the container holds when it is full.Then; $$\frac{7}{24} \ x=3.5→x=\frac{24 \ × \ 3.5}{7}=12$$ 24- Choice A is correct The correct answer is $$27$$The quadrilateral is a trapezoid.Use the formula of the area of trapezoids.Area $$=\frac{1}{2} \ h \ (b_{1} \ + \ b_{2} )$$You can find the height of the trapezoid by finding the difference of the values of $$y$$ for the points A and D.(or points B and C)$$h=8 \ - \ 2=6$$AB $$=\sqrt{(x_{1} \ - \ x_{2} )^2 \ + \ (y_{1} \ - \ y_{2})^2 }=\sqrt{(6 \ - \ 3)^2 \ + \ (8 \ - \ 8)^2 }=\sqrt{9 \ + \ 0}=3$$CD $$=\sqrt{(x_{1} \ - \ x_{2} )^2 \ + \ (y_{1} \ - \ y_{2})^2 }=\sqrt{(8 \ - \ 2)^2 \ + \ (2 \ - \ 2)^2 }=\sqrt{36 \ + \ 0}=6$$Area of the trapezoid is: $$\frac{1}{2} \ h \ (b_{1} \ + \ b_{2} )=\frac{1}{2} \ (6) \ (3 \ + \ 6)=27$$ 25- Choice D is correct The correct answer is $$2 \ a \ - \ 2$$Choose a random number for a and check the options.Let $$a$$ be equal to $$15$$ which is divisible by $$5$$, then:A. $$a \ - \ 1=15 \ - \ 1=14$$ is not divisible by $$4$$B. $$a \ + \ 1=15 \ + \ 1=16$$ is divisible by $$4$$but if $$a=5→a \ + \ 1=5 \ + \ 1=6$$ is not divisible by $$4$$C. $$2 \ a=2 \ × \ 15=30$$ is not divisible by $$4$$D. $$2 \ a \ - \ 2=(2 \ × \ 15) \ - \ 2=28$$ is divisible by $$4$$ 26- Choice C is correct The correct answer is $$4$$$$(3^a )^b=81→3^{a \ b}=81$$$$81=3^4→3^{a \ b}=3^4$$$$→a \ b=4$$ 27- Choice A is correct The correct answer is January and FebruaryFirst find the number of pants sold in each month.January: $$110$$, February: $$88$$, March: $$90$$, April: $$70$$, May: $$85$$, June: $$65$$Check each option provided.A. January and February,    $$(\frac{110 \ - \ 88}{110}) \ × \ 100=\frac{22}{110} \ × \ 100=20\%$$B. February and March, there is an increase from February to March.C. March and April   $$(\frac{90 \ - \ 70}{90}) \ × \ 100=\frac{20}{90} \ × \ 100=22.22\%$$D. April and May: there is an increase from April to May 28- Choice D is correct The correct answer is $$147.5, 30$$First, order the number of shirts sold each month:$$130,140,145,150,160,170$$median is: $$\frac{145 \ + \ 150}{2}=147.5$$Put the number of shoes sold per month in order:$$20,25,25,35,35,40$$mean is: $$\frac{20 \ + \ 25 \ + \ 25 \ + \ 35 \ + \ 35 \ + \ 40}{6}=\frac{180}{6}=30$$ 29- Choice D is correct The correct answer is $$50$$The ratio of number of pants to number of shoes in May equals $$\frac{85}{25}$$.Five-seventeenth of this ratio is $$(\frac{5}{17}) \ (\frac{85}{25})$$.Now, Let $$x$$ be the number of shoes needed to be added in April.$$\frac{70}{20 \ + \ x}=(\frac{5}{17})\ (\frac{85}{25})→\frac{70}{20 \ + \ x}=\frac{425}{425}=1→70=20 \ + \ x→x=50$$ 30- Choice C is correct The correct answer is $$\frac{5}{2}$$The value of $$y$$ in the $$x-$$intercept of a line is zero. Then:$$y=0→2 \ x \ - \ 2 \ (0)=5→2 \ x=5→x=\frac{5}{2}$$then, $$x-$$intercept of the line is $$\frac{5}{2}$$ 31- Choice A is correct The correct answer is $$4$$ cmThe sum of the lengths of any two sides of triangle is greater than the length of the third side, therefore the greatest possible value of the biggest side equal to $$4$$ cm.$$4 \ < \ 6$$ 32- Choice B is correct The correct answer is $$2$$$$(x \ - \ 2)^3=27→$$ Find the third root of both sides. Then:$$x \ - \ 2=3→x=5$$$$→(x \ - \ 4) \ (x \ - \ 3)=(5 \ - \ 4) \ (5 \ - \ 3)=(1) \ (2)=2$$ 33- Choice B is correct The correct answer is $$31,752$$Number of Mathematics book: $$0.3 \ × \ 840=252$$Number of English book: $$0.15 \ × \ 840=126$$Product of number of Mathematics and number of English books:$$252 \ × \ 126=31,752$$ 34- Choice D is correct The correct answer is $$108^\circ, 45^\circ$$The angle $$α$$ is: $$0.3 \ × \ 360=108^\circ$$The angle $$β$$ is: $$0.15 \ × \ 360=54^\circ$$ 35- Choice B is correct The correct answer is $$120$$According to the chart, $$50\%$$ of the books are in the Mathematics and Chemistry sections. Therefore, there are $$420$$ books in these two sections.$$0.50 \ × \ 840 = 420$$$$\gamma \ + \ \alpha=420$$, and $$\gamma=\frac{2}{5} \ \alpha$$Replace $$\gamma$$ by $$\frac{2}{5} \ \alpha$$ in the first equation.$$\gamma \ + \ \alpha=420→\frac{2}{5} \ \alpha \ + \ \alpha=420→\frac{7}{5} \ \alpha=420→$$ multiply both sides by $$\frac{5}{7}$$$$(\frac{5}{7}) \ \frac{7}{5} \ \alpha=420 \ × \ (\frac{5}{7})→\alpha=\frac{420 \ × \ 5}{7}=300$$$$\alpha=300→\gamma=\frac{2}{5} \ \alpha→\gamma=\frac{2}{5} \ × \ 300=120$$There are $$120$$ books in the Chemistry section. 36- Choice A is correct The correct answer is $$𝐼 \ > \ 2000 \ x \ + \ 24000$$Let $$x$$ be the number of years.Therefore, $$2,000$$ per year equals $$2,000 \ x$$. Starting from $$24,000$$ annual salary means you should add that amount to $$2,000 \ x$$. Income more than that is:$$𝐼 \ > \ 2000 \ x \ + \ 24000$$ 37- Choice C is correct The correct answer is $$\frac{100 \ x \ + \ 800}{x}$$The amount of money for $$x$$ bookshelf is: $$100 \ x$$Then, the total cost of all bookshelves is equal to: $$100 \ x \ + \ 800$$The total cost, in dollar, per bookshelf is: $$\frac{Total \ cost}{number \ of \ items}=\frac{100 \ x \ + \ 800}{x}$$ 38- Choice C is correct The correct answer is $$0$$$$\sqrt{x}=4→x=16$$then; $$\sqrt{x} \ - \ 7=\sqrt{16} \ - \ 7=4 \ - \ 7=- \ 3$$ and $$\sqrt{x \ - \ 7}=\sqrt{16 \ - \ 7}=\sqrt{9}=3$$Then: $$(\sqrt{x \ - \ 7}) \ + \ (\sqrt{x \ - \ 7})=3 \ + \ (- \ 3)=0$$ 39- Choice B is correct The correct answer is $$25$$The angles on a straight line add up to $$180$$ degrees. Then:$$x \ + \ 25 \ + \ y \ + \ 2 \ x \ + \ y=180$$Then, $$3 \ x \ + \ 2 \ y=180 \ - \ 25→3 \ (35) \ + \ 2 \ y=155$$$$→2 \ y=155 \ - \ 105=50→y=25$$ 40- Choice B is correct The correct answer is $$10 \ π$$The distance of A to B on the coordinate plane is: $$\sqrt{(x_{1} \ - \ x_{2} )^2 \ + \ (y_{1} \ - \ y_{2} )^2 }= \sqrt{(10 \ - \ 4)^2 \ + \ (11 \ - \ 3)^2 }=\sqrt{6^2 \ + \ 8^2}$$$$=\sqrt{36 \ + \ 64}=\sqrt{100}=10$$The diameter of the circle is $$10$$ and the radius of the circle is $$5$$.Then: the circumference of the circle is: $$2 \ π \ r=2 \ π \ (5)=10 \ π$$ 41- Choice C is correct The correct answer is $$37$$Square root of $$16$$ is $$\sqrt{16}=4 \ < \ 6$$Square root of $$25$$ is $$\sqrt{25}=5\ < \ 6$$Square root of $$37$$ is $$\sqrt{37}=\sqrt{36 \ + \ 1} \ > \ \sqrt{36}=6$$Square root of $$49$$ is $$\sqrt{49}=7 \ > \ 6$$Since, $$\sqrt{37} \ < \ \sqrt{49}$$, then the answer is C. 42- Choice C is correct The correct answer is $$46$$ cmThe area of the trapezoid is: Area $$=\frac{1}{2} \ h \ (b_{1} \ + \ b_{2} )=\frac{1}{2} \ (x) \ (13 \ + \ 8)=126$$$$→10.5 \ x=126→x=12$$$$y=\sqrt{5^2 \ + \ 12^2}=\sqrt{25 \ + \ 144}=\sqrt{169}=13$$The perimeter of the trapezoid is: $$12 \ + \ 13 \ + \ 8 \ + \ 13=46$$ 43- Choice A is correct The correct answer is $$x \ ≥ \ 5 \ ∪ \ x \ ≤ \ − \ 1$$$$|x \ - \ 2| \ ≥ \ 3$$Then:$$x \ - \ 2 \ ≥ \ 3→x \ ≥ \ 3 \ + \ 2→x \ ≥ \ 5$$Or$$x \ - \ 2 \ ≤ \ - \ 3→x \ ≤ \ - \ 3 \ + \ 2→x \ ≤ \ - \ 1$$Then, the solution is: $$x \ ≥ \ 5 \ ∪ \ x \ ≤ \ − \ 1$$ 44- Choice B is correct The correct answer is $$50$$Since, E is the midpoint of AB, then the area of all triangles DAE, DEF, CFE and CBE are equal.Let $$x$$ be the area of one of the triangle, Then: $$4 \ x=100→x=25$$The area of DEC $$=2 \ x=2 \ (25)=50$$ 45- Choice A is correct The correct answer is $$− \ 8 \ < \ x \ < \ − \ 5$$$$13 \ < \ - \ 3 \ x \ - \ 2 \ < \ 22→$$ Add $$2$$ to all sides.$$13 \ + \ 2 \ < \ - \ 3 \ x \ - \ 2 \ + \ 2 \ < \ 22 \ + \ 2$$$$→15 \ < \ - \ 3 \ x \ < \ 24→$$ Divide all sides by $$- \ 3$$.(Remember that when you divide all sides of an inequality by a negative number, the inequality sing will be swapped. $$<$$ becomes $$>$$)$$\frac{15}{- \ 3} \ > \ \frac{- \ 3 \ x}{- \ 3} \ > \ \frac{24}{- \ 3}$$$$- \ 8 \ < \ x \ < \ - \ 5$$ 46- Choice C is correct The correct answer is $$6.93$$Based on triangle similarity theorem: $$\frac{a}{a \ + \ b}=\frac{c}{3}→c=\frac{3 \ a}{a \ + \ b}=\frac{3 \ \sqrt{3}}{3 \ \sqrt{3}}=1→$$ area of the shaded region is: $$(\frac{c \ + \ 3}{2}) \ (b)=4 \ \sqrt{3}$$Round $$4 \ \sqrt{3}$$ to the nearest hundredths place gives $$6.93$$. 47- Choice B is correct The correct answer is $$0.94$$sin⁡$$(A)=\frac{opposite}{hypotenuse}=\frac{1}{3}⇒$$ We have the following triangle, then:$$c=\sqrt{3^2 \ - \ 1^2}=\sqrt{9 \ - \ 1}=\sqrt{8}$$cos⁡$$(A)=\frac{\sqrt{8}}{3}$$Rounding the answer to the nearest hundredths, gives $$0.94$$ 48- Choice C is correct The correct answer is $$80$$One liter $$=1000$$ cm$$^3→ 6$$ liters $$= 6,000$$ cm$$^3$$$$6,000=15 \ × \ 5 \ × \ h→h=\frac{6,000}{75}=80$$ cm 49- Choice C is correct The correct answer is $$12$$Based on corresponding members of each matrix, write two equations:$$\begin{cases}2 \ x=x \ + \ 3 \ y \ - \ 5\\4 \ x = 2 \ y \ - \ 10\end{cases} \rightarrow \begin{cases}x \ - \ 3 \ y= - \ 5\\4 \ x \ - \ 2 \ y =10\end{cases}$$Multiply first equation by $$(- \ 4)$$, then:$$\begin{cases}- \ 4 \ x \ + \ 12 \ y =20\\4 \ x \ - \ 2 \ y =10\end{cases}$$ Add two equations:$$→10 \ y=30→y=3→x=4→ x \ × \ y=12$$

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