## Full Length SHSAT Mathematical Practice Test

If you want to prepare for the SHSAT Mathematical Practice Test? It’s time to taking a Full-length SHSAT Mathematical Practice Test. It is the best way to simulate test day. To challenge your skills and simulate the full length SHSAT Mathematical Practice Test day experience, score your tests using the answer keys.

### The Most Comprehensive SHSAT Math Preparation Bundle

$76.99$39.99
48% Off*

Includes SHSAT Math Prep Books, Workbooks, and Practice Tests

## SHSAT Mathematical Reasoning Practice Test 42019

Two Parts

Total number of questions: 46

Part 1 (Non-Calculator): 5 questions

Part 2 (Calculator): 41 questions

Total time for two Part: 115 Minutes

SHSAT Mathematical Reasoning

Practice Test 4

Part 1 (Non-Calculator)

5 questions

Total time for two parts (Non-Calculator, and Calculator parts): 115 Minutes

## You may NOT use a calculator on this part.

1- What is the slope of a line that is perpendicular to the line $$8 \ x \ - \ y=2$$?
(A) $$− \ \frac{1}{8}$$
(B) $$− \ \frac{1}{4}$$
(C) $$−\ 8$$
(D) $$8$$
2- What is the value of the expression $$4 \ (x \ - \ 5 \ y) \ + \ (6 \ - \ x)^2$$ when $$x=2$$ and $$y= - \ 4$$?
(A) $$- \ 104$$
(B) $$104$$
(C) $$103$$
(D) $$- \ 103$$
3- $$\left[ \ 5 \ × \ (18) \ - \ 57 \ \right] \ – \ (– \ 12) \ + \ \left[ \ 5 \ × \ 9 \ \right] \ ÷ \ 2=$$?
(A) 67.5
(B) 67.5
(C) 67.5
4- What is the product of all possible values of $$x$$ in the following equation?
$$|2\ x \ - \ 8|=26$$
(A) $$152$$
(B) $$- \ 152$$
(C) $$- \ 154$$
(D) $$- \ 153$$
5- A tree $$46$$ feet tall casts a shadow $$22$$ feet long. Alex  is $$12$$ feet tall. How long is Alex’s shadow?
(A) $$5.73$$ ft
(B) $$5.72$$ ft
(C) $$3.72$$ ft
(D) $$4.72$$ ft

Mathematical Reasoning

Practice Test 4

Part 2 (Calculator)

41 questions

Total time for two parts (Non-Calculator, and Calculator parts): 115 Minutes

You may use a calculator on this part.

6- Which of the following graphs represents the compound inequality $$- \ 2 \ \leq \ 7 \ x \ - \ 2 \ < \ 12$$?
(A)
(B)
(C)
(D)
7- Simplify the expression.
$$(6 \ x^2 \ - \ 7 \ x^4 \ + \ 6 \ x^3 ) \ - \ (3\ x^5 \ - \ 9 \ x^2 \ + \ 5 \ x^3 )$$
(A) $$-\ 3 \ x^5 \ + \ 7 \ x^4 \ + \ 15 \ x^2\ + \ x^3$$
(B) $$-\ 3 \ x^5 \ + \ 7 \ x^4 \ + \ 15 \ x^2\ - \ x^3$$
(C) $$-\ 3 \ x^5 \ - \ 7 \ x^4 \ + \ 15 \ x^2\ + \ x^3$$
(D) $$-\ 3 \ x^5 \ + \ 7 \ x^4 \ + \ 15 \ x^2\ - \ x^3$$
8- What is the value of $$7^3$$?
(A) 343
(B) 343.0
(C) 343
9- What is the volume of a box with the following dimensions?
Hight $$= 6$$ cm       Width $$= 8$$ cm       Length $$= 2$$ cm
(A) $$94$$ cm$$^3$$
(B) $$90$$ cm$$^3$$
(C) $$92$$ cm$$^3$$
(D) $$96$$ cm$$^3$$
10- What is the perimeter of a square in centimeters that has an area of $$387.3$$ cm$$^2$$?
(A) 78.4
(B) 78.4
(C) 78.4
11- In two successive years, the population of a town is increased by $$25\%$$ and $$35\%$$. What percent of the population is increased after two years?
(A) $$68\%$$
(B) $$48\%$$
(C) $$0.087\%$$
(D) $$87.5\%$$
12- Which of the following shows the numbers in descending order?
$$\frac{4}{3 }, 0.48, 55\%, \frac{2}{5}$$
(A) $$\frac{2}{5}, 55\%, 0.48, \frac{4}{3}$$
(B) $$\frac{4}{3}, 55\%, 0.48, \frac{2}{5}$$
(C) $$\frac{4}{3}, 0.48, 55\%, \frac{2}{5}$$
(D) $$\frac{2}{5}, 0.48, 55\%, \frac{4}{3}$$
13- Last week $$45,000$$ fans attended a football match. This week four times as many bought tickets, but one Fifth of them cancelled their tickets. How many are attending this week?
(A) $$142,000$$
(B) $$140,000$$
(C) $$144,000$$
(D) $$143,000$$
14- Two dice are thrown simultaneously, what is the probability of getting a sum of $$4$$ or $$5$$?
(A)  $$\frac{1}{6}$$
(B)  $$\frac{1}{4}$$
(C)  $$\frac{1}{3}$$
(D)  $$\frac{1}{2}$$
15- The perimeter of the trapezoid below is $$54$$ cm. What is its area?
(A) $$36$$ cm$$^2$$
(B) $$18$$ cm$$^2$$
(C) $$32$$ cm$$^2$$
(D) $$180$$ cm$$^2$$
16- The mean of $$60$$ test scores was calculated as $$68$$. But, it turned out that one of the scores was misread as $$32$$ but it was $$23$$. What is the correct mean of the test scores?
(A) $$68.8$$
(B) $$67.8$$
(C) $$78.8$$
(D) $$98.8$$
17- In a stadium the ratio of home fans to visiting fans in a crowd is $$9:6$$. Which of the following could be the total number of fans in the stadium? (Select one or more answer choices)
(A) $$12,324$$
(B) $$78,120$$
(C) $$42,326$$
(D) $$33,000$$
(E) $$66,812$$
18- A swimming pool holds $$3,000$$ cubic feet of water. The swimming pool is $$20$$ feet long and $$25$$ feet wide. How deep is the swimming pool?
(A) 6
(B) 6
(C) 6.0
19-  What is the area of a square whose diagonal is $$6$$?
(A) $$2 \ \sqrt{18}$$
(B) $$\sqrt{18}$$
(C) $$36$$
(D) $${18}$$
20- Anita’s trick–or–treat bag contains $$11$$ pieces of chocolate, $$8$$ suckers, $$16$$ pieces of gum, $$13$$ pieces of licorice. If she randomly pulls a piece of candy from her bag, what is the probability of her pulling out a piece of sucker?
(A) $$\frac{1}{7}$$
(B) $$\frac{1}{6}$$
(C) $$\frac{1}{8}$$
(D) $$\frac{1}{2}$$
21- Mr. Carlos family are choosing a menu for their reception. They have $$7$$ choices of appetizers, $$3$$ choices of entrees, $$2$$ choices of cake. How many different menu combinations are possible for them to choose?
(A) $$42$$
(B) $$40$$
(C) $$44$$
(D) $$34$$
22- A card is drawn at random from a standard $$64–$$card deck, what is the probability that the card is of Hearts? (The deck includes $$14$$ of each suit clubs, diamonds, hearts, and spades)
(A) $$\frac{1}{4}$$
(B) $$\frac{5}{4}$$
(C) $$\frac{3}{2}$$
(D) $$\frac{3}{4}$$
23- The average of $$4$$ numbers is $$31$$. The average of $$3$$ of those numbers is $$23$$. What is the average of the other four   numbers?
(A) $$24$$
(B) $$17$$
(C) $$18$$
(D) $$20$$
24- Which of the following points lies on the line $$4\ x \ - \ y=8$$? (Select one or more answer choices)
(A) $$(- \ 2,3)$$
(B) $$(1,2)$$
(C) $$(- \ 1,3)$$
(D) $$(- \ 3,4)$$
(E) $$(4,8)$$
25- The perimeter of a rectangular yard is $$56$$ meters. What is its length if its width is three times bigger its length?
(A) $$8$$ meters
(B) $$10$$ meters
(C) $$6$$ meters
(D) $$7$$ meters
26- The average of three numbers is $$12$$. If a fouth  number that is greater than $$52$$ is added, then, which of the following could be the new average? (Select one or more answer choices)
(A) $$16$$
(B) $$25$$
(C) $$21$$
(D) $$18$$
(E) $$30$$
27- What is the value of $$x$$ in the following system of equations?
$$3 \ x \ + \ 6\ y=18$$
$$x \ - \ 4 \ y=\ - \ 6$$
(A) $$2$$
(B) $$6$$
(C) $$10$$
(D) $$-\ 2$$
28- Mr. nik saves $$3,000$$ out of his monthly family income of $$45,000$$. What fractional part of his income does he save?
(A) $$\frac{1}{5}$$
(B) $$\frac{1}{4}$$
(C) $$\frac{1}{10}$$
(D) $$\frac{1}{8}$$

### SHSAT Math for Beginners

$24.99$17.99
28% Off*

The Ultimate Step by Step Guide to Preparing for the SHSAT Math Test

29- The diagonal of a rectangle is $$5$$ inches long and the height of the rectangle is $$3$$ inches. What is the perimeter of the rectangle in inches?
(A) 14
(B) 14
(C) 14.00
30- What is the surface area of the cylinder below?
(A) $$360 \ π$$ in$$^2$$
(B) $$72 \ π$$ in$$^2$$
(C) $$720 \ π$$ in$$^2$$
(D) $$36 \ π$$ in$$^2$$
31- The ratio of boys and girls in a class is $$6:8$$. If there are $$56$$ students in the class, how many more boys should be enrolled to make the ratio $$1:1$$?
(A) $$10$$
(B) $$8$$
(C) $$6$$
(D) $$4$$
32- Alex needs an $$82\%$$ average in his writing class to pass. On his first $$4$$ exams, he earned scores of $$62\%, 95\%, 78\%$$, and $$90\%$$. What is the minimum score Jason can earn on his fifth and final test to pass?
(A) 85%
(B) 85
(C) 85
33- Simplify: $$5 \ x^4 \ y^6 \ (4 \ x^3 \ y)^2=$$
(A) $$80 \ x^{8} \ y^8$$
(B) $$80 \ x^{9} \ y^8$$
(C) $$80 \ x^{10} \ y^8$$
(D) $$40 \ x^{10} \ y^6$$
34- The square of a number is $$\frac{16}{49}$$. What is the cube of that number?
(A) $$\frac{64}{343}$$
(B) $$\frac{12}{343}$$
(C) $$\frac{12}{21}$$
(D) $$\frac{4}{21}$$
35- What is the value of $$x$$ in the following equation?
$$\frac{4}{5} \ x \ + \ \frac{1}{3}= \frac{1}{5}$$
(A) $$\frac{4}{3}$$
(B) $$\frac{2}{3}$$
(C) $$\frac{1}{3}$$
(D) $$\frac{7}{3}$$
36- What is the median of these numbers? $$3, 27, 14, 30, 85, 46, 52$$
(A) $$27$$
(B) $$52$$
(C) $$12$$
(D) $$30$$
37- A bank is offering $$0.5\%$$ simple interest on a savings account. If you deposit $$25,000$$, how much interest will you earn in five years?
(A) $$6250$$
(B) $$6.25$$
(C) $$625$$
(D) $$62.5$$
38- A cruise line ship left Port A and traveled $$30$$ miles due west and then $$40$$ miles due north. At this point, what is the shortest distance from the cruise to port A in miles?
(A) 50
(B) 50
(C) 50
39- The circle graph below shows all Mr. Jones’s expenses for last month. If he spent $$264$$ on his car, how much did he spend for his other?
(A) $$336$$
(B) $$335$$
(C) $$334$$
(D) $$332$$
40- If $$75\%$$ of a number is $$48$$, then what is the $$25\%$$ of that number?
(A) $$64$$
(B) $$48$$
(C) $$18$$
(D) $$16$$
41- Mia  is $$14$$ miles ahead of Ella running at $$6$$ miles per hour and Joe is running at the speed of $$8$$ miles per hour. How long does it take Joe to catch Jason?
(A) $$6$$ hours
(B) $$2$$ hours
(C) $$7$$ hours
(D) $$8$$ hours
42- What is the equivalent temperature of $$100^°$$F in Celsius?
C $$= \frac{7}{8}$$ (F $$– \ 36$$)
(A) $$56$$
(B) $$64$$
(C) $$49$$
(D) $$36$$
43- $$80$$ students took an exam and $$12$$ of them failed. What percent of the students passed the exam?
(A) $$15\%$$
(B) $$85\%$$
(C) $$75\%$$
(D) $$80\%$$
44- If $$25\%$$ of a number is $$14$$, what is the number?
(A) $$36$$
(B) $$56$$
(C) $$64$$
(D) $$49$$
45- A football team had $$18,000$$ to spend on supplies. The team spent $$11,000$$ on new balls. New sport shoes cost $$100$$ each. Which of the following inequalities represent the number of new shoes the team can purchase?
(A) $$100 \ x \ - \ 11,000 \ ≤ \ 18,000$$
(B) $$- \ 100 \ x \ - \ 11,000 \ ≤ \ 18,000$$
(C) $$100 \ x \ + \ 11,000 \ ≤ \ 18,000$$
(D) $$100 \ x \ + \ 11,000 \ \geq \ 18,000$$
46- What is the slope of the line: $$3 \ x \ - \ y=9$$
(A) 3
(B) 3
(C) 3
 1- Choice A is correct The correct answer is $$− \ \frac{1}{8}$$The equation of a line in slope intercept form is: $$y=m \ x \ + \ b$$Solve for $$y$$.$$8 \ x \ - \ y=2→ \ - \ y= \ - \ 8 \ x \ + \ 2$$Divide both sides by $$(- \ 1)$$.Then: $$- \ y= \ - \ 8 \ x \ + \ 2→y=8 \ x \ - \ 2$$The slope of this line is $$8$$.The product of the slopes of two perpendicular lines is $$- \ 1$$. Therefore, the slope of a line that is perpendicular to this line is:$$m_{1} \ × \ m_{2} = \ - \ 1 ⇒ 8 \ × \ m_{2} = \ - \ 1 ⇒ m_{2} = \frac{- \ 1}{8}= \ - \ \frac{1}{8}$$ 2- Choice B is correct The correct answer is $$104$$Plug in the value of $$x$$ and $$y$$.$$4 \ (x \ - \ 5 \ y) \ + \ (6 \ - \ x)^2$$ when $$x=2$$ and $$y= - \ 4$$$$x=2$$ and $$y= - \ 4$$$$4 \ (x \ - \ 5 \ y) \ + \ (6 \ - \ x)^2=4 \ (2 \ - \ 5 \ (- \ 4)) \ + \ (6 \ - \ 2)^2=4 \ (2 \ + \ 20) \ + \ ( 4)^2 = 88\ + \ 16=104$$ 3- Choice C is correct The correct answer is $$67.5$$Use PEMDAS (order of operation):$$\left[ 5 \ × \ (18) \ - \ 57 \ \right] \ – \ (– \ 12) \ + \ \left[ \ 5 \ × \ 9 \ \right] \ ÷ \ 2=$$$$\left[ 90 \ - \ 57 \ \right] \ + \ 12 \ + \ 45 \ ÷ \ 2=$$$$33\ + \ 12 \ + \ 22.5 = \ 67.5$$ 4- Choice D is correct The correct answer is $$− \ 153$$To solve absolute values equations, write two equations. $$2 \ x \ - \ 8$$ can equal positive $$26$$, or negative $$26$$. Therefore, $$2 \ x \ - \ 8= 26 ⇒ 2 \ x=34⇒ x=17$$$$2 \ x \ - \ 8= - \ 26 ⇒ 2 \ x= - \ 26 \ + \ 8= - \ 18⇒ x= - \ 9$$Find the product of solutions: $$- \ 9 \ × \ 17= - \ 153$$ 5- Choice A is correct The correct answer is $$5.73$$ ftWrite a proportion and solve for the missing number.$$\frac{46}{22} = \frac{12}{x}→ 46\ x=12\ × \ 22=264$$$$46 \ x=264 →x=\frac{246}{46}=5.73$$ 5- Choice A is correct The correct answer is $$5.73$$ ftWrite a proportion and solve for the missing number.$$\frac{46}{22} = \frac{12}{x}→ 46\ x=12\ × \ 22=264$$$$46 \ x=264 →x=\frac{246}{46}=5.73$$ 6- Choice C is correct Solve for $$x$$.$$- \ 2 \ ≤ \ 7 \ x \ - \ 2 \ < \ 12 ⇒$$ (add $$4$$ all sides)$$- \ 2 \ + \ 2 \ ≤ \ 7 \ x \ - \ 2 \ + \ 2 \ < \ 12\ + \ 2 ⇒$$ $$0 \ ≤ \ 7 \ x \ < \ 14 ⇒$$ (divide all sides by $$7$$) $$0 \ ≤ \ x \ < \ 2$$$$x$$ is between $$0$$ and $$2$$.Choice B represent this inequality. 7- Choice A is correct The correct answer is $$-\ 3 \ x^5 \ + \ 7 \ x^4 \ + \ 15 \ x^2\ + \ x^3$$Simplify and combine like terms.$$(6 \ x^2 \ - \ 7 \ x^4 \ + \ 6 \ x^3 ) \ - \ (3 \ x^5 \ - \ 9 \ x^2 \ + \ 5 \ x^3 ) ⇒$$$$(6 \ x^2 \ - \ 7 \ x^4 \ + \ 7 \ x^3 ) \ - \ 3 \ x^5 \ + \ 9 \ x^2 \ - \ 5 \ x^3⇒$$$$-\ 3 \ x^5 \ + \ 7 \ x^4 \ + \ 15 \ x^2\ + \ x^3$$ 8- Choice C is correct The correct answer is $$343$$$$7^3 = 7 \ × \ 7 \ × \ 7 = 343$$ 9- Choice D is correct The correct answer is $$96$$ cm$$^3$$Volume of a box $$=$$ length $$×$$ width $$×$$ height $$= 6 \ × \ 8 \ × \ 2 = 96$$ 10- Choice C is correct The correct answer is $$78.4$$The area of the square is $$387.3$$.Therefore, the side of the square is square root of the area.$$\sqrt{387.3}=19.6$$Four times the side of the square is the perimeter:$$4 \ × \ 19.6 = 78.4$$ 11- Choice A is correct The correct answer is $$68\%$$the population is increased by $$25\%$$ and $$35\%$$.$$15\%$$ increase changes the population to $$125\%$$ of original population.For the second increase, multiply the result by $$135\%$$.$$(1.25) \ × \ (1.35) =168\%$$$$68$$ percent of the population is increased after two years. 12- Choice B is correct The correct answer is $$\frac{4}{3}, 55\%, 0.48, \frac{2}{5}$$Change the numbers to decimal and then compare.$$\frac{4}{3} = 1.333$$…$$0.48$$$$55\% = 0.55$$$$\frac{2}{5} = 0.4$$Therefore$$\frac{4}{3} \ < \ 55\% \ < \ 0.48 \ < \ \frac{ 2}{5}$$ 13- Choice C is correct The correct answer is $$144,000$$Three times of $$45,000$$ is $$180,000$$.One sixth of them cancelled their tickets.One sixth of $$180,000$$ equals $$36,000\ (\frac{1}{5} \ × \ 180000 = 36000)$$. $$144,000 \ (180000 \ – \ 36000 = 144000)$$ fans are attending this week 14- Choice A is correct The correct answer is $$\frac{1}{6}$$To get a sum of $$5$$ for two dice, we can get $$4$$ different options:$$(1, 4), (4, 1), (3, 2), (2, 3)$$To get a sum of $$4$$ for two dice, we can get $$2$$ different options:$$(2, 2), (1, 3)$$Therefore, there are $$6$$ options to get the sum of $$5$$ or $$4$$. Since, we have $$6 \ × \ 6 = 36$$ total options, the probability of getting a sum of $$5$$ and $$4$$ is $$6$$ out of $$36$$ or $$\frac{1}{6}$$. 15- Choice D is correct The correct answer is $$180$$ cm$$^2$$The perimeter of the trapezoid is $$36$$ cm.Therefore, the missing side (height) is $$= 54 \ – \ 6 \ – \ 10 \ – \ 4 = 36$$Area of a trapezoid: A $$= \frac{1}{2} \ h \ (b_1 \ + \ b_2) = \frac{1}{2} \ (36) \ (4 \ + \ 6) = 180$$ 16- Choice B is correct The correct answer is $$67.8$$average (mean) $$= \frac{sum \ of \ terms}{number \ of \ terms} ⇒$$$$60= \frac{sum \ of \ terms}{68} ⇒$$ sum $$= 60\ × \ 68 = 4080$$The difference of $$32$$ and $$23$$ is $$10$$.Therefore, $$10$$ should be subtracted from the sum.$$4080 \ – \ 10 = 4070$$mean $$= \frac{sum \ of \ terms}{number \ of \ terms} ⇒$$mean $$= \frac{4070}{60} = 67.8$$ 17- Choice D is correct The correct answer is $$33,000$$ and $$78,120$$(If you selected $$3$$ choices and $$2$$ of them are correct, then you get one point. If you answered $$2$$ or $$3$$ choices and one of them is correct, you receive one point. If you selected more than $$3$$ choices, you won’t get any point for this question.)In the stadium the ratio of home fans to visiting fans in a crowd is $$9:6$$.Therefore, total number of fans must be divisible by $$15: \ 9 \ + \ 6 = 15$$. Let’s review the choices: ☐A. $$12,324$$:      $$12,324 \ ÷ \ 15 = 821.6$$☐B. $$78,120$$:      $$16,788 \ ÷ \ 15 = 5,208$$☐C. $$42,326$$:      $$42,326 \ ÷ \ 15 =2,821.7$$☐D. $$33,000$$:      $$33,000 \ ÷ \ 15 = 22,000$$☐E. $$66,812$$:      $$66,812 \ ÷ \ 15 =4,454.1333$$Only choices D and B when divided by $$15$$ result a whole number. 18- Choice C is correct The correct answer is $$6$$Use formula of rectangle prism volume.V $$=$$ (length) (width) (height) $$⇒ 4000 = (20) \ (25)$$ (height) $$⇒$$ height $$= 3000 \ ÷ \ 500 = 6$$ 19- Choice D is correct The correct answer is $$18$$The diagonal of the square is $$6$$.Let $$x$$ be the side. Use Pythagorean Theorem: $$a^2 \ + \ b^2 = c^2$$$$x^2 \ + \ x^2 = 6^2 ⇒$$$$2 \ x^2 = 6^2 ⇒$$$$2 \ x^2 = 36 ⇒$$$$x^2 = 18 ⇒$$$$x= \sqrt{18}$$The area of the square is:$$\sqrt{18} \ × \ \sqrt{18} =18$$ 20- Choice B is correct The correct answer is $$\frac{1}{6}$$Probability $$= \frac{number \ of \ desired \ outcomes}{number \ \ of \ total \ outcomes} = \frac{8}{11 \ + \ 8 \ + \ 16 \ + \ 13} = \frac{8}{48} = \frac{1}{6}$$ 21- Choice A is correct The correct answer is $$42$$To find the number of possible outfit combinations, multiply number of options for each factor:$$7 \ × \ 3 \ × \ 2= 42$$ 22- Choice D is correct The correct answer is $$\frac{3}{4}$$The probability of choosing a Hearts is $$\frac{14}{64}=\frac{3}{4}$$ 23- Choice B is correct The correct answer is $$17$$average $$= \frac{sum \ of \ terms}{number \ of \ terms} ⇒$$ (average of $$4$$ numbers) $$31 = \frac{sum \ of \ numbers}{4} ⇒$$sum of $$4$$ numbers is $$31 \ × \ 4 = 124$$(average of $$3$$ numbers) $$23 = \frac{sum \ of \ numbers}{3} ⇒$$ sum of $$3$$ numbers is $$23 \ × \ 3 = 56$$sum of $$4$$ numbers $$–$$ sum of $$3$$ numbers $$=$$ sum of $$4$$ numbers$$124 \ – \ 56 = 68$$, average of $$4$$ numbers $$= \frac{68}{4 }= 17$$ 24- Choice E is correct The correct answer is $$(− \ 2,3)$$ and $$(0, 2)$$(If you selected $$3$$ choices and $$2$$ of them are correct, then you get one point.If you answered $$2$$ or $$3$$ choices and one of them is correct, you receive one point.If you selected more than $$3$$ choices, you won’t get any point for this question.)$$4\ x \ - \ y=8$$. Plug in the values of $$x$$ and $$y$$ from choices provided. Then:☐A. $$(- \ 2,3)$$:      $$4 \ x \ - \ y=8→ \ - \ 4 \ (2)\ - \ 3 =8→ \ - \ 8 \ - \ 3=11$$ This is NOT  true!☐B. $$(1,2)$$:          $$4 \ x \ -\ y=8→4\ (1) \ - \ 2 =8→4 \ - \ 2=2$$ This is NOT true!☐C. $$(- \ 1,3)$$:      $$4 \ x \ - \ y=8→ \ 4\ (- \ 1) \ - \ 3=4→ \ - \ 4 \ - \ 3=- \ 7$$ This is NOT true!☐D. $$(- \ 3,4)$$:     $$4 \ x \ - \ y=8→ \ 4\ (- \ 3) \ - \ 4=8→ \ - \ 12 \ - \ 4=8$$ This is  true!☐E. $$(4,8)$$:         $$4 \ x \ - \ y=8→4 \ (4) \ - \ 8 =8→16 \ - \ 8=8$$ This is true! 25- Choice A is correct The correct answer is $$8$$ metersThe width of the rectangle is twice its length.Let $$x$$ be the length. Then, width $$=3 \ x$$Perimeter of the rectangle is $$2$$ (width $$+$$ length) $$= 2 \ (3 \ x \ + \ x)=56 ⇒ 7\ x=56 ⇒ x=8$$Length of the rectangle is $$8$$ meters. 26- Choice E is correct The correct answer is $$30$$ and $$25$$(If you selected $$3$$ choices and $$2$$ of them are correct, then you get one point.If you answered $$2$$ or $$3$$ choices and one of them is correct, you receive one point.If you selected more than $$3$$ choices, you won’t get any point for this question.)First, find the sum of five numbers. average $$= \frac{sum \ of \ terms}{number \ of \ terms} ⇒$$$$12 = \frac{sum \ of \ 3\ numbers}{3 }⇒$$sum of $$3$$ numbers $$= 12 \ × \ 3 = 36$$The sum of $$3$$ numbers is $$36$$.If a fouth number that is greater than $$52$$ is added to these numbers, then the sum of $$4$$ numbers must be greater than $$88$$. $$36 \ + \ 52 = 88$$If the number was $$52$$, then the average of the numbers is: average $$= \frac{sum \ of \ terms}{number \ of \ terms} = \frac{88}{4} = 22$$Since the number is bigger than $$52$$.Then, the average of six numbers must be greater than $$22$$. Choices B and E are greater than $$22$$. 27- Choice A is correct The correct answer is $$2$$Solving Systems of Equations by EliminationMultiply the first equation by $$(– \ 3)$$, then add it to the second equation.\cfrac{\begin{align} \ 3 \ x \ + \ 6 \ y \ = \ 18 \\- \ 3 \ ( x \ - \ 4 \ y \ = \ - \ 6 )\end{align}}{\cfrac{\begin{align} 3 \ x \ + \ 6\ y \ = 18 \\ -\ 3 \ x \ + \ 12 \ y \ = 18 \end{align}}{{\begin{align} 18\ y \ = 36 \\ ⇒ y \ = \ 2 \end{align}} } } ⇒Plug in the value of $$y$$ into one of the equations and solve for $$x$$.$$3 \ x \ + \ 6 \ (2)= 18 ⇒$$$$3 \ x \ + \ 12= 18 ⇒$$$$3 \ x= 6 ⇒ x= 2$$ 28- Choice C is correct The correct answer is $$\frac{1}{10}$$$$3,000$$ out of $$45,000$$ equals to $$\frac{3000}{45000 }= \frac{1500}{15000} =\frac{1}{10}$$ 29- Choice C is correct The correct answer is $$14$$Let $$x$$ be the width of the rectangle. Use Pythagorean Theorem: $$a^2 \ + \ b^2 = c^2$$$$x^2 \ + \ 3^2 = 5^2 ⇒$$$$x^2 \ + \ 9 = 25 ⇒$$$$x^2 = 25 \ – \ 9 = 16 ⇒ x = 4$$Perimeter of the rectangle $$= 2$$ (length $$+$$ width) $$= 2 \ (3 \ + \ 4) = 2 \ (7) = 14$$ 30- Choice C is correct The correct answer is $$720 \ π$$ in$$^2$$Surface Area of a cylinder $$= 2 \ π \ r \ (r \ + \ h)$$,The radius of the cylinder is $$6 \ (12 \ ÷ \ 2)$$ inches and its height is $$10$$ inches. Therefore, Surface Area of a cylinder $$= 2 \ π \ (6) \ (6 \ + \ 10) = 720 \ π$$ in$$^2$$ 31- Choice B is correct The correct answer is $$8$$The ratio of boy to girls is $$6:8$$.Therefore, there are $$6$$ boys out of $$14$$ students.To find the answer, first divide the total number of students by $$14$$, then multiply the result by $$4$$. $$56 \ ÷ \ 14 = 4 ⇒ 4 \ × \ 6 = 24$$There are $$24$$ boys and $$32 \ (56 \ – \ 24)$$ girls.So, $$8$$ more boys should be enrolled to make the ratio $$1:1$$ 32- Choice C is correct The correct answer is $$85$$Jason needs an $$82\%$$ average to pass for five exams.Therefore, the sum of $$5$$ exams must be at least $$5 \ × \ 82 =410$$The sum of $$4$$ exams is: $$62\ + \ 95 \ + \ 78 \ + \ 90 = 325$$.The minimum score Jason can earn on his fifth and final test to pass is: $$410\ – \ 325 = 85$$ 33- Choice C is correct The correct answer is $$80 \ x^{10} \ y^8$$Simplify: $$5 \ x^4 \ y^6 \ (4 \ x^3 \ y)^2= 5 \ x^4 \ y^6 \ (16 \ x^6 \ y^2 ) = 80 \ x^{10} \ y^8$$ 34- Choice A is correct The correct answer is $$\frac{64}{343}$$The square of a number is $$\frac{16}{49}$$, then the number is the square root of $$\frac{16}{49}$$$$\sqrt{\frac{16}{49}}= \frac{4}{7}$$The cube of the number is: $$(\frac{4}{7})^3 = \frac{64}{343}$$ 35- Choice B is correct The correct answer is $$\frac{2}{3}$$Isolate and solve for $$x$$. $$\frac{4}{5} \ x \ + \ \frac{1}{3}= \frac{1}{5} ⇒$$$$\frac{4}{5} \ x= \frac{1}{5} \ - \ \frac{1}{3} = \frac{8}{15} ⇒$$$$\frac{4}{5} \ x= \frac{8}{15}$$ Multiply both sides by the reciprocal of the coefficient of $$x$$.$$(\frac{5}{4}) \ \frac{4}{5} \ x= \frac{8}{15} \ (\frac{5}{4}) ⇒$$$$x= \frac{8}{12}=\frac{2}{3}$$ 36- Choice D is correct The correct answer is $$30$$Write the numbers in order:$$3, 14, 27, 30, 46, 52, 85$$Median is the number in the middle.So, the median is $$30$$. 37- Choice C is correct The correct answer is $$625$$Use simple interest formula: $$I=prt$$($$I =$$ interest, $$p =$$ principal, $$r =$$ rate, $$t =$$ time)$$I=(25000) \ (0.005) \ (5)=625$$ 38- Choice C is correct The correct answer is $$50$$Use the information provided in the question to draw the shape.Use Pythagorean Theorem: $$a^2 \ + \ b^2 = c^2$$$$40^2 \ + \ 30^2 = c^2 ⇒$$$$1600\ + \ 900 = c^2 ⇒$$$$2500= c^2 ⇒ c = 50$$ 39- Choice A is correct The correct answer is $$336$$Let $$x$$ be all expenses, then:$$\frac{22}{100} \ x=264 →x=\frac{100 \ × \ 264}{22}=1,200$$He spent for his rent:$$\frac{28}{100} \ × \ 1,200=336$$ 40- Choice D is correct The correct answer is $$16$$First, find the number.Let $$x$$ be the number.Write the equation and solve for $$x$$. $$75\%$$ of a number is $$48$$, then: $$0.75\ × \ x=48 ⇒ x=48 \ ÷ \ 0.75=64$$$$25\%$$ of $$64$$ is: $$0.25\ × \ 64 = 16$$ 41- Choice C is correct The correct answer is $$7$$ hoursThe distance between Jason and Joe is $$14$$ miles.Jason running at $$6$$ miles per hour and Joe is running at the speed of $$8$$ miles per hour.Therefore, every hour the distance is $$2$$ miles less. $$14 \ ÷ \ 2 = 7$$ 42- Choice A is correct The correct answer is $$56$$Plug in $$100$$ for F and then solve for C.C $$= \frac{7}{8}$$ (F $$– \ 36) ⇒$$ C $$= \frac{7}{8} (100 \ – \ 36) ⇒$$ C $$= \frac{7}{8} \ (64) = 56$$ 43- Choice B is correct The correct answer is $$85\%$$The failing rate is $$12$$ out of $$80 = \frac{12}{80}$$Change the fraction to percent: $$\frac{12}{80} \ × \ 100\%=15%$$$$15$$ percent of students failed.Therefore, $$85$$ percent of students passed the exam. 44- Choice B is correct The correct answer is $$56$$Let $$x$$ be the number.Write the equation and solve for $$x$$. $$25\%$$ of $$x=14⇒ 0.25 \ x=14 ⇒ x=14 \ ÷ \ 0.25=56$$ 45- Choice C is correct The correct answer is $$100 \ x \ + \ 11,000 \ ≤ \ 18,000$$Let $$x$$ be the number of new shoes the team can purchase.Therefore, the team can purchase $$100 \ x$$.The team had $$18,000$$ and spent $$11,000$$.Now the team can spend on new shoes $$7,000$$ at most. Now, write the inequality: $$100 \ x \ + \ 11,000 \ ≤ \ 18,000$$ 46- Choice C is correct The correct answer is $$3$$Solve for $$y$$.$$3 \ x \ - \ y=9 ⇒ -\ y=9 \ - \ 3 \ x ⇒ y=3 \ x \ - \ 9$$The slope of the line is $$3$$.

### The Most Comprehensive SHSAT Math Preparation Bundle

$76.99$39.99
48% Off*

Includes SHSAT Math Prep Books, Workbooks, and Practice Tests

### Practice Test 1

Simulate test day with an official practice test. Then, score your test. The answers come with explanations so you can learn from your mistakes.

### Practice Test 2

Simulate test day with an official practice test. Then, score your test. The answers come with explanations so you can learn from your mistakes.

## More Articles

### GED Math Full Study Guide 2022-2023

$25.99$13.99

### The Most Comprehensive ASVAB Math Preparation Bundle

$76.99$36.99

### AFOQT Math in 10 Days

$19.99$14.99

### AFOQT Math Study Guide 2020 – 2021

$18.99$13.99