SHSAT Math Practice 1 — Questions and Answers

Question 1: A football squad had a budget of $20,000 for supplies. New balls cost $14,000 for the team. Each pair of new sports shoes costs $120. Which of the following inequities represents the team's ability to buy new shoes?

20𝑥 + 14,000 ≥ 20,000
14,000𝑥 +120 ≤ 20,000
120𝑥 + 14,000 ≤ 20,000 (Correct answer)
14,000𝑥 + 12,0 ≥ 20,000

Correct answer: 120𝑥 + 14,000 ≤ 20,000

The total budget is $20,000. The team already spent $14,000 on new balls. Each pair of new sports shoes costs $120, and 'x' represents the number of pairs of shoes. The total cost of shoes (120x) plus the cost of balls ($14,000) must be less than or equal to the total budget ($20,000), hence 120x + 14,000 ≤ 20,000.

Question 2: In a class, the ratio of boys to girls is 4:7. How many more boys should be enrolled in a class with 44 students to achieve a 1:1 ratio?

14
10
8
12 (Correct answer)

Correct answer: 12

With 44 students and a boy-to-girl ratio of 4:7, there are 4 parts boys and 7 parts girls, totaling 11 parts. Each part represents 44 students / 11 parts = 4 students. So, there are 4 * 4 = 16 boys and 7 * 4 = 28 girls. To achieve a 1:1 ratio, the number of boys needs to equal the number of girls (28). Therefore, 28 - 16 = 12 more boys are needed.

Question 3: A rectangular yard has a perimeter of 60 meters. If its width is double its length, what is its length?

18 meters
10 meters (Correct answer)
24 meters
20 meters

Correct answer: 10 meters

The perimeter of a rectangle is calculated as 2(length + width). Let the length be 'L'. The problem states the width is double its length, so width = 2L. Given the perimeter is 60 meters, we set up the equation: 2(L + 2L) = 60. This simplifies to 2(3L) = 60, or 6L = 60. Dividing by 6, we find L = 10 meters.

Question 4: What is the slope of a perpendicular line? 4𝑥−2𝑦 = 12?

- 1/2 (Correct answer)
4
-1/4
-2

Correct answer: - 1/2

First, find the slope of the given line 4x - 2y = 12 by rearranging it into slope-intercept form (y = mx + b). Subtract 4x from both sides to get -2y = -4x + 12, then divide by -2 to get y = 2x - 6. The slope of this line (m1) is 2. The slope of a perpendicular line (m2) is the negative reciprocal of m1, which is -1/2.

Question 5: In the following system of equations, what is the value of x? 2𝑥+5𝑦 = 11 4𝑥−2𝑦 = −14

-2 (Correct answer)
-1
4
1

Correct answer: -2

To solve this system of equations for x, we can use the elimination method. Multiply the first equation (2x + 5y = 11) by 2 to get 4x + 10y = 22. Now, subtract the second equation (4x - 2y = -14) from this new equation: (4x + 10y) - (4x - 2y) = 22 - (-14), which simplifies to 12y = 36, so y = 3. Substitute y = 3 into the first equation: 2x + 5(3) = 11, which becomes 2x + 15 = 11. Subtract 15 from both sides: 2x = -4. Finally, divide by 2 to find x = -2.

Question 6: A swimming pool has a water capacity of 2,000 cubic feet. The pool measures 25 feet long by 10 feet wide. How deep is the pool?

8 (Correct answer)
12
16
20

Correct answer: 8

The volume of a rectangular prism, such as a swimming pool, is calculated by multiplying its length, width, and depth (Volume = Length × Width × Depth). We are given the volume (2,000 cubic feet), length (25 feet), and width (10 feet). So, the equation is 2000 = 25 × 10 × Depth. This simplifies to 2000 = 250 × Depth. To find the depth, divide 2000 by 250, which equals 8 feet.

Question 7: Marcus used his $25 to go bowling. He paid $4.00 for each game after renting sneakers for $5.25. How many games could Marcus have played in total?

24
16
4 (Correct answer)
8

Correct answer: 4

This response represents the correct solution to the word problem. The student may have set up and solved the inequality as shown below, where x represents the number of games played: 4x + 5.25 < 25 4x < 19.75 X < 4.9375 The student who selects this response understands that the greatest number of games played has to be a whole number less than 4.9375.

Question 8: What is the equivalent expression of (7x – 5 ) – (3x – 2 )?

10x - 3
10 - 7
4x - 3 (Correct answer)
4x -7

Correct answer: 4x - 3

This response represents the correct equivalent expression. (6x - 5 ) - (3x - 2) = 7x - 3z - 5 - ( - 2) = 4x - 3

Question 9: Last season, the Cougar team won 16 games. The Cougar team won 20 games this season. From last year to this year, what is the percentage increase in the number of games the Cougar team have won?

70%
125%
25% (Correct answer)
30%

Correct answer: 25%

This response represents the correct percent increase in the number of games the Cougar team won from last year to this year. 20/16 = 125/100 125 - 100 = 25

Question 10: When x=3 and y=2 what is the value of the expression (5(x2y)+(2x))2?

60
32
36 (Correct answer)
18

Correct answer: 36

Plug in the value of x and y. 𝑥=3 and 𝑦=−2 (5(𝑥−2𝑦)+(2−𝑥))2 = (5(3−2(−2))+(2−3))2 = (5(3+4)+(−1))2 =(34)2 = 36

Question 11: [6×(−24)+8]–(−4)+[4×5]÷2=?

-144
-122 (Correct answer)
-112
111

Correct answer: -122

Use PEMDAS (order of operation): [6×(−24)+8]– (−4) + [4×5]÷2 [−144+8]– (−4) + [20]÷2= [−144+8]– (−4)+10 [−136]– (−4) + 10=10 [−136] + 4+10 = 14 –122

Question 12: Angela rented shoes, played three games of bowling, and purchased one order of nachos. She saved ½ off the price on her bowling games by using a coupon. What was Angela's total price before taxes?

$13
$4
$8.25 (Correct answer)
$5.35

Correct answer: $8.25

This response represents the correct total amount Angela paid. The student may have used the following representations to solve the problem: X = 2.75 + 3(2.5) /2 + 1./75 X = 2.65 + 3.65 + 1.75 X = 8/25

Question 13: What is the value of the number 36?

26
36 (Correct answer)
15
43

Correct answer: 36

Answer : 729 (36)=3×3×3×3×3×3=729

Question 14: A city's population is predicted to rise by 7.5 percent next year. Which expression indicates the predicted population next year if p represents the current population?

1 + 0.075
1.75 p
1.075 p (Correct answer)
p + 0.075

Correct answer: 1.075 p

This response represents the correct expression that shows the expected population in the following year. A student who selects this response understands how the quantities in the expression are related in this problem context.

Question 15: Texas offers a middle school math tournament every year. Students must, however, score 92 on a total of six qualifying tests in order to be considered. Ava's first five examinations scores of 88, 91, 99, 86, and 92. What score must she achieve on her sixth test in order to qualify for the competition?

86
88
96 (Correct answer)
84
95

Correct answer: 96

We can solve this problem using the concept average. That is, the average of 6 tests is 92. Let "x" be the score of 6th test (88 + 91 + 99 + 86 + 92 + x)/6 = 92 (456 + x)/6 = 92 Multiply by 6 on both sides 456 + x = 92 (6) 456 + x = 552 Subtract by 456 on both sides 456 + x - 456 = 552 - 456 x = 96 Hence option (96) is correct.

Question 16: A town's population grows by 15% and 20% in two consecutive years. After two years, how much of the population has grown?

14%
38% (Correct answer)
58%
36%

Correct answer: 38%

The population is increased by 15% and 20%. 15% increase changes the population to 115% of original population. For the second increase, multiply the result by 120%. (1.15)×(1.20)=1.38=138% 38 percent of the population is increased after two years.

Question 17: The price of a $200 tool has been reduced by 15%. After a month, the tool is reduced by 15% further. Which of the following expressions can be used to calculate the tool's selling price?

(200)(0.85)(0.85) (Correct answer)
(200)(0.15)–(200)(0.15)
(200)–200(0.30)
(200)(0.70)

Correct answer: (200)(0.85)(0.85)

To find the discount, multiply the number by (100%–rate of discount). Therefore, for the first discount we get: (200)(100%–15%)=(200)(0.85)=170 For the next 15% discount: (200)(0.85)(0.85)

Question 18: On the line x+2y=4, which of the following points lies?

(−3,4)
(− 2,3) (Correct answer)
(1,2)
(−1,3)

Correct answer: (− 2,3)

𝑥+2𝑦=4. Plug in the values of 𝑥 and 𝑦 from choices provided. Then: A. (−3,4)𝑥+2𝑦=4(→)−3+2(4)=4(→)−3+8=4 (This is NOT true!) B. (−2,3)𝑥+2𝑦=4(→)−2+2(3)=4(→)−2+6=4 This is true! C. (1,2)𝑥+2𝑦=4(→)1+2(2)=4(→)1+4=4 (This is NOT true!) D. (−1,3)𝑥+2𝑦=4(→)−1+2(3)=4(→)−1+6=4 (This is NOT true!)

Question 19: Rose and Kate are planning a weekend get-together somewhere between their 420-mile distances. Throughout her trip, Rose maintains a speed of 80 mph. What speed did Kate drive to reach their meeting site if they both left home at 10 a.m. and met at 1 p.m.?

70 mph
65 mph
60 mph (Correct answer)
75 mph

Correct answer: 60 mph

Kate drove 180 miles at 60 mph to reach the meeting place where Rose arrived after driving 240 miles at 80 mph.

Question 20: The ratio of home fans to visiting fans in a stadium is 5:7. Which of the following might be the stadium's total number of fans?

22,301
32,0144
12,324 (Correct answer)
61,251

Correct answer: 12,324

In the stadium the ratio of home fans to visiting fans in a crowd is 5:75:7. Therefore, total number of fans must be divisible by 12:5+7=12.12:5+7=12. Let’s review the choices: A. 42,326:42,326÷12=3,527.16642,326:42,326÷12=3,527.166 B. 66,812:66,812÷12=5,567.66666,812:66,812÷12=5,567.666 C. 12,324:12,324÷12=102712,324:12,324÷12=1027 D. 44,566:44,566÷12=3,713.83344,566:44,566÷12=3,713.833 Only choice A when divided by 12 results a whole number.

Question 21: One-fifth of a supplement is an angle. What is the angle's measurement?

35
40
28
30 (Correct answer)

Correct answer: 30

The sum of supplement angles is 180. Let 𝑥x be that angle. Therefore, 𝑥+5𝑥=180x+5x=180 6𝑥=1806x=180, divide both sides by 6: 𝑥=30

Question 22: How many 8 cm² tiles are required to cover a 6 cm by 24 cm floor?

18 (Correct answer)
13
9
22

Correct answer: 18

The area of the floor is: 6 cm × 24 cm = 144 cm² The number of tiles needed =144÷8=18

Question 23: Noel is 14 years old and was a third of his uncle's age 5 years ago. What is his uncle's age now?

43
19
22
32 (Correct answer)
35

Correct answer: 32

Let "x" be his uncle's present age 5 years ago, his uncle's age = x - 5 5 years ago, Noel's age = 14 - 5 = 9 (x - 5)/3 = 9 Multiply by 3 on both sides x - 5 = 9 (3) x - 5 = 27 Add 5 on both sides x - 5 + 5 = 27 + 5 x = 32 Hence option (32) is correct.

Question 24: What is the value of y in terms of x if 14x - 7y - 4 = 45?

7 - 7x
2x + 7
2x - 7 (Correct answer)
7 + 7x
7 - 2x

Correct answer: 2x - 7

14x - 7y - 4 = 45 Subtract 14x and add 4 on both sides 14x - 7y - 4 - 14x + 4 = 45 - 14x + 4 -7y = 45 - 14x + 4 -7y = 49 - 14x Divide by -7 into both sides -7y/(-7) = (49 - 14x)/(-7) y = (14x - 49)/7 y = (14x/7) - (49/7) y = 2x - 7

Question 25: As demonstrated, the centers of two congruent circles are P and Q. What is the PXQ angle's measurement?

52°
70°
28°
33°
60° (Correct answer)

Correct answer: 60°

Here PX is the radius of the first circle, QX is the radius of the second circle. PQ is the distance between two centers. PX = PQ = QX Hence the required angle is 60°.

Question 26: Jack has d dollars. He's got a third of Neil's money. Sean has $80, which is less than half of Jack's and Neil's total. How much money does Sean have in terms of d?

2d – 40
4d – 40
2d – 80 (Correct answer)
2d + 40
2d + 80

Correct answer: 2d – 80

Jack has d dollars. Neil has 3d dollars Number of dollars that Sean has = (1/2)(d + 3d) - 80 = (1/2) 4d - 80 = 2d - 80 Hence the answer is 2d - 80.

Question 27: How many x values does the function not equal 1? f(x) = (x - 3)/(x - 3)

3
0
23
infinitely many (Correct answer)
3

Correct answer: infinitely many

Since the numerator and denominator are the same, we always get the value 1 for f(x). So, the answer is infinitely many.

Question 28: Lerry spent the same amount on four pants and a $20 shirt. Before-tax, the items she purchased cost a total of $160. How much did each pants cost?

$23
$35 (Correct answer)
$42
$46

Correct answer: $35

This response represents the correct cost of each pants, $35, which results from solving the equation 4x + 20 = 160. The student who selects this response understands how to solve the given word problem. 4x + 20 = 150 4x = 140 X = 35

Question 29: Between 4 and 16 inclusive, how many prime numbers are there?

3
2
5
4 (Correct answer)
6

Correct answer: 4

4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 Prime numbers are 5, 7, 11, 13 Hence there are 4 prime numbers between 4 and 16.

Question 30: Ms. Kelly's class has 28 pupils. In this class, there are 2 to 5 boys for every 5 girls. How many new boys must be added to the class in order for the boy-to-girl ratio to equal 1:2?

6
14
3
5
2 (Correct answer)

Correct answer: 2

Number of students in the class = 28 Number of boys = (2/(2+5)) ⋅ 28 = (2/7) ⋅ 28 = 2(4) = 8 Number of girls = 5/(2+5) ⋅ 28 = (5/7) ⋅ 28 = 5(4) = 20 (8 + y) : (20 + y) = 1 : 2 (8 + y) / (20 + y) = 1/2 2(8 + y) = 1 (20 + y) 16 + 2y = 20 2y = 20 - 16 2y = 4 y = 2 Hence the number of students to be added is 2.

SHSAT Math Practice 1

A football squad had a budget of $20,000 for supplies.
New balls cost $14,000 for the team.
Each pair of new sports shoes costs $120.
Which of the following inequities represents the team's ability to buy new shoes?