SHSAT Math Practice
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?
120𝑥 + 14,000 ≤ 20,000
Let x be the number of new shoes the team can purchase. Therefore, the team can purchase 120𝑥120x.
The team had $20,000 and spent $14000. Now the team can spend on new shoes $6000 at most.
Now, write the inequality:
120𝑥+14,000≤20,000
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?
The ratio of boys to girls is 4:7.
Therefore, there are 4 boys out of 11 students.
First, divide the total number of students by 11, then multiply the result by 4.
44÷11=4⇒4×4=16
There are 16 boys and 28(44–16) girls. So, 12 more boys should be enrolled to make the ratio 1:1
A rectangular yard has a perimeter of 60 meters. If its width is double its length, what is its length?
The width of the rectangle is twice its length. Let 𝑥 be the length. Then, width =2𝑥
Perimeter of the rectangle is (2 (width + length) =2(2𝑥+𝑥)=60⇒6𝑥=60⇒𝑥=10
The length of the rectangle is 10 meters.
What is the slope of a perpendicular line?
4𝑥−2𝑦 = 12?
The equation of a line in slope intercept form is: 𝑦=𝑚𝑥+𝑏y
Solve for y.
4𝑥−2𝑦=12⇒−2𝑦 = 12−4𝑥⇒𝑦=(12−4𝑥)÷(−2)⇒𝑦=2𝑥−6
The slope of this line is 2.
The product of the slopes of two perpendicular lines is −1.
Therefore, the slope of a line that is perpendicular to this line is:
𝑚1×𝑚2=−1⇒2×𝑚2=−1⇒𝑚2=−1/2
In the following system of equations, what is the value of x?
2𝑥+5𝑦 = 11
4𝑥−2𝑦 = −14
Solving Systems of Equations by Elimination
Multiply the first equation by (-2), then add it to the second equation.
−2(2𝑥+5𝑦=11) 4𝑥−2𝑦=−14⇒−4𝑥−10𝑦=−22 4𝑥−2𝑦=−14⇒−12𝑦=−36⇒𝑦=3
Plug in the value of y into one of the equations and solve for x.
2𝑥+5(3) = 11⇒2𝑥+15 = 11⇒2𝑥 = −4⇒𝑥= −2
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?
Answer : 8
Use formula of rectangle prism volume.
𝑉=(𝑙𝑒𝑛𝑔𝑡ℎ)(𝑤𝑖𝑑𝑡ℎ)(ℎ𝑒𝑖𝑔ℎ𝑡)⇒2000 = (25)(10)(ℎ𝑒𝑖𝑔ℎ𝑡)⇒ℎ𝑒𝑖𝑔ℎ𝑡 = 2000÷250 = 8
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?
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.
What is the equivalent expression of (7x – 5 ) – (3x – 2 )?
This response represents the correct equivalent expression.
(6x - 5 ) - (3x - 2) =
7x - 3z - 5 - ( - 2) =
4x - 3
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?
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
When x=3 and y=2 what is the value of the expression (5(x2y)+(2x))2?
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
[6×(−24)+8]–(−4)+[4×5]÷2=?
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
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?
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
What is the value of the number 36?
Answer : 729
(36)=3×3×3×3×3×3=729
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?
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.
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?
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.
A town's population grows by 15% and 20% in two consecutive years. After two years, how much of the population has grown?
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.
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?
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)
On the line x+2y=4, which of the following points lies?
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!)
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.?
Kate drove 180 miles at 60 mph to reach the meeting place where Rose arrived after driving 240 miles at 80 mph.
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?
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.
One-fifth of a supplement is an angle. What is the angle's measurement?
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
How many 8 cm² tiles are required to cover a 6 cm by 24 cm floor?
The area of the floor is: 6 cm × 24 cm = 144 cm²
The number of tiles needed =144÷8=18
Noel is 14 years old and was a third of his uncle's age 5 years ago. What is his uncle's age now?
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.
What is the value of y in terms of x if 14x - 7y - 4 = 45?
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
As demonstrated, the centers of two congruent circles are P and Q. What is the PXQ angle's measurement?
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°.
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?
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.
How many x values does the function not equal 1?
f(x) = (x - 3)/(x - 3)
Since the numerator and denominator are the same, we always get the value 1 for f(x).
So, the answer is infinitely many.
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?
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
Between 4 and 16 inclusive, how many prime numbers are there?
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.
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?
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.