Math Practice Flashcards

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?

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.

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?

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.

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

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.

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

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.

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

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.

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

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.

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?

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 4x X 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 )?

Answer: 4x - 3

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?

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

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

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

[6×(−24)+8]–(−4)+[4×5]÷2=?

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

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?

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

What is the value of the number 36?

Answer: 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?

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.

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?

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.

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

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.

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?

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)

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

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!)

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.?

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.

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?

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.