Algebra Sample Quiz 2
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Welcome to the SelectiveMath Sample Question Showcase!
Each individual quiz contains less than 10 questions and takes only a few minutes to complete.
Instructions: Read the questions carefully. Feel free to use a scratch pad to work out your answers. When you think that you know the answer, click on the appropriate button. Then click the “Show Answer and Next Question” button. You will be given a detailed explanation on how you could have solved the problem. At that point you can move on to the next question.
At the end of the quiz, you’ll be given your final score out of 100 points.
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Question 1 of 7
1. Question
Jack’s magic beanstalk grows at an incredibly fast rate – each day, it doubles in size! As soon as Jack planted the bean – on day 0 – it shot 100 feet into the air. If the bean’s height is represented by y, which of the following equations best describes the bean’s height on day x?
Correct
Your answer of c. y = 2x+1 x 100 was correct.The answer is: c. y = 2x+1 x 100
Since the beanstalk was 100 feet tall on day 1, that means it is 200 feet tall on day 2 (i.e. 21 x 100) , 400 feet on day 3 (i.e. 22 x 100), and so on. This means that we must take day 1 into consideration when creating an equation for the beanstalk’s height – the beanstalk’s height on day x will be equal to 2x+1 x 100.
Incorrect
Your answer was incorrect.The answer is: c. y = 2x+1 x 100
Since the beanstalk was 100 feet tall on day 1, that means it is 200 feet tall on day 2 (i.e. 21 x 100) , 400 feet on day 3 (i.e. 22 x 100), and so on. This means that we must take day 1 into consideration when creating an equation for the beanstalk’s height – the beanstalk’s height on day x will be equal to 2x+1 x 100.
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Question 2 of 7
2. Question
The area of a rectangular piece of land is 300 square meters. If the width is 5 meters longer than one-half of the length, find the length and width of the land?
Correct
Your answer of a. length = 20 meters and width = 15 meters was correct.
The answer is: a. length = 20, width = 15
Let x be length in meters. Since the width is 5 meters longer than half the length, width =
+ 5.
Since the formula for area of a rectangle equals length x width,
x
= 300. Multiply out this expression to get 
+ 5x = 300 which is 
= 300; multiply by 2 to get rid of the fraction to get x2 + 10x = 600 and then bring all terms to the left side of the equation, x2 + 10x – 600 = 0. Factor this equation until you get: (x – 20)(x+ 30) = 0 so x = 20 or –30. Since length cannot be negative, the only real choice is x = 20. Now width = + 5 = 10 + 5 = 15.Incorrect
Your answer was incorrect.
The answer is: a. length = 20, width = 15
Let x be length in meters. Since the width is 5 meters longer than half the length, width =
+ 5.
Since the formula for area of a rectangle equals length x width,
x = 300. Multiply out this expression to get + 5x = 300 which is = 300; multiply by 2 to get rid of the fraction to get x2 + 10x = 600 and then bring all terms to the left side of the equation, x2 + 10x – 600 = 0. Factor this equation until you get: (x – 20)(x+ 30) = 0 so x = 20 or –30. Since length cannot be negative, the only real choice is x = 20. Now width = + 5 = 10 + 5 = 15. -
Question 3 of 7
3. Question
Ari, a lemonade stand vendor, sells lemonade p cents per glass. He has to pay his mother m dollars per hour for her assistance when his stand is open. If he works at his lemonade stand for three hours and sells 300 glasses of lemonade, what is his profit in dollars?
Correct
Your answer of a. 3(p – m) was correct.The answer is: a. 3(p – m)
Hint: Be aware of inconsistencies in units!
Note that the rate Ari pays his mother is in dollars and the profit per glass of lemonade is in cents. Convert to the same units by dividing the 300p by 100 to put everything in cents so you get 3p – 3m which is the same as 3(p – m).
Incorrect
Your answer was incorrect.
Correct answer is: a. 3(p – m)The answer is: a. 3(p – m)
Hint: Be aware of inconsistencies in units!
Note that the rate Ari pays his mother is in dollars and the profit per glass of lemonade is in cents. Convert to the same units by dividing the 300p by 100 to put everything in cents so you get 3p – 3m which is the same as 3(p – m).
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Question 4 of 7
4. Question
Matthew the plumber works for $r/hour between 9 am and 5 pm and makes 50% more per hour if he works overtime (e.g., after 5 pm). His grateful customers also pay him t dollars in tips when he helps them with a plumbing emergency after 5 pm. On Monday he works for 12 hours and does 7 jobs after 5 pm. In terms of r and t, how much money did Matthew make on Monday?
Correct
Your answer of b. 14r + 7t was correct.The answer is: b. 14r + 7t
Matthew works for 12 hours: 8 regular hours and 4 hours at time and one half or 4 x 1.5 + 8 = 6 + 8 or 14 hours and then gets 7 x t in tips for his jobs after hours.
Incorrect
Your answer was incorrect.The answer is: b. 14r + 7t
Matthew works for 12 hours: 8 regular hours and 4 hours at time and one half or 4 x 1.5 + 8 = 6 + 8 or 14 hours and then gets 7 x t in tips for his jobs after hours.
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Question 5 of 7
5. Question
Which of the following, when combined with 4x + 3y = -2, yields no solution?
Correct
Your answer of c. 9y = 14 – 12x was incorrect.The answer is: c. 9y = 14 – 12x
The answer with no solution will have x and y in the same proportion as the original equation. Re-arrange choice c and you’ll get 12x + 9y = 140. 12x + 9y is simply 4x + 3y, so no solution can be found.
Incorrect
Your answer was incorrect.
Correct answer is: c. 9y = 14 – 12xThe answer is: c. 9y = 14 – 12x
The answer with no solution will have x and y in the same proportion as the original equation. Re-arrange choice c and you’ll get 12x + 9y = 140. 12x + 9y is simply 4x + 3y, so no solution can be found.
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Question 6 of 7
6. Question
Paul has 53 coins, quarters and dimes, which total $10.70.
How many of each does he have?Correct
Your answer of a. 36 quarters and 17 dimes was correct.The answer is: a. 36 quarters and 17 dimes
Let x be the number of quarters and y be the number of dimes. The total number of coins: x + y = 53; the total value of coins: .25x + .10y = 10.70. Let’s multiply the second equation by 100 to eliminate the decimals: 25x + 10y = 1070 and then divide by 5 to make it more manageable: 5x + 2y = 214. To get rid of one variable, multiply the first equation by 2 and then subtract:
If there are 53 total coins, then y = 17.
Incorrect
Your answer was incorrect.
Correct answer is: a. 36 quarters and 17 dimesThe answer is: a. 36 quarters and 17 dimes
Let x be the number of quarters and y be the number of dimes. The total number of coins: x + y = 53; the total value of coins: .25x + .10y = 10.70. Let’s multiply the second equation by 100 to eliminate the decimals: 25x + 10y = 1070 and then divide by 5 to make it more manageable: 5x + 2y = 214. To get rid of one variable, multiply the first equation by 2 and then subtract:
If there are 53 total coins, then y = 17.
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Question 7 of 7
7. Question
Three consecutive odd numbers sum to 57. The largest of these numbers is:
Correct
Your answer of c. 21 was correct.
The answer is: c. 21
Let the three consecutive integers be x, x + 2, x + 4.
Set these variables equal to 57: x + x + 2 + x + 4 = 57.
Then solve for x: 3x + 6 = 57, 3x = 51, so x = 17.
Remember that the question asks for the largest integer, so the correct choice is 21.
Incorrect
Your answer was incorrect.
The answer is: c. 21
Let the three consecutive integers be x, x + 2, x + 4.
Set these variables equal to 57: x + x + 2 + x + 4 = 57.
Then solve for x: 3x + 6 = 57, 3x = 51, so x = 17.
Remember that the question asks for the largest integer, so the correct choice is 21.