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Basic Math

Basic Math Practice Test: Practice Test 3

Practice Test 3 for Basic Math: real questions and explanations from the Varsity Tutors practice-test pool.

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Question 1 of 25

Convert to a percent.

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Question 1

Convert to a percent.

  1. (correct answer)

Explanation: To convert a decimal into percent, multiply the decimal by 100 and then add a "%" sign. Add a % sign.

Question 2

Paul had video games. On Monday, he gave video games to his friend Chris. On Tuesday, he sold of his video games to the local video game shop. On Wednesday, Paul accidentally broke video games and threw them away. How many video games does Paul have left?

  1. (correct answer)

Explanation: This is a simple subtraction problem. First, subtract the number of video games Paul gave to Chris on Monday. Now, subtract the number of video games Paul sold from the number he has left. Finally, subtract the number of video games Paul broke and threw away.

Question 3

What is the result of the above equation?

  1. (correct answer)

Explanation: We first multiply the numerators: Then we multiply the denominators: The resulting fraction is: We divide the numerator and denominator by 12. The numerator is: The denominator results in: Our resulting fraction is:

Question 4

In 2012, a university received 150,249 applicants. In 2013, the same university received 190,201 applicants. By what percent did the total number of applicants increase from 2012 to 2013?

  1. (correct answer)

Explanation: To find the percent change, use the following formula: Our new number of applicants is 190,201, while the original number of applicants is 150,249.

Question 5

What is the perimeter of a semicircle with an area of ?

  1. (correct answer)

Explanation: This is a multi-step problem. The perimeter of a semicircle is the sum of the circumference and diameter. First, since we are given the area, we will need to find the radius. For the area of a semicircle: Since the area is , substitute this into A to find radius r. Since the radius is 2, the diameter is 4. The circumference for a semicircle is: The perimeter is the sum of the circumference and diameter:

Question 6

Subtract.

  1. (correct answer)

Explanation: To subtract two fractions, they need to both share the same denominator. Since 81 is a multiple of 9, we only need to change the 1st fraction. Now subtract the two fractions.

Question 7

Determine the answer as a mixed number:

  1. (correct answer)

Explanation: 1. Find the least common denominator: The lowest number that both 4 and 6 can go into is 12 meaning that it is the least common denominator. 2. Use the new least common denominator to create two equivalent fractions with a denominator of 12. 3. Add the two fractions together. 4. Convert the fraction to a mixed number:

Question 8

Billy earned for shoveling his driveway. He wants to buy a new toy and a candy bar, and then add the rest to his piggy bank. The new toy costs and the candy bar costs How much money will Billy have left over to add to his piggy bank?

  1. (correct answer)

Explanation: Billy had . After buying the toy he had left over: . After buying the candy bar he then had left for his piggy bank, .

Question 9

Multiply these fractions:

  1. (correct answer)

Explanation: When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together: Simplify the fraction to get the final answer:

Question 10

Multiply:

  1. (correct answer)

Explanation: Multiply the numerators together, then multiply the denominators together. To simplfy we can pull out a from the numerator and denominator, thus canceling them. The following answer is the result:

Question 11

Find the sum.

  1. (correct answer)

Explanation: First add the digits in the ones colume, this would be . Make sure to carry the 1 from the 17 to the tens colume. Then add the digits in the tens colume, this would be . Lastly, add the digits in the hundrends colume, this would be Therefore the result is as follows: Sum

Question 12

Factor the following expression completely

  1. (correct answer)

Explanation: First, we need to factor the numerator and the denominator separately. To factor an expression with the form , we will need to find factors of that add up to be. For the numerator, , and . Write down the factors of and add them up. Since and add up to , Now, do the same thing with the denominator, . Since and add up to , . Now, stack these factors up as fractions: Since both the numerator and denominator have the factors (x+6), they cancel each other out because they divide to 1. Then,

Question 13

Kevin has won toys from a competition and decides to keep toys for himself. He would like to give the rest of the toys to four of his close friends.

If each of Kevin's friends receive the same number of toys from Kevin, how many will be remaining?

  1. (correct answer)

Explanation: The correct answer is 2 remaining toys. Kevin has 34 toys to start and he keeps 4 for himself. This means that he has 30 toys to give to four friends. When we divide 30 by 4, we get 7.5. Since each friend cannot get half a toy, each friend can receive 7 toys. This means that of the 30 toys, there will be 2 toys remaining.

Question 14

What is the least common denominator of the following fractions: ?

  1. (correct answer)

Explanation: The correct answer is 36. The best way to approach this problem is to take each denominator and list out its multiples. You can then find the common multiple between each denominator. Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48 Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42 Multiples of 12: 12, 24, 36, 48, 60 Multiples of 36: 36, 72, 108 Multiples of 18: 18, 36, 54, 72 From the above multiples, we can see that the least common denominator is 36.

Question 15

How many minutes are in a hours?

  1. minutes (correct answer)
  2. minutes
  3. minutes
  4. minutes

Explanation: Knowing that there are 60 minutes in an hour, multiply that amount by the total number of hours (3.5): minutes

Question 16

Solve:

  1. (correct answer)

Explanation: The answer is . The goal is to isolate the variable, , on one side of the equation sign and have all numerical values on the other side of the equation. Since is a negative number, you must add to both sides. Then, divide both sides of the equation by :

Question 17

What is the reciprocal of ?

  1. (correct answer)

Explanation: To get the reciprocal of a fraction, you simply switch the numerator and the denominator. In our case our numerator is and our denominator is . So becomes .

Question 18

Convert to a percent.

  1. (correct answer)

Explanation: To convert a decimal into percent, multiply the decimal by 100 and then add a "%" sign. Add a % sign.

Question 19

Round to the nearest hundredth:

  1. (correct answer)
  2. (correct answer)

Explanation: The hundredth place is the 2nd number after the decimal. Because the thousandth place is great than 5, we will need to round up to

Question 20

What is ?

  1. (correct answer)

Explanation: When terms with the same base are multiplied, multiply the coefficients together then add up all the exponents. For the coefficients: For the exponents: Thus, the answer is

Question 21

Jane bought a pencil for , a skirt for , a coat for , and a headband for . How much did Jane pay in total for all the items she bought?

  1. (correct answer)

Explanation: Add up all the individual items. Add

Question 22

In March, an athlete weighed pounds. In April, the same athlete weighed pounds. What is the athlete's percentage of weight loss?

  1. (correct answer)

Explanation: The formula to find percentage change is . So for our athlete, our new weight is 170 pounds, and the original weight is 195 pounds. Because the question already tells us that we need to find the percent lost, or percent decrease, we can drop the negative sign in the answer.

Question 23

What is expressed as a percentage rounded to the nearest tenth?

  1. (correct answer)

Explanation: Percents are numbers expressing parts of : means part of , or . The simplest way to convert a decimal to a percentage is to move the decimal place over two places to the right. We move the decimal point to after the hundredths place because we are rewriting the decimal as a portion of . Therefore: Now, we need to round the percentage to the nearest tenth. The number after the tenths place is a five, so we need to round up: is therefore our final answer.

Question 24

Lucy is a real estate agent who is paid a commission on the value of each house she sells every month. She is also paid a base monthly rate of as part of her salary. If represents the value of the houses she sells per month, which of the following equations would accurately predict how much money she makes per month?

  1. (correct answer)

Explanation: To start, we need to convert the percent into a decimal. Now, we know that Lucy receives 17% of the value of the homes she sells as her commission. Her commission can then be written as the expression . Lucy is also paid $1000 regardless of if she sells any houses or not that month. In a linear equation, this would be our y-intercept. Putting the pieces of the salary together, we get the following equation:

Question 25

Henry has taken a lot of tests this semester in his biology class. In total, he has taken tests. His scores on the tests were , , , , , , , , , . What is the mode of all his test scores?

  1. (correct answer)

Explanation: The mode is the number that appears most often in a set of numbers. If we order our number set we get the following: In this case, because Henry scored 88 three times, that is the mode.