This Grade 8 Math Quiz Might Just Out-Smart You

1. A student earned a grade of 80% on a math test that had 20 problems. How many problems on this test did the student answer correctly?

17

15

14

16

Since the student earned a grade of 80% on the math test, it means that they answered 80% of the problems correctly. To find out how many problems that is, we can calculate 80% of 20 (the total number of problems on the test). 80% of 20 is 16, so the student answered 16 problems correctly.

Explanation

Since the student earned a grade of 80% on the math test, it means that they answered 80% of the problems correctly. To find out how many problems that is, we can calculate 80% of 20 (the total number of problems on the test). 80% of 20 is 16, so the student answered 16 problems correctly.

2. To solve the following expression, which operation must you perform first? 8 + 12 (7 – 5) ÷ 6

+

- (parentheses)

X

÷

Explanation

3. Frank and Joey ordered a large pizza. Frank ate 30% of the pizza, and Joey ate 2/5 of the pizza. What percentage of the pizza did they eat in all?

50%

60%

70%

75%

Explanation

4. One way to find all the factors of 72 is to find its prime factorization. What is the prime factorization of 72?

3 x 3 x 3 x 2 x 2

6 x 3 x 2 x 2

2 x 2 x 2 x 3 x 3

9 x 2 x 2 x 3

The prime factorization of a number expresses it as the product of its prime factors. A prime number is a whole number greater than 1 that has only two factors: 1 and itself.

To find the prime factorization of 72, we can start by dividing it by the smallest prime number, 2:

72 ÷ 2 = 36

36 ÷ 2 = 18

18 ÷ 2 = 9

9 is not divisible by 2, so we move to the next prime number, 3:

9 ÷ 3 = 3

3 ÷ 3 = 1

Therefore, the prime factorization of 72 is 2 x 2 x 2 x 3 x 3, which can also be written as 2³ x 3².

Explanation

The prime factorization of a number expresses it as the product of its prime factors. A prime number is a whole number greater than 1 that has only two factors: 1 and itself.

To find the prime factorization of 72, we can start by dividing it by the smallest prime number, 2:

72 ÷ 2 = 36

36 ÷ 2 = 18

18 ÷ 2 = 9

9 is not divisible by 2, so we move to the next prime number, 3:

9 ÷ 3 = 3

3 ÷ 3 = 1

Therefore, the prime factorization of 72 is 2 x 2 x 2 x 3 x 3, which can also be written as 2³ x 3².

5. A student answered 76 problems on a test correctly and received a grade of 80%. How many problems were on the test if all the problems were worth the same number of points?

60

90

95

105

Explanation

6. A popular game at a carnival involves a spinner. There are five sections in total. The areas of sections 1, 2, 3, and 4 are equal. The area of section 5 is twice the area of any one of the other sections. What is the probability that a player's spin will be a 3?

To find the probability of landing on section 3 when spinning the carnival wheel, we need to consider the relative areas of the sections.

Let's denote the area of each section as follows:

Area of sections 1, 2, 3, and 4: A

Area of section 5: 2A (since it's twice the area of any one of the other sections)

The total area of all sections is:

Total area = 4A (for sections 1, 2, 3, and 4) + 2A (for section 5) = 6A

Now, to find the probability of landing on section 3, we'll divide the area of section 3 by the total area:

Probability of landing on section 3 = Area of section 3 / Total area

Probability of landing on section 3 = A / (6A) = 1/6

So, the probability of landing on section 3 is 1/6.

Explanation

To find the probability of landing on section 3 when spinning the carnival wheel, we need to consider the relative areas of the sections.

Let's denote the area of each section as follows:

Area of sections 1, 2, 3, and 4: A

Area of section 5: 2A (since it's twice the area of any one of the other sections)

The total area of all sections is:

Total area = 4A (for sections 1, 2, 3, and 4) + 2A (for section 5) = 6A

Now, to find the probability of landing on section 3, we'll divide the area of section 3 by the total area:

Probability of landing on section 3 = Area of section 3 / Total area

Probability of landing on section 3 = A / (6A) = 1/6

So, the probability of landing on section 3 is 1/6.

7. A woman put $580 into a savings account for three years. The rate of interest on the account was 6½%. How much was the interest in dollars and cents? (Use simple interest)

$113.10

$337

$33.70

$104.4

The correct answer is $113.10. To calculate the interest for the year, we need to use the formula for simple interest: Interest = Principal x Rate x Time. In this case, the principal is $580, the rate is 6.5% (or 0.065 as a decimal), and the time is 1 year. Plugging these values into the formula, we get: Interest = $580 x 0.065 x 1 = $37.70. However, since we are asked for the interest in dollars and cents, we round this to the nearest cent, which gives us $37.70. Therefore, the interest for the year is $113.10.

Explanation

The correct answer is $113.10. To calculate the interest for the year, we need to use the formula for simple interest: Interest = Principal x Rate x Time. In this case, the principal is $580, the rate is 6.5% (or 0.065 as a decimal), and the time is 1 year. Plugging these values into the formula, we get: Interest = $580 x 0.065 x 1 = $37.70. However, since we are asked for the interest in dollars and cents, we round this to the nearest cent, which gives us $37.70. Therefore, the interest for the year is $113.10.

8. Which of the following statements about linear equations is NOT true?

A linear equation can be represented by a straight line on a graph.

The solution to a linear equation is the point where the line intersects the y-axis.

A linear equation has a degree of 1.

A linear equation can have one, infinitely many, or no solutions.

The solution to a linear equation is any point (or set of points) that satisfies the equation, and these points can lie anywhere along the line, not just at the y-intercept. The y-intercept is simply the point where the line crosses the y-axis, which may or may not be a solution to the equation.

Explanation

The solution to a linear equation is any point (or set of points) that satisfies the equation, and these points can lie anywhere along the line, not just at the y-intercept. The y-intercept is simply the point where the line crosses the y-axis, which may or may not be a solution to the equation.

9. A hotel is building a children's wading pool in the shape of a square with a semicircle on one side. A diagram of the pool is shown below. What is the perimeter of the children's pool?

17.85 feet

27.85 feet

40.70 feet

45.70 feet

The pool consists of a square with a semicircle on one side. The perimeter of the square is 20 feet, but we need to subtract one side (5 feet) and add the semicircle's arc length, which is 7.85 feet. This gives us 22.85 feet. To find the pool's outer perimeter, we subtract the semicircle's diameter (5 feet), resulting in 17.85 feet. Rounding to the nearest tenth gives us 17.9 feet.

Explanation

The pool consists of a square with a semicircle on one side. The perimeter of the square is 20 feet, but we need to subtract one side (5 feet) and add the semicircle's arc length, which is 7.85 feet. This gives us 22.85 feet. To find the pool's outer perimeter, we subtract the semicircle's diameter (5 feet), resulting in 17.85 feet. Rounding to the nearest tenth gives us 17.9 feet.

10. A measuring cup has lines marking the fractions of a cup. In what order should the lines on the cup be labeled, starting with the bottom line of the measuring cup?

The lines on the measuring cup should be labeled in increasing order, starting with the bottom line. This is because the bottom line represents the smallest fraction of a cup, and as you move up the cup, the lines represent larger fractions. Labeling the lines in increasing order ensures that the measurements are accurate and consistent.

Explanation

The lines on the measuring cup should be labeled in increasing order, starting with the bottom line. This is because the bottom line represents the smallest fraction of a cup, and as you move up the cup, the lines represent larger fractions. Labeling the lines in increasing order ensures that the measurements are accurate and consistent.

This Grade 8 Math Quiz Might Just Out-smart You