Test Your 6th Grade Math IQ Quiz

1. What is the value of x in the equation 3x = 12?

4

3

5

2

To solve for x in the equation 3x = 12, divide both sides of the equation by 3. This isolates x, giving x = 12 ÷ 3, which equals 4. This method works because dividing both sides of an equation by the same number keeps the equation balanced. Solving equations like this is a fundamental skill in algebra and helps in solving more complex mathematical problems. It’s important to remember that isolating the variable by performing the same operation on both sides is the key to finding the solution.

Explanation

To solve for x in the equation 3x = 12, divide both sides of the equation by 3. This isolates x, giving x = 12 ÷ 3, which equals 4. This method works because dividing both sides of an equation by the same number keeps the equation balanced. Solving equations like this is a fundamental skill in algebra and helps in solving more complex mathematical problems. It’s important to remember that isolating the variable by performing the same operation on both sides is the key to finding the solution.

2. What is 49% of 130?

54.2

61.2

63.7

58.4

The correct answer is 63.7. To find 49% of 130, multiply 130 by 0.49:

Percentage problems like this involve converting the percentage into a decimal and multiplying it by the total value. This approach works for any percentage calculation and is an essential skill for solving real-world problems, such as determining discounts or increases. Understanding percentages helps with budgeting, analyzing data, and everyday math tasks. Always remember to convert the percentage correctly and double-check your calculations to avoid errors.

$63.7$

Explanation

The correct answer is 63.7. To find 49% of 130, multiply 130 by 0.49:

Percentage problems like this involve converting the percentage into a decimal and multiplying it by the total value. This approach works for any percentage calculation and is an essential skill for solving real-world problems, such as determining discounts or increases. Understanding percentages helps with budgeting, analyzing data, and everyday math tasks. Always remember to convert the percentage correctly and double-check your calculations to avoid errors.

$63.7$

3. What is the prime factorization of 36?

2 x 2 x 3 x 3

2 x 2 x 9

2 x 3

4 x 9

The prime factorization of a number involves breaking it down into its prime factors. In this case, the number 36 can be broken down into 2 x 2 x 3 x 3. This means that 2 and 3 are the prime factors of 36, and they are repeated twice each. Understanding prime factorization is important in mathematics as it helps simplify complex numbers and identify their fundamental building blocks. By breaking down a number into its prime factors, we can easily find the greatest common factor or least common multiple when working with fractions or simplifying expressions.

Explanation

The prime factorization of a number involves breaking it down into its prime factors. In this case, the number 36 can be broken down into 2 x 2 x 3 x 3. This means that 2 and 3 are the prime factors of 36, and they are repeated twice each. Understanding prime factorization is important in mathematics as it helps simplify complex numbers and identify their fundamental building blocks. By breaking down a number into its prime factors, we can easily find the greatest common factor or least common multiple when working with fractions or simplifying expressions.

4. What is the greatest common divisor (GCD) of 24 and 36?

12

6

8

4

The greatest common divisor (GCD) is the largest number that can divide two or more numbers without leaving a remainder. To find the GCD of 24 and 36, list their factors:

Factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

The largest number that appears in both lists is 12. Therefore, the GCD of 24 and 36 is 12. Knowing how to find the GCD is useful for simplifying fractions, solving ratio problems, and understanding numerical relationships.

Explanation

The greatest common divisor (GCD) is the largest number that can divide two or more numbers without leaving a remainder. To find the GCD of 24 and 36, list their factors:

Factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

The largest number that appears in both lists is 12. Therefore, the GCD of 24 and 36 is 12. Knowing how to find the GCD is useful for simplifying fractions, solving ratio problems, and understanding numerical relationships.

5. If the perimeter of a square is 20 centimeters, how long are its sides?

10 Centimeters

4.5 Centimeters

5 Centimeters

4 Centimeters

The perimeter of a square is the total length of all four sides. Since a square has equal sides, you can calculate the length of one side by dividing the perimeter by 4. In this case, the perimeter is 20 centimeters. Dividing 20 by 4 gives 5 centimeters. Therefore, each side of the square is 5 centimeters long. This method works for all squares, as their sides are always equal. Knowing how to calculate the side length of a square is helpful for solving problems related to shapes, geometry, and area. It also simplifies understanding how to measure and compare shapes.

Explanation

The perimeter of a square is the total length of all four sides. Since a square has equal sides, you can calculate the length of one side by dividing the perimeter by 4. In this case, the perimeter is 20 centimeters. Dividing 20 by 4 gives 5 centimeters. Therefore, each side of the square is 5 centimeters long. This method works for all squares, as their sides are always equal. Knowing how to calculate the side length of a square is helpful for solving problems related to shapes, geometry, and area. It also simplifies understanding how to measure and compare shapes.

6. What is the prime factorization of 264?

2 x 3 x 3 x 11

8 x 3 x 11

2 x 2 x 2 x 3 x 11

2 x 2 x 2 x 33

Explanation

7. What is the square of 14?

3.74

28

140

196

The correct answer is 196. To find the square of a number, multiply it by itself:

14×14=196

Squaring is used in geometry (area calculations) and algebra. For example, the square of a side length gives the area of a square. Understanding squares is foundational for working with exponents and solving quadratic equations.

Explanation

The correct answer is 196. To find the square of a number, multiply it by itself:

14×14=196

Squaring is used in geometry (area calculations) and algebra. For example, the square of a side length gives the area of a square. Understanding squares is foundational for working with exponents and solving quadratic equations.

8. Approximately how many centimeters are in one foot?

90 Centimeters

2.4 Centimeters

30 Centimeters

52 Centimeters

The correct answer is 30 centimeters. One foot equals 12 inches, and each inch is 2.54 centimeters. Multiply 12 by 2.54:

12×2.54=30.48

This conversion is essential in measurement systems, particularly when converting between imperial and metric units. Understanding these conversions is useful in science, construction, and everyday tasks requiring precise measurements.

Explanation

The correct answer is 30 centimeters. One foot equals 12 inches, and each inch is 2.54 centimeters. Multiply 12 by 2.54:

12×2.54=30.48

This conversion is essential in measurement systems, particularly when converting between imperial and metric units. Understanding these conversions is useful in science, construction, and everyday tasks requiring precise measurements.

9. Which of the examples demonstrates the Multiplicative Identity?

3 x 1 = 3

3 x (1/3) = 1

3 + (-3) = 0

None of the above

The example 3 x 1 = 3 demonstrates the multiplication identity. The multiplicative identity is the number 1 in mathematics, which, when multiplied by any other number, leaves that number unchanged. In this example, when a number (3) is multiplied by 1, the result is the same number (3). This is because multiplying any number by 1 does not change the value of the number. Therefore, 3 x 1 = 3 represents the property of a multiplicative identity.

Explanation

The example 3 x 1 = 3 demonstrates the multiplication identity. The multiplicative identity is the number 1 in mathematics, which, when multiplied by any other number, leaves that number unchanged. In this example, when a number (3) is multiplied by 1, the result is the same number (3). This is because multiplying any number by 1 does not change the value of the number. Therefore, 3 x 1 = 3 represents the property of a multiplicative identity.

10. Which number is divisible by 3?

192

196

197

292

A number is divisible by 3 if the sum of its digits is a multiple of 3. Let’s check each option:

For 192, the sum of the digits is 1 + 9 + 2 = 12, and 12 is divisible by 3.

For 196, the sum is 1 + 9 + 6 = 16, which is not divisible by 3.

For 197, the sum is 1 + 9 + 7 = 17, which is not divisible by 3.

For 292, the sum is 2 + 9 + 2 = 13, which is also not divisible by 3.

Thus, the correct answer is 192. This rule simplifies checking divisibility quickly without long division.

Explanation

A number is divisible by 3 if the sum of its digits is a multiple of 3. Let’s check each option:

For 192, the sum of the digits is 1 + 9 + 2 = 12, and 12 is divisible by 3.

For 196, the sum is 1 + 9 + 6 = 16, which is not divisible by 3.

For 197, the sum is 1 + 9 + 7 = 17, which is not divisible by 3.

For 292, the sum is 2 + 9 + 2 = 13, which is also not divisible by 3.

Thus, the correct answer is 192. This rule simplifies checking divisibility quickly without long division.

11. What is the cube of 12?

144

1728

120

1200

The correct answer is 1728. To calculate the cube of a number, multiply it by itself three times:

12×12×12=1728

Cubes are used in geometry (volume calculations) and algebraic equations. Understanding cubes helps solve real-world problems like determining the volume of a cube-shaped object. Mastering this skill strengthens your ability to work with exponents and larger numbers confidently.

Explanation

The correct answer is 1728. To calculate the cube of a number, multiply it by itself three times:

12×12×12=1728

Cubes are used in geometry (volume calculations) and algebraic equations. Understanding cubes helps solve real-world problems like determining the volume of a cube-shaped object. Mastering this skill strengthens your ability to work with exponents and larger numbers confidently.

12. What is the measure of an angle that covers 5% of a circle?

50 Degrees

5 Degrees

9 Degrees

18 Degrees

The correct answer is 18 degrees. A circle has 360 degrees. To find 5%, multiply 360×0.05=18. Percentages of angles are used in geometry, particularly in pie charts, measuring arcs, and solving problems involving circles. Knowing this allows you to connect percentages with geometry, which is helpful for real-life scenarios and academic tasks.

Explanation

The correct answer is 18 degrees. A circle has 360 degrees. To find 5%, multiply 360×0.05=18. Percentages of angles are used in geometry, particularly in pie charts, measuring arcs, and solving problems involving circles. Knowing this allows you to connect percentages with geometry, which is helpful for real-life scenarios and academic tasks.

13. If a $100 item is discounted 25% and then that price is raised by 25%, what is the new price?

100

93.75

75

125

If a $100 item is first discounted by 25% and then the discounted price is raised by 25%, you can calculate the new price as follows:

1. First, calculate the discounted price after a 25% discount:

Discounted Price = Original Price - (Discount Percentage * Original Price)

Discounted Price = $100 - (0.25 * $100)

Discounted Price = $100 - $25

Discounted Price = $75

2. Now, calculate the price after raising the discounted price by 25%:

New Price = Discounted Price + (Raise Percentage * Discounted Price)

New Price = $75 + (0.25 * $75)

New Price = $75 + $18.75

New Price = $93.75

So, the new price after the 25% discount and then a 25% raise is $93.75.

Explanation

If a $100 item is first discounted by 25% and then the discounted price is raised by 25%, you can calculate the new price as follows:

1. First, calculate the discounted price after a 25% discount:

Discounted Price = Original Price - (Discount Percentage * Original Price)

Discounted Price = $100 - (0.25 * $100)

Discounted Price = $100 - $25

Discounted Price = $75

2. Now, calculate the price after raising the discounted price by 25%:

New Price = Discounted Price + (Raise Percentage * Discounted Price)

New Price = $75 + (0.25 * $75)

New Price = $75 + $18.75

New Price = $93.75

So, the new price after the 25% discount and then a 25% raise is $93.75.

14. What is the measure of the angle that covers 81% of a circle?

271.9 Degrees

81 Degrees

145.8 Degrees

291.6 Degrees

A full circle measures 360 degrees. To find the measure of an angle that covers a specific percentage of a circle, multiply the total degrees of the circle (360) by the given percentage (81%). First, convert 81% into a decimal by dividing it by 100, which gives 0.81. Then, multiply 360 by 0.81. The result is 291.6 degrees. This calculation applies to any percentage of a circle. Understanding how to calculate angles as a portion of a circle helps in various geometry and trigonometry problems. It’s also useful for interpreting pie charts and other circular diagrams.

Explanation

A full circle measures 360 degrees. To find the measure of an angle that covers a specific percentage of a circle, multiply the total degrees of the circle (360) by the given percentage (81%). First, convert 81% into a decimal by dividing it by 100, which gives 0.81. Then, multiply 360 by 0.81. The result is 291.6 degrees. This calculation applies to any percentage of a circle. Understanding how to calculate angles as a portion of a circle helps in various geometry and trigonometry problems. It’s also useful for interpreting pie charts and other circular diagrams.

15. How do you write 0.013 in scientific notation?

1.3 x 10^2

1.3 x 10^-1

1.3 x 10

1.3 x 10^-2

To write a number in scientific notation, we move the decimal point to the right or left until there is only one non-zero digit to the left of the decimal point. In this case, 0.013 can be written as 1.3 x 10^-2 because we moved the decimal point two places to the right to get the non-zero digit 1.3. The negative exponent indicates that the decimal point was moved to the left.

Explanation

To write a number in scientific notation, we move the decimal point to the right or left until there is only one non-zero digit to the left of the decimal point. In this case, 0.013 can be written as 1.3 x 10^-2 because we moved the decimal point two places to the right to get the non-zero digit 1.3. The negative exponent indicates that the decimal point was moved to the left.