Check In Test for Middle School Math Mixed Review Assessment Quiz ... - Free Printable

Problem Analysis:

The image contains a math worksheet for 6th-grade students. The tasks involve basic arithmetic, geometry, and measurement concepts. Below, I will solve each problem step by step and explain the reasoning.

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Problem 1: Prime Numbers

Question: Which of the following is a set of prime numbers?
- a. 2, 4, 8, 10
- b. 2, 3, 5, 7, 11
- c. 4, 5, 16, 32

Solution:
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Let's analyze each option:

- Option (a): 2, 4, 8, 10
- 2 is prime, but 4, 8, and 10 are not prime (they have divisors other than 1 and themselves).
- Not all numbers in this set are prime.

- Option (b): 2, 3, 5, 7, 11
- All these numbers are prime:
- 2: Divisors are 1 and 2.
- 3: Divisors are 1 and 3.
- 5: Divisors are 1 and 5.
- 7: Divisors are 1 and 7.
- 11: Divisors are 1 and 11.
- All numbers in this set are prime.

- Option (c): 4, 5, 16, 32
- 5 is prime, but 4, 16, and 32 are not prime (they have divisors other than 1 and themselves).
- Not all numbers in this set are prime.

Correct Answer: (b) 2, 3, 5, 7, 11

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Problem 2: Metric Unit of Gram

Question: A gram is a metric unit of:
- a. Capacity
- b. Speed
- c. Volume
- d. Mass

Solution:
- Capacity refers to the amount a container can hold (e.g., liters).
- Speed is measured in units like meters per second.
- Volume measures the space occupied by an object (e.g., cubic meters).
- Mass measures the amount of matter in an object (e.g., grams, kilograms).

A gram is a unit of mass.

Correct Answer: (d) Mass

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Problem 3: Reduce 2/4

Question: Reduce the fraction 2/4.
- a. 1/2
- b. 1/4
- c. 1/3

Solution:
To reduce a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD). For 2/4:
- The GCD of 2 and 4 is 2.
- Divide both the numerator and the denominator by 2:
\[
\frac{2 \div 2}{4 \div 2} = \frac{1}{2}
\]

Correct Answer: (a) 1/2

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Problem 4: Decimal Equivalent of 2/8

Question: What is the decimal equivalent of 2/8?
- a. 0.25
- b. 0.5
- c. 0.75

Solution:
To convert a fraction to a decimal, divide the numerator by the denominator:
\[
\frac{2}{8} = 2 \div 8 = 0.25
\]

Correct Answer: (a) 0.25

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Problem 5: Sides of a Rhombus

Question: How many sides does a rhombus have?
- a. 4
- b. 5

Solution:
A rhombus is a type of quadrilateral, which means it has 4 sides. All sides of a rhombus are equal in length.

Correct Answer: (a) 4

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Problem 6: Number of Square Units in a Closed Figure

Question: The number of square units in a closed figure represents:
- a. Area
- b. Perimeter
- c. Length plus width
- d. None of the above

Solution:
The area of a closed figure is the total number of square units that fit inside the boundary of the figure. For example, if a rectangle is 3 units long and 2 units wide, its area is:
\[
\text{Area} = \text{length} \times \text{width} = 3 \times 2 = 6 \text{ square units}
\]

Correct Answer: (a) Area

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Problem 7: Likely to Hold 8 oz?

Question: Which one would most likely hold 8 oz?
- a. Cup
- b. Balloon
- c. Spoon
- d. Bathtub

Solution:
- An 8-ounce cup is a common household item used to measure liquids.
- A balloon is not designed to hold liquid consistently.
- A spoon holds much less than 8 ounces.
- A bathtub holds far more than 8 ounces.

Correct Answer: (a) Cup

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Problem 8: Solve for x in 2x + 1 = 9

Question: If \(2x + 1 = 9\), what is \(x\)?
- a. 6
- b. 4
- c. 9
- d. 10

Solution:
Solve the equation step by step:
1. Start with the equation:
\[
2x + 1 = 9
\]
2. Subtract 1 from both sides:
\[
2x = 8
\]
3. Divide both sides by 2:
\[
x = 4
\]

Correct Answer: (b) 4

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Problem 9: 6% of 25

Question: What is 6% of 25?
- a. 1.2
- b. 1.5
- c. 1.7
- d. 1.8

Solution:
To find 6% of 25, multiply 25 by 0.06:
\[
6\% \text{ of } 25 = 25 \times 0.06 = 1.5
\]

Correct Answer: (b) 1.5

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Final Answers:

1. (b) 2, 3, 5, 7, 11
2. (d) Mass
3. (a) 1/2
4. (a) 0.25
5. (a) 4
6. (a) Area
7. (a) Cup
8. (b) 4
9. (b) 1.5

Boxed Final Answer:
\[
\boxed{(b), (d), (a), (a), (a), (a), (a), (b), (b)}
\]