Weekly Math Review Answer Key

Weekly Math Review: Answer Key & Comprehensive Explanations

This comprehensive guide provides answer keys and detailed explanations for a typical week's worth of math review problems. It's designed to help students solidify their understanding of key mathematical concepts, identify areas needing further attention, and build confidence in their problem-solving abilities. Whether you're preparing for a test, reinforcing classroom learning, or simply brushing up on your math skills, this resource will serve as a valuable tool. We'll cover a range of topics, from basic arithmetic to more advanced algebra and geometry concepts. Remember, understanding the why behind the answer is just as crucial as getting the correct solution.

Monday: Arithmetic & Number Sense

Problems:

1. Calculate: 345 + 678 - 211 + 45
2. Find the product of 12 and 15.
3. Divide 875 by 25.
4. What is 25% of 60?
5. Simplify the fraction 18/24.

Answer Key & Explanations:

1. 345 + 678 - 211 + 45 = 857

   • First, add 345 and 678: 1023
   • Then, subtract 211 from the sum: 812
   • Finally, add 45 to get the final answer: 857

2. 12 x 15 = 180

   • You can use standard multiplication or break it down: (10 x 15) + (2 x 15) = 150 + 30 = 180

3. 875 / 25 = 35

   • Long division or recognizing that 25 x 30 = 750 and 25 x 7 = 175 (750 + 175 = 875) will give you the answer.

4. 25% of 60 = 15

   • Convert 25% to a decimal (0.25) and multiply by 60: 0.25 x 60 = 15 Alternatively, find 10% of 60 (6) and multiply by 2.5 (2.5 x 6 = 15).

5. 18/24 = 3/4

   • Find the greatest common divisor (GCD) of 18 and 24, which is 6. Divide both the numerator and denominator by 6 to simplify the fraction.

Tuesday: Algebra Basics

Problems:

1. Solve for x: 3x + 7 = 16
2. Simplify the expression: 4(2a + 3b) - 2(a - b)
3. Solve for y: y/5 - 2 = 8
4. If a = 4 and b = -2, what is the value of 3a - 2b?
5. Solve for z: 2z + 5 = z - 3

Answer Key & Explanations:

1. 3x + 7 = 16

   • Subtract 7 from both sides: 3x = 9
   • Divide both sides by 3: x = 3

2. 4(2a + 3b) - 2(a - b) = 6a + 14b

   • Distribute the 4 and the -2: 8a + 12b - 2a + 2b
   • Combine like terms: 6a + 14b

3. y/5 - 2 = 8

   • Add 2 to both sides: y/5 = 10
   • Multiply both sides by 5: y = 50

4. 3a - 2b = 16

   • Substitute a = 4 and b = -2: 3(4) - 2(-2) = 12 + 4 = 16

5. 2z + 5 = z - 3

   • Subtract z from both sides: z + 5 = -3
   • Subtract 5 from both sides: z = -8

Wednesday: Geometry Fundamentals

Problems:

1. Find the area of a rectangle with length 12 cm and width 5 cm.
2. Calculate the perimeter of a square with side length 8 inches.
3. What is the area of a triangle with base 10 m and height 6 m?
4. Find the circumference of a circle with a radius of 7 cm (use π ≈ 22/7).
5. A cube has a side length of 4 cm. What is its volume?

Answer Key & Explanations:

1. Area of a rectangle = length x width = 12 cm x 5 cm = 60 cm²

2. Perimeter of a square = 4 x side length = 4 x 8 inches = 32 inches

3. Area of a triangle = (1/2) x base x height = (1/2) x 10 m x 6 m = 30 m²

4. Circumference of a circle = 2πr = 2 x (22/7) x 7 cm = 44 cm

5. Volume of a cube = side length³ = 4 cm x 4 cm x 4 cm = 64 cm³

Thursday: Data Handling & Probability

Problems:

1. Find the mean of the following data set: {5, 8, 12, 15, 20}
2. What is the median of the data set: {2, 4, 6, 8, 10, 12}?
3. A bag contains 3 red marbles and 5 blue marbles. What is the probability of picking a red marble?
4. A coin is tossed twice. What is the probability of getting two heads?
5. A dice is rolled. What is the probability of rolling an even number?

Answer Key & Explanations:

1. Mean = (sum of data) / (number of data points) = (5 + 8 + 12 + 15 + 20) / 5 = 60 / 5 = 12

2. Median: Since there's an even number of data points, the median is the average of the two middle values: (6 + 8) / 2 = 7

3. Probability of picking a red marble = (number of red marbles) / (total number of marbles) = 3 / 8

4. Probability of getting two heads = (1/2) x (1/2) = 1/4 (Each toss is an independent event)

5. Probability of rolling an even number = (number of even numbers) / (total number of possible outcomes) = 3/6 = 1/2 (Even numbers are 2, 4, and 6)

Friday: Mixed Review

Problems:

1. Solve the equation: 2(x + 3) = 10
2. Find the area of a circle with a diameter of 14 cm (use π ≈ 22/7).
3. Simplify the expression: 5x + 2y - 3x + 4y
4. What is 30% of 150?
5. A bag contains 4 green apples and 6 red apples. What is the probability of picking a green apple?

Answer Key & Explanations:

1. 2(x + 3) = 10

   • Distribute the 2: 2x + 6 = 10
   • Subtract 6 from both sides: 2x = 4
   • Divide by 2: x = 2

2. Area of a circle = πr² The radius is half the diameter, so r = 7 cm. Area = (22/7) x 7² cm² = 154 cm²

3. 5x + 2y - 3x + 4y = 2x + 6y Combine like terms.

4. 30% of 150 = 0.30 x 150 = 45

5. Probability of picking a green apple = (number of green apples) / (total number of apples) = 4/10 = 2/5

Frequently Asked Questions (FAQ)

• Q: What if I get a different answer?

  • A: Carefully review your steps. Double-check your calculations and ensure you've applied the correct formulas and mathematical principles. If you're still stuck, try working through the problem again, perhaps using a different approach. Consider seeking help from a teacher or tutor.

• Q: Can I use a calculator?

  • A: While calculators can be helpful for complex calculations, try to solve as much as possible manually. This will help you build a stronger understanding of the underlying concepts. Calculators are tools, but understanding the process is paramount.

• Q: Are these problems representative of a typical weekly review?

  • A: These problems are representative of the types of questions you might encounter in a typical weekly math review, covering fundamental concepts across various areas of mathematics. However, the specific topics and difficulty level may vary depending on your grade level and curriculum.

• Q: Where can I find more practice problems?

  • A: Your textbook, online resources, and math workbooks are excellent sources for additional practice problems. The key is consistent practice to reinforce your understanding.

Conclusion

This weekly math review provides a comprehensive overview of essential mathematical concepts and problem-solving techniques. Consistent practice and understanding the underlying principles are crucial for success in mathematics. Remember to review your work carefully, seek help when needed, and celebrate your progress along the way. Mathematics is a journey of continuous learning and improvement. Don't be discouraged by challenges; embrace them as opportunities for growth. With dedication and perseverance, you can master these concepts and achieve your academic goals. This detailed explanation and answer key should equip you to tackle similar problems confidently and independently. Keep practicing, and you’ll see improvement in your math skills.