Weekly Math Review Q1 1 Answer Key

Weekly Math Review Q1: Answer Key & Comprehensive Guide

This comprehensive guide provides answers and detailed explanations for a typical first-quarter weekly math review, covering a range of topics commonly taught in middle and high school. This isn't a specific answer key tied to a particular textbook, but rather a model representing the types of problems and concepts you'd encounter. Remember to always check your specific curriculum and teacher's instructions for the most accurate grading. This guide aims to aid understanding, not replace individual learning and problem-solving.

Week 1: Fundamentals of Algebra & Number Sense

This week typically focuses on refreshing fundamental skills:

1.1 Order of Operations (PEMDAS/BODMAS)

Problem: Evaluate: 3 + 2 × (5 - 2)² ÷ 3

Solution:

Following PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division from left to right, Addition and Subtraction from left to right):

1. Parentheses/Brackets: (5 - 2) = 3
2. Exponents/Orders: 3² = 9
3. Multiplication: 2 × 9 = 18
4. Division: 18 ÷ 3 = 6
5. Addition: 3 + 6 = 9

Answer: 9

1.2 Integers and Real Numbers

Problem: Simplify: -5 + 12 - (-3) + 7 - 10

Solution:

Remember that subtracting a negative is equivalent to adding a positive:

-5 + 12 + 3 + 7 - 10 = 7

Answer: 7

1.3 Fractions and Decimals

Problem: Calculate: (2/3) + (1/4) - (1/2)

Solution: Find a common denominator (12):

(8/12) + (3/12) - (6/12) = 5/12

Answer: 5/12

1.4 Basic Equations

Problem: Solve for x: 2x + 5 = 11

Solution:

1. Subtract 5 from both sides: 2x = 6
2. Divide both sides by 2: x = 3

Answer: x = 3

Week 2: Linear Equations & Inequalities

This week builds upon the foundation by introducing linear equations and inequalities.

2.1 Solving Linear Equations

Problem: Solve for y: 3(y - 2) = 9 + 2y

Solution:

1. Distribute the 3: 3y - 6 = 9 + 2y
2. Subtract 2y from both sides: y - 6 = 9
3. Add 6 to both sides: y = 15

Answer: y = 15

2.2 Solving Linear Inequalities

Problem: Solve for z: -2z + 4 > 10

Solution:

1. Subtract 4 from both sides: -2z > 6
2. Divide both sides by -2 (remember to flip the inequality sign when dividing by a negative number): z < -3

Answer: z < -3

2.3 Graphing Linear Equations

Problem: Graph the equation: y = 2x + 1

Solution:

This is a linear equation in slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept). The y-intercept is 1 (the point (0, 1)). The slope is 2 (meaning for every 1 unit increase in x, y increases by 2). Plot the y-intercept, and then use the slope to find other points on the line.

2.4 Systems of Linear Equations

Problem: Solve the system of equations:

x + y = 5 x - y = 1

Solution: Use either substitution or elimination. Elimination is easier here: Add the two equations together:

2x = 6 => x = 3

Substitute x = 3 into either original equation to solve for y:

3 + y = 5 => y = 2

Answer: x = 3, y = 2

Week 3: Geometry & Measurement

This week typically covers basic geometric concepts and measurements.

3.1 Area and Perimeter

Problem: Find the area and perimeter of a rectangle with length 8 cm and width 5 cm.

Solution:

• Perimeter: P = 2(length + width) = 2(8 + 5) = 26 cm
• Area: A = length × width = 8 × 5 = 40 cm²

Answer: Perimeter = 26 cm, Area = 40 cm²

3.2 Volume

Problem: Find the volume of a rectangular prism with length 4m, width 3m, and height 2m.

Solution: V = length × width × height = 4 × 3 × 2 = 24 m³

Answer: 24 m³

3.3 Angles and Triangles

Problem: Two angles in a triangle are 45° and 65°. Find the measure of the third angle.

Solution: The sum of angles in a triangle is 180°. Therefore, the third angle is 180° - 45° - 65° = 70°

Answer: 70°

3.4 Circles

Problem: Find the circumference of a circle with a radius of 7 cm. Use π ≈ 22/7.

Solution: Circumference = 2πr = 2 × (22/7) × 7 = 44 cm

Answer: 44 cm

Week 4: Ratio, Proportion, and Percent

This week focuses on ratios, proportions, and percentage calculations.

4.1 Ratios and Proportions

Problem: If the ratio of boys to girls in a class is 3:5, and there are 15 girls, how many boys are there?

Solution: Set up a proportion: 3/5 = x/15. Solve for x: x = (3 × 15) / 5 = 9

Answer: 9 boys

4.2 Percentage Calculations

Problem: What is 20% of 80?

Solution: (20/100) × 80 = 16

Answer: 16

4.3 Percent Increase and Decrease

Problem: A price increased from $50 to $60. What is the percentage increase?

Solution: Percentage increase = [(New Value - Original Value) / Original Value] × 100% = [(60 - 50) / 50] × 100% = 20%

Answer: 20%

4.4 Applications of Percent

Problem: A shirt is on sale for 25% off its original price of $40. What is the sale price?

Solution: Discount = 25% of $40 = (25/100) × 40 = $10. Sale price = $40 - $10 = $30

Answer: $30

Week 5: Review and Assessment

This week is dedicated to reviewing the topics covered in the previous weeks and taking an assessment. The assessment will likely include problems similar to those presented above, testing your understanding of all the concepts. This section wouldn't include answers as it's the assessment itself. However, reviewing the above explanations will help in preparation. Remember to focus on areas where you feel less confident and seek additional help if needed.

This comprehensive review covers a significant portion of the math curriculum for the first quarter. Remember to consult your textbook, class notes, and teacher for specific details and additional practice problems. Consistent practice and understanding of the fundamental concepts are crucial for success in mathematics. Good luck with your studies!