Weekly Math Review Q2 6 Answer Key

Weekly Math Review Q2 6 Answer Key: A Comprehensive Guide

This comprehensive guide provides answers and detailed explanations for a hypothetical "Weekly Math Review Q2 6." Since I don't have access to a specific, pre-existing "Weekly Math Review Q2 6," I will create a sample review covering various mathematical concepts typically taught in a middle or high school curriculum during the second quarter. This will allow for a detailed walkthrough demonstrating how to approach different problem types and explain the underlying concepts. Remember to always refer to your actual review sheet for the correct questions and context.

Section 1: Algebra

1.1 Solving Linear Equations:

Question: Solve for x: 3x + 7 = 16

Answer:

1. Subtract 7 from both sides: 3x = 9
2. Divide both sides by 3: x = 3

Explanation: The goal is to isolate 'x'. We perform inverse operations to undo the addition and multiplication. Subtracting 7 cancels out the +7, and dividing by 3 cancels out the multiplication by 3.

1.2 Systems of Equations:

Question: Solve the system of equations:

x + y = 5 2x - y = 4

Answer:

This can be solved using either substitution or elimination. Let's use elimination:

1. Add the two equations: (x + y) + (2x - y) = 5 + 4 which simplifies to 3x = 9
2. Solve for x: x = 3
3. Substitute x = 3 into either original equation to solve for y: 3 + y = 5 => y = 2

Solution: x = 3, y = 2

Explanation: Elimination works by adding or subtracting equations to eliminate one variable. In this case, adding the equations eliminated 'y', allowing us to solve for 'x'. Substitution involves solving one equation for one variable and substituting that expression into the other equation.

1.3 Inequalities:

Question: Solve and graph the inequality: 2x - 5 > 3

Answer:

1. Add 5 to both sides: 2x > 8
2. Divide both sides by 2: x > 4

Graph: The graph would be a number line with an open circle at 4 and an arrow pointing to the right (representing all values greater than 4).

Explanation: Solving inequalities is similar to solving equations, but the inequality sign flips if you multiply or divide by a negative number.

Section 2: Geometry

2.1 Area and Perimeter:

Question: A rectangle has a length of 12 cm and a width of 5 cm. Find its area and perimeter.

Answer:

• Area: Area = length x width = 12 cm x 5 cm = 60 cm²
• Perimeter: Perimeter = 2(length + width) = 2(12 cm + 5 cm) = 34 cm

Explanation: Area measures the space inside a shape, while perimeter measures the distance around it.

2.2 Pythagorean Theorem:

Question: A right-angled triangle has legs of length 6 cm and 8 cm. Find the length of the hypotenuse.

Answer:

The Pythagorean theorem states: a² + b² = c² where a and b are the legs and c is the hypotenuse.

1. Substitute values: 6² + 8² = c²
2. Simplify: 36 + 64 = c² => 100 = c²
3. Take the square root: c = 10 cm

Explanation: The Pythagorean theorem is fundamental to right-angled triangles, relating the lengths of its sides.

2.3 Similar Triangles:

Question: Two similar triangles have corresponding sides in the ratio 2:3. If the smaller triangle has an area of 12 cm², what is the area of the larger triangle?

Answer:

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides.

1. Square the ratio: (2/3)² = 4/9
2. Set up a proportion: 12/x = 4/9
3. Solve for x: x = 27 cm²

Explanation: The ratio of areas of similar figures is always the square of the ratio of their corresponding sides.

Section 3: Statistics and Probability

3.1 Mean, Median, and Mode:

Question: Find the mean, median, and mode of the data set: {2, 4, 6, 6, 8, 10}

Answer:

• Mean: (2 + 4 + 6 + 6 + 8 + 10) / 6 = 6
• Median: The middle value(s) when the data is ordered. In this case, (6 + 6) / 2 = 6
• Mode: The most frequent value. In this case, 6.

Explanation: Mean is the average, median is the middle value, and mode is the most frequent value.

3.2 Probability:

Question: A bag contains 3 red marbles and 5 blue marbles. What is the probability of drawing a red marble?

Answer:

Probability = (Number of favorable outcomes) / (Total number of outcomes) = 3 / (3 + 5) = 3/8

Explanation: Probability is expressed as a fraction, where the numerator is the number of ways the event can occur, and the denominator is the total number of possible outcomes.

Section 4: Word Problems

4.1 Mixture Problems:

Question: A chemist needs to mix a 20% acid solution with a 50% acid solution to obtain 10 liters of a 30% acid solution. How many liters of each solution should be used?

Answer: Let x be the liters of 20% solution and y be the liters of 50% solution.

We have two equations:

1. x + y = 10 (total volume)
2. 0.20x + 0.50y = 0.30(10) (acid concentration)

Solving this system of equations (using substitution or elimination) gives: x = 5 liters and y = 5 liters.

4.2 Distance-Rate-Time Problems:

Question: A train travels 200 miles at a speed of 50 mph. How long does it take?

Answer:

Time = Distance / Speed = 200 miles / 50 mph = 4 hours

Explanation: This is a direct application of the formula: Time = Distance / Speed.

Section 5: Advanced Topics (Depending on Grade Level)

The following sections would be included only if relevant to the specific "Weekly Math Review Q2 6." These are examples and would need to be tailored to the actual content.

5.1 Quadratic Equations:

Question: Solve the quadratic equation: x² - 5x + 6 = 0

Answer: This can be factored as (x - 2)(x - 3) = 0. Therefore, x = 2 or x = 3. Alternatively, the quadratic formula can be used.

5.2 Functions:

Question: Given the function f(x) = 2x + 1, find f(3).

Answer: Substitute x = 3 into the function: f(3) = 2(3) + 1 = 7

5.3 Trigonometry (If applicable):

Question: Find the sine, cosine, and tangent of a 30-degree angle.

Answer: These values are standard trigonometric ratios often found in trigonometric tables or calculated using a calculator. sin(30°) = 1/2, cos(30°) = √3/2, tan(30°) = 1/√3

This expanded answer key provides not only the solutions but also detailed explanations of the underlying mathematical concepts. Remember to always cross-reference with your specific "Weekly Math Review Q2 6" for accuracy. This comprehensive approach aims to build a strong understanding, enhancing learning and preparing students for assessments. Using this model, you can easily adapt it to other math review sheets by simply changing the questions and solutions. Remember to always check your school's specific curriculum for the most accurate and relevant information.