Revision Test 3 Chapters 6 And 7 Math Problems With Solutions

This article provides a detailed walkthrough of the solutions to a revision test covering Chapters 6 and 7, likely focusing on basic algebraic concepts. This comprehensive guide aims to help students understand the underlying principles and problem-solving techniques involved. Each question is addressed with a clear explanation, ensuring a thorough grasp of the material. Let's dive into the problems!

Question 1: Evaluating Algebraic Expressions

The first question presents a straightforward algebraic expression evaluation. When x = 8, we need to find the value of 18 - x. This question tests the fundamental skill of substituting a given value into an expression and performing the arithmetic operation. To solve this, we replace the variable x with the number 8 in the expression 18 - x. This results in the calculation 18 - 8. Performing the subtraction, we find that 18 - 8 equals 10. Therefore, the correct answer is C. 10. This type of question is crucial for building a strong foundation in algebra, as it reinforces the concept of variables and their substitution. Understanding how to correctly substitute values is essential for tackling more complex algebraic problems later on. It also highlights the importance of accurate arithmetic skills in solving mathematical expressions. Students should practice similar problems to solidify their understanding of this concept. The ability to evaluate expressions is not only useful in mathematics but also in various real-world applications where quantities and their relationships are expressed algebraically. For example, in physics, one might need to calculate the velocity of an object given its initial velocity, acceleration, and time using an algebraic formula. In economics, one might use algebraic expressions to model supply and demand curves. Therefore, mastering this basic skill is paramount for success in many fields.

Question 2: Solving Simple Equations

The second question focuses on solving a basic linear equation. If 13 = a - 9 is a true sentence, then what is the value of a? This question assesses the student's ability to isolate a variable in an equation. To find the value of a, we need to isolate it on one side of the equation. The equation is given as 13 = a - 9. To isolate a, we perform the inverse operation of subtracting 9, which is adding 9, to both sides of the equation. This maintains the equality. Adding 9 to both sides, we get 13 + 9 = a - 9 + 9. Simplifying this, we have 22 = a. Therefore, the value of a is 22, and the correct answer is E. 22. Solving equations is a fundamental skill in algebra, and this question provides a good example of how to solve a simple linear equation. The key is to perform the same operation on both sides of the equation to maintain balance and isolate the variable. This concept is used extensively in various mathematical and scientific contexts. For example, in physics, one might need to solve equations to determine unknown forces or accelerations. In chemistry, equations are used to balance chemical reactions and calculate the amounts of reactants and products. Understanding how to solve equations is also crucial for problem-solving in everyday life. For instance, if you want to calculate how much money you need to save each month to reach a certain goal, you would need to set up and solve an equation. Therefore, mastering this skill is essential for both academic and practical purposes.

Question 3: Age Word Problems and Algebraic Representation

This question introduces a word problem that requires translating a real-world scenario into an algebraic expression. Maria is x years old. How old will she be in two years? This problem tests the ability to represent future age using algebraic notation. To determine Maria's age in two years, we need to add 2 to her current age, which is represented by x. Therefore, Maria's age in two years will be x + 2. This question highlights the importance of understanding how to represent real-world situations using algebraic expressions. Word problems often require careful reading and translation of the given information into mathematical language. The ability to do this is crucial for solving a wide range of problems in mathematics and other fields. For example, in finance, one might use algebraic expressions to represent investment returns over time. In engineering, expressions might be used to model the behavior of physical systems. Word problems also help to develop critical thinking and problem-solving skills. By breaking down a problem into smaller parts and identifying the relevant information, students can learn to approach complex situations in a systematic way. Furthermore, this type of question reinforces the concept of variables and their use in representing unknown quantities. Practice with word problems is essential for developing a strong understanding of algebra and its applications.