Grade 10 Direct Substitution Worksheet Answer Key Overview
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Direct substitution is a common technique used in mathematics to evaluate expressions or functions. This method involves replacing variables in an expression with specific values and then simplifying the expression to find the final result. Grade 10 students often encounter direct substitution in algebra and calculus problems, where they are required to substitute values for variables in equations or functions.
Direct substitution worksheets are a great way for Grade 10 students to practice and improve their skills in this concept. These worksheets typically contain a series of equations or functions with variables that need to be substituted with given values. Students are then asked to evaluate the expressions or functions using direct substitution and provide the final result. To help students check their work and understand the process better, answer keys are provided for these worksheets. In this article, we will provide a Grade 10 direct substitution worksheet answer key that covers various examples and scenarios.
1. Example 1:
Evaluate the expression 3x + 5 for x = 4.
Solution:
3(4) + 5 = 12 + 5 = 17
Answer: 17
2. Example 2:
Evaluate the function f(x) = x^2 – 2x + 3 for x = 3.
Solution:
f(3) = (3)^2 – 2(3) + 3 = 9 – 6 + 3 = 6
Answer: 6
3. Example 3:
Evaluate the expression 2y^2 – 3y + 4 for y = -2.
Solution:
2(-2)^2 – 3(-2) + 4 = 2(4) + 6 + 4 = 8 + 6 + 4 = 18
Answer: 18
4. Example 4:
Evaluate the function g(x) = 4x^3 – 2x^2 + 5x – 1 for x = 1.
Solution:
g(1) = 4(1)^3 – 2(1)^2 + 5(1) – 1 = 4 – 2 + 5 – 1 = 6
Answer: 6
5. Example 5:
Evaluate the expression 5a – b + 2c for a = 2, b = 3, and c = -1.
Solution:
5(2) – 3 + 2(-1) = 10 – 3 – 2 = 5
Answer: 5
By practicing these examples and using the provided answer key, Grade 10 students can enhance their understanding of direct substitution and gain confidence in evaluating expressions and functions. It is essential for students to grasp this concept as it forms the basis for more complex mathematical operations and problem-solving in higher grades.
In addition to individual examples, Grade 10 direct substitution worksheets may also include mixed problems that require students to apply direct substitution in various contexts. Students should pay attention to the order of operations (PEMDAS) when solving these problems to ensure accuracy in their calculations.
Overall, direct substitution is a fundamental skill that Grade 10 students need to master in mathematics. By regularly practicing with worksheets and utilizing answer keys for feedback, students can improve their proficiency in this concept and build a strong foundation for their future studies in algebra, calculus, and other advanced math courses.
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