GRADE 8 Mathematics – Algebraic Expressions Quiz
1. What is the simplified form of 4y - 7y?
The correct answer is -3y. When you subtract 7y from 4y, you get -3y.
2. Simplify the expression 2(a + 3) - 4a.
The correct answer is -2a + 6. Distribute the 2 to both terms inside the parentheses to get 2a + 6. Then subtract 4a from 2a to get -2a.
3. What is the simplified form of 5(2x + 3) - x?
The correct answer is 9x + 15. Distribute the 5 to both terms inside the parentheses to get 10x + 15. Then subtract x from 10x to get 9x.
4. Simplify the expression 3x^2 + 2x - x^2 + 5.
The correct answer is 2x^2 + 2x + 5. Combine like terms by adding the coefficients of x^2 and x terms to get 2x^2 + 2x. Then add the constant term 5.
5. Simplify the expression 4(2y - 3) + 5(2 + y).
The correct answer is 8y - 6 + 10 + 5y. Distribute the coefficients to terms in parentheses and then combine like terms.
6. What is the simplified form of 2x^2 + 3y - x^2 + 2y - 5?
The correct answer is x^2 + 5y - 5. Combine like terms by adding the coefficients of x^2 and y terms, and then subtract 5 at the end.
7. What is the simplified form of 2x^2 + 5x - 4(3x - 2)?
The correct answer is 2x^2 + 5x - 12x + 8. Distribute the -4 to both terms inside the parentheses and then combine like terms.
8. What is the simplified form of 3x + 7x + 2x?
Combining like terms, 3x + 7x + 2x = 12x.
9. Which of the following is not an algebraic expression?
4 + 6 = 10 is a numerical operation, not an algebraic expression.
10. Simplify the expression: 5(2x - 3)
Distributing the 5, you get 5(2x) - 5(3) = 10x - 15.
11. Which is the simplified form of 4x - (2x + 3)?
When subtracting, distribute the negative sign: 4x - 2x - 3 = 2x - 3.
12. What is the sum of 5x^2 + 3x + 2 and 2x^2 - 4x + 3?
Combine like terms for each variable: 5x^2 + 2x^2 + 3x - 4x + 2 + 3 = 7x^2 - x + 5.
13. Which of the following is equivalent to 2(x + 3) - 3(2x - 4)?
Simplify by distributing and then combining like terms: 2x + 6 - 6x + 12 = -4x + 18. Therefore, 2(x + 3) - 3(2x - 4) = -x + 8.
14. What is the value of 2x^2 - 5x + 3 when x = 4?
Substitute x = 4 into the expression to get 2(4)^2 - 5(4) + 3 = 32 - 20 + 3 = 15. Therefore, 2x^2 - 5x + 3 when x = 4 is 11.
15. What term describes the number in front of a variable in an algebraic expression?
The coefficient is the number in front of the variable in an algebraic expression.
16. Which of the following is a constant term?
A constant term is a number without a variable attached, so 7 is a constant term.
17. If x = 2, what is x^2 + 3x - 4?
Substitute x = 2 into the expression to get 2^2 + 3(2) - 4 = 4 + 6 - 4 = 10. Therefore, x^2 + 3x - 4 when x = 2 is 10.
18. Expand and simplify the expression: (2x + 3)(x - 4)
Use the distributive property to expand: 2x * x + 2x * -4 + 3 * x + 3 * -4 = 2x^2 - 8x - 12.
19. Which of the following is a binomial expression?
A binomial expression consists of two terms, such as 3x + 7.
20. What is the simplified form of 2x^2 + 5x - x^2 + 3?
Combine like terms to get 2x^2 - x^2 + 5x + 3 = x^2 + 4x + 3.
21. If 3y = 15, what is the value of y?
Divide both sides of the equation by 3 to find y: 3y / 3 = 15 / 3. Therefore, y = 5.
22. What is the result of 2(3x + 5) - x when x = 2?
Substitute x = 2 into the expression: 2(3(2) + 5) - 2 = 2(6 + 5) - 2 = 2(11) - 2 = 22 - 2 = 20.
23. Solve for x: 3(x + 4) = 15
Distribute the 3 and then solve for x: 3x + 12 = 15. Therefore, x = 3.
24. Which of the following is a trinomial expression?
A trinomial expression consists of three terms, such as 2x^2 - 3x + 5.
25. What is the value of 2(x + y) when x = 3 and y = 4?
Substitute x = 3 and y = 4 into the expression: 2(3 + 4) = 2(7) = 14.
26. Which of the following expressions is in standard form?
Standard form of an algebraic expression requires terms to be arranged in descending order of exponents, hence 4x^2 - x + 3.
27. Evaluate the expression 3x^2 - 2x + 5 when x = 1
Substitute x = 1 into the expression: 3(1)^2 - 2(1) + 5 = 3 - 2 + 5 = 6.
28. What is the simplified form of 2(a + b) - 3(a - b)?
Apply distribution: 2(a + b) = 2a + 2b, -3(a - b) = -3a + 3b. Combine like terms: 2a - 3a = -a, 2b + 3b = 5b. Therefore, 2(a + b) - 3(a - b) simplifies to 5a + 5b.
29. What is the simplified form of 3(p + 2q) + 4(p - 3q)?
Apply distribution: 3(p + 2q) = 3p + 6q, 4(p - 3q) = 4p - 12q. Combine like terms: 3p + 4p = 7p, 6q - 12q = -6q. Therefore, 3(p + 2q) + 4(p - 3q) simplifies to 7p - 10q.
30. What is the simplified form of 6(x - 2y) - 2(x + 3y)?
Apply distribution: 6(x - 2y) = 6x - 12y, -2(x + 3y) = -2x - 6y. Combine like terms: 6x - 2x = 4x, -12y - 6y = -8y. Therefore, 6(x - 2y) - 2(x + 3y) simplifies to 4x - 8y.
31. What is the simplified form of 5(x + y) - 2(x - y)?
Apply distribution: 5(x + y) = 5x + 5y, -2(x - y) = -2x + 2y. Combine like terms: 5x - 2x = 3x, 5y + 2y = 7y. Therefore, 5(x + y) - 2(x - y) simplifies to 5x + 7y.
32. Simplify: 3(x + 2y) + 2(x - y)
Apply distribution: 3(x + 2y) = 3x + 6y, 2(x - y) = 2x - 2y. Combine like terms: 3x + 2x = 5x, 6y - 2y = 4y. Therefore, 3(x + 2y) + 2(x - y) simplifies to 5x + 4y.