Basic algebra: variables linear equations and identities. - Question Bank

1. Solve for 'm' in the equation: m/5 = 10
A) m = 2
B) m = 5
C) m = 15
D) m = 50
2. If a number is represented by 'n', what is 'n squared'?
A) 2n
B) n + 2
C) n²
D) n/2
3. The equation 2(x + 1) = 2x + 2 is an example of:
A) A conditional equation
B) A contradiction
C) An identity
D) A linear equation
4. Which expression means 'the product of a number and 7'?
A) x + 7
B) x - 7
C) 7x
D) x/7
5. In the equation 5x - 10 = 0, what is the value of 'x'?
A) x = 1
B) x = 2
C) x = 5
D) x = 10
6. Which equation represents 'a number divided by 3 is equal to 6'?
A) 3n = 6
B) n + 3 = 6
C) n - 3 = 6
D) n/3 = 6
7. Solve for 'p': 4p + 5 = 21
A) p = 3
B) p = 4
C) p = 5
D) p = 16
8. The expression (a - b)² = a² - 2ab + b² is:
A) A conditional equation
B) A contradiction
C) An identity
D) A definition
9. If you subtract 7 from a number and get 3, what is the number?
A) 3
B) 7
C) 10
D) 21
10. What does the variable 'x' represent in the equation 2x = 10?
A) A constant value
B) A quantity to be found
C) A coefficient
D) An exponent
11. Which of the following is a pair of like terms?
A) 3x and 3y
B) 5a and -2a
C) 4x² and 4x
D) 7b and 7
12. Solve for 'y': 15 - 2y = 7
A) y = 3
B) y = 4
C) y = 8
D) y = 11
13. If the cost of 'n' books at $5 each is $C, which equation represents this relationship?
A) C = n + 5
B) C = n - 5
C) C = 5n
D) C = n/5
14. The equation x + 5 = 5 + x is an example of:
A) A conditional equation
B) A contradiction
C) An identity
D) An inequality
15. What is the value of 'x' if 3x + 2 = 11?
A) x = 2
B) x = 3
C) x = 4
D) x = 9
16. Which equation has no solution?
A) 2x = 6
B) x + 1 = x + 1
C) 3x - 2 = 3x - 5
D) x - 3 = 0
17. The expression 'half of a number decreased by four' can be written as:
A) 4 - x/2
B) x/2 + 4
C) x/2 - 4
D) 2x - 4
18. Solve for 'a': 7a + 3 = 24
A) a = 3
B) a = 4
C) a = 7
D) a = 21
19. Which of the following is a variable?
A) 10
B) π
C) y
D) -5
20. What is the value of 'x' in the equation 2x - 1 = 9?
A) x = 4
B) x = 5
C) x = 10
D) x = 18
21. If a rectangle has a length 'l' and a width 'w', its area is given by the formula:
A) l + w
B) 2l + 2w
C) l * w
D) l / w
22. The statement 'a + b = b + a' is an example of:
A) A conditional equation
B) A contradiction
C) An identity (Commutative Property)
D) A definition
23. Solve for 'k': k/4 = 5
A) k = 1
B) k = 4
C) k = 9
D) k = 20
24. Simplify: 8x - 3y + 2x + 5y
A) 10x + 2y
B) 6x + 8y
C) 10x - 8y
D) 6x + 2y
25. Which equation represents 'five more than a number is equal to twelve'?
A) n - 5 = 12
B) 5n = 12
C) n + 5 = 12
D) 5 + 12 = n
26. If the sum of two numbers is 15 and one number is 'n', what is the other number?
A) 15n
B) 15 - n
C) n - 15
D) 15 + n
27. An equation that is true for some values of the variable but not all is called a:
A) Identity
B) Contradiction
C) Conditional equation
D) Statement
28. In the expression 4a² + 7b - 3, the number 7 is a:
A) Variable
B) Constant
C) Coefficient
D) Exponent
29. Solve the equation: 5(m - 2) = 20
A) m = 2
B) m = 4
C) m = 6
D) m = 10
30. Which of the following is an algebraic term?
A) x + 5
B) 3y
C) 2x - y
D) a = b
31. If 'x' is a variable, what does '3x' represent?
A) Three more than x
B) Three times x
C) x divided by three
D) The square of x
32. The equation 2x - 5 = 2x + 1 is an example of:
A) An identity
B) A contradiction
C) A conditional equation
D) A linear equation
33. Which expression represents 'the sum of three consecutive integers'?
A) n + (n+1) + (n+2)
B) 3n
C) n + 3
D) n(n+1)(n+2)
34. Solve for 'z': 3z = 18
A) z = 3
B) z = 6
C) z = 9
D) z = 54
35. What is the value of the constant term in the expression 2x + 5y - 8?
A) 2
B) 5
C) -8
D) x
36. If a number is multiplied by 3 and then 5 is added to the result, the answer is 20. What is the number?
A) 5
B) 6
C) 7
D) 15
37. The expression (a + b)² = a² + 2ab + b² is a well-known algebraic:
A) Equation
B) Identity
C) Inequality
D) Formula
38. Which of the following is NOT a linear equation?
A) x/2 + 1 = 5
B) 4m - 3 = 9
C) y² = 16
D) 0.5n + 2 = 7
39. Solve for 'p' in the equation: 10 - p = 3
A) p = 7
B) p = 13
C) p = -7
D) p = 3
40. Simplify the expression: 3a + 5b - a + 2b
A) 2a + 3b
B) 4a + 7b
C) 2a + 7b
D) 4a + 3b
41. Which term represents a quantity that can change or vary?
A) Constant
B) Coefficient
C) Variable
D) Term
42. If the perimeter of a square is represented by 4s, where 's' is the side length, and the perimeter is 20 units, what is the value of 's'?
A) 4
B) 5
C) 10
D) 20
43. The equation 3(x + 2) = 3x + 6 is an example of a(n):
A) Conditional equation
B) Contradiction
C) Identity
D) Inequality
44. What is the coefficient of the 'y' term in the expression 7x - 4y + 9?
A) 7
B) -4
C) 4
D) 9
45. Solve the equation: 2(x + 3) = 14
A) x = 4
B) x = 5
C) x = 7
D) x = 11
46. If 'a' represents a variable, which expression correctly represents 'five less than twice a number'?
A) 2a - 5
B) 5 - 2a
C) 2(a - 5)
D) 5a - 2
47. An identity is an equation that is true for:
A) Only one specific value of the variable
B) Only two specific values of the variable
C) All possible values of the variable
D) No values of the variable
48. Which of the following is an example of a linear equation in one variable?
A) x² + 2x - 1 = 0
B) 3y - 5 = 10
C) a + b = 5
D) sin(θ) = 1/2
49. In the equation 5x + 7 = 22, what is the value of the variable 'x'?
A) 2
B) 3
C) 4
D) 5
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