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Question 1: What is a mathematical sentence that says two expressions are equal and includes an equal sign?
- Variable
- Equation
- Expression
- Constant
Answer: B. Equation
Explanation: An equation is defined as a mathematical sentence that states two expressions are equal, which is indicated by the presence of an equal sign.
Question 2: Which of these is a letter, such as x or y, that stands for an unknown number?
- Exponent
- Operator
- Variable
- Constant
Answer: C. Variable
Explanation: In algebra, a variable is a symbol, typically a letter like x or y, used to represent an unknown value in an equation.
Question 3: What is the specific number that makes an equation true called?
- Variable
- Intercept
- Solution
- Expression
Answer: C. Solution
Explanation: A solution is the specific numerical value that, when substituted for the variable, makes the mathematical statement of the equation true.
Question 4: What is the shape of the graph of a linear equation when plotted on a coordinate grid?
- Straight line
- Curve
- Parabola
- Circle
Answer: A. Straight line
Explanation: By definition, the graph of a linear equation always forms a straight line when plotted on a standard coordinate grid.
Question 5: To solve a one-step equation involving addition, what operation must you perform on both sides?
- Multiplication
- Addition
- Division
- Subtraction
Answer: D. Subtraction
Explanation: To isolate the variable in an addition equation, you must perform the inverse operation, which is subtracting the same number from both sides.
Question 6: What is the y-intercept of a linear equation?
- Where y is 1
- Where y is 0
- Where x is 1
- Where x is 0
Answer: D. Where x is 0
Explanation: The y-intercept is the point where the line crosses the y-axis, which occurs specifically when the value of x is 0.
Question 7: What does a positive slope indicate on a coordinate graph?
- Line is flat
- Values increase together
- Line goes down
- Values decrease together
Answer: B. Values increase together
Explanation: A positive slope means that as the values on the horizontal axis increase, the values on the vertical axis also increase.
Question 8: Which of these is a mathematical expression that does NOT have an equal sign?
- x + 5 = 10
- 2x = 8
- x + 5
- y = x + 2
Answer: C. x + 5
Explanation: An algebraic expression is a combination of numbers, variables, and operations that does not contain an equal sign, whereas an equation must always include an equal sign to show that two values are equivalent.
Question 9: Which of the following is a characteristic of a linear equation?
- Contains no variables
- Variable raised to power 3
- Variable raised to power 2
- No variable power > 1
Answer: D. No variable power > 1
Explanation: A linear equation is defined by having one or two variables where no variable is raised to a power greater than 1.
Question 10: In the equation 3x = 12, what is the first step to isolate the variable x?
- Subtract 3 from both sides
- Divide both sides by 3
- Multiply both sides by 3
- Add 3 to both sides
Answer: B. Divide both sides by 3
Explanation: Since 3 is multiplied by x, you must perform the inverse operation, which is division, to isolate the variable.