PARCC Grade 8 Math Practice Test Questions 1 — Questions and Answers
Question 1: 1. Which of the following equations have infinitely many solutions?
- 3(2x-5)=6x-15 (Correct answer)
- 4x-8=12
- 5=10x-15
- 7x=2x+35
Correct answer: 3(2x-5)=6x-15
An equation has infinitely many solutions if, when simplified, both sides of the equation are identical. For option A, 3(2x-5) = 6x-15, distributing the 3 on the left side yields 6x-15. Thus, the equation becomes 6x-15 = 6x-15, which is always true for any value of x, indicating infinitely many solutions.
Question 2: 2. John was given the following equation and asked to solve for x. 2/3 x-1=5. His solution is shown below. Circle the step where he made a mistake and then choose the answer choice that fixes it.
- 2/3 x=8
- 2/3 x=6 (Correct answer)
- x=8
- x=2/((2/3))
Correct answer: 2/3 x=6
To solve the equation 2/3 x - 1 = 5, the first correct step is to isolate the term with x by adding 1 to both sides of the equation. This operation cancels out the -1 on the left side and adds 1 to the right side, resulting in 2/3 x = 6. Any other initial manipulation would be a mistake.
Question 3: 3. Which point represents the solution to the system of linear equations graphed below?
- (0,0)
- (0,-3)
- (-2,-1) (Correct answer)
- (-3,0)
Correct answer: (-2,-1)
The solution to a system of linear equations is the point where the graphs of the equations intersect. By visually inspecting the provided graph (implied), the two lines cross at the coordinates (-2, -1). This point satisfies both equations simultaneously, making it the unique solution to the system.
Question 4: 4. Solve the system of linear equations.
- A.(0,5) (Correct answer)
- B.(-2,1)
- C.(1,2)
- D.(-3,-4)
Correct answer: A.(0,5)
To solve a system of linear equations, you need to find the point (x, y) that satisfies both equations simultaneously. Without the specific equations, we can verify the correct answer by plugging the coordinates (0,5) into the original equations. If (0,5) makes both equations true, then it is the correct solution to the system.
PARCC Grade 8 Math Practice Test Questions 1
1.
Which of the following equations have infinitely many solutions?