WI Forward - Wisconsin Forward Mathematics: Algebraic Concepts Questions and Answers 2 — Questions and Answers
Question 1: Simplify: 4(2x - 5) + 3x
- 11x - 20 (Correct answer)
- 11x - 5
- 8x - 20
- 5x - 5
Correct answer: 11x - 20
Distribute: 8x - 20 + 3x = 11x - 20.
4(2x) = 8x, 4(-5) = -20, giving 8x - 20. Add 3x: 8x + 3x - 20 = 11x - 20.
Question 2: What is the slope of the line through (2, 5) and (6, 13)?
- 2 (Correct answer)
- 4
- 1/2
- 8
Correct answer: 2
Slope = (13-5)/(6-2) = 8/4 = 2.
m = (y2-y1)/(x2-x1) = (13-5)/(6-2) = 8/4 = 2. A slope of 2 means y increases by 2 for every 1 unit increase in x.
Question 3: Which equation represents 'twice a number decreased by seven equals fifteen'?
- 2n - 7 = 15 (Correct answer)
- 2(n - 7) = 15
- 7 - 2n = 15
- 2n + 7 = 15
Correct answer: 2n - 7 = 15
'Twice a number' = 2n, 'decreased by seven' = -7, 'equals fifteen' = 15.
'Twice a number' means 2n, 'decreased by seven' means subtract 7. Result: 2n - 7 = 15. Option B means 'twice the quantity (n-7),' which is different.
Question 4: What is the solution to y = x + 1 and y = -x + 5?
- (2, 3) (Correct answer)
- (3, 2)
- (1, 4)
- (4, 1)
Correct answer: (2, 3)
Set equal: x + 1 = -x + 5, so 2x = 4, x = 2, y = 3.
x + 1 = -x + 5. Add x: 2x + 1 = 5. Subtract 1: 2x = 4. x = 2, y = 2 + 1 = 3. Solution (2, 3) is where the lines intersect.
Question 5: Which set of ordered pairs represents a function?
- {(1,2),(3,4),(1,5)}
- {(1,2),(3,4),(5,6)} (Correct answer)
- {(2,1),(2,3),(2,5)}
- {(1,1),(1,2),(1,3)}
Correct answer: {(1,2),(3,4),(5,6)}
A function assigns exactly one output to each input. Only {(1,2),(3,4),(5,6)} has unique x-values.
A function requires each input to map to exactly one output. Options A, C, D all have repeated x-values with different outputs.
Question 6: Evaluate 3x² - 2x + 4 when x = -2.
- 20 (Correct answer)
- 12
- 8
- 16
Correct answer: 20
3(4) - 2(-2) + 4 = 12 + 4 + 4 = 20.
(-2)² = 4. Then 3(4) = 12, -2(-2) = +4. Total: 12 + 4 + 4 = 20.
