MAP 8th Grade Math 2 — Questions and Answers

Question 1: A rectangle has a length of 3x + 2 and a width of x - 1. Which expression represents its perimeter?

4x + 1
8x + 2 (Correct answer)
3x² - x - 2
4x² + 2x - 2

Correct answer: 8x + 2

Perimeter = 2(length + width) = 2((3x+2)+(x-1)) = 2(4x+1) = 8x+2.

To find the perimeter of a rectangle, use P = 2(l + w). Substitute: P = 2((3x+2)+(x-1)) = 2(4x+1) = 8x+2. Be careful not to confuse perimeter (addition of sides) with area (multiplication of sides).

Question 2: Which of the following is the slope-intercept form of a line passing through (0, 4) with slope -2?

y = -2x
y = 4x - 2
y = -2x + 4 (Correct answer)
y = 2x + 4

Correct answer: y = -2x + 4

Slope-intercept form is y = mx + b. With slope m = -2 and y-intercept b = 4, the equation is y = -2x + 4.

Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Since the line passes through (0, 4), the y-intercept b = 4. The slope m = -2. Substituting gives y = -2x + 4.

Question 3: A bag contains 5 red, 3 blue, and 2 green marbles. What is the probability of drawing a blue marble?

1/3
3/10 (Correct answer)
3/8
1/5

Correct answer: 3/10

Total marbles = 5 + 3 + 2 = 10. P(blue) = 3/10.

The total number of marbles is 5 + 3 + 2 = 10. There are 3 blue marbles. The probability of drawing a blue marble is 3/10 = 0.3 or 30%. Always find the total first before computing the probability.

Question 4: What is the value of x in the equation 2(x + 3) = 14?

x = 2
x = 4 (Correct answer)
x = 5
x = 8

Correct answer: x = 4

2(x+3) = 14 → x+3 = 7 → x = 4.

To solve 2(x+3) = 14, first divide both sides by 2: x+3 = 7. Then subtract 3 from both sides: x = 4. You can verify by substituting back: 2(4+3) = 2(7) = 14.

Question 5: Which of the following represents a function?

A circle
A vertical line
{(1,2),(1,3),(2,4)}
{(1,2),(2,3),(3,4)} (Correct answer)

Correct answer: {(1,2),(2,3),(3,4)}

A function requires each input (x-value) to map to exactly one output. {(1,2),(2,3),(3,4)} has unique x-values, so it is a function.

A relation is a function if every input x has exactly one output y. A circle fails the vertical line test. A vertical line is not a function. In {(1,2),(1,3),(2,4)}, x=1 maps to both 2 and 3 — not a function. {(1,2),(2,3),(3,4)} has all unique x-values, so it is a function.

Question 6: A triangle has angles measuring 55 degrees, 70 degrees, and x degrees. What is the value of x?

35
45
55 (Correct answer)
65

Correct answer: 55

The sum of angles in a triangle = 180 degrees. 55 + 70 + x = 180, so x = 55.

The Triangle Angle Sum Theorem states that the interior angles of any triangle sum to 180 degrees. Setting up the equation: 55 + 70 + x = 180, which gives 125 + x = 180, so x = 55 degrees. This is also an isosceles triangle since two angles are equal.

MAP 8th Grade Math 2

A rectangle has a length of 3x + 2 and a width of x - 1.
Which expression represents its perimeter?