MAP HS Math 2 — Questions and Answers

Question 1: What are the solutions to x squared minus 5x plus 6 = 0?

x = 1 and x = 6
x = 2 and x = 3 (Correct answer)
x = -2 and x = -3
x = -1 and x = 6

Correct answer: x = 2 and x = 3

Factor: (x-2)(x-3) = 0. Solutions are x = 2 and x = 3.

To solve x^2 - 5x + 6 = 0, factor the trinomial. We need two numbers that multiply to +6 and add to -5: those are -2 and -3. So the equation factors as (x-2)(x-3) = 0. Setting each factor to zero: x-2=0 gives x=2, and x-3=0 gives x=3.

Question 2: Which of the following is the equation of a line perpendicular to y = 3x + 1?

y = 3x - 4
y = -3x + 2
y = (1/3)x + 5
y = -(1/3)x + 2 (Correct answer)

Correct answer: y = -(1/3)x + 2

Perpendicular lines have slopes that are negative reciprocals. The slope of y=3x+1 is 3, so the perpendicular slope is -1/3. Only y = -(1/3)x + 2 has slope -1/3.

Two lines are perpendicular if the product of their slopes equals -1 (the slopes are negative reciprocals). The slope of y = 3x + 1 is 3. The negative reciprocal of 3 is -1/3. Among the choices, y = -(1/3)x + 2 has slope -1/3, making it perpendicular to the original line.

Question 3: If f(x) = 2x squared minus 3, what is f(-2)?

1
5 (Correct answer)
11
-11

Correct answer: 5

f(-2) = 2(-2)^2 - 3 = 2(4) - 3 = 8 - 3 = 5.

To evaluate f(-2), substitute x = -2 into f(x) = 2x^2 - 3: f(-2) = 2(-2)^2 - 3. Calculate the exponent first: (-2)^2 = 4. Then multiply: 2 times 4 = 8. Finally subtract: 8 - 3 = 5. So f(-2) = 5.

Question 4: A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?

13 (Correct answer)
15
17
square root of 119

Correct answer: 13

Using the Pythagorean theorem: c^2 = 5^2 + 12^2 = 25 + 144 = 169. c = sqrt(169) = 13.

The Pythagorean theorem states a^2 + b^2 = c^2 for a right triangle, where c is the hypotenuse. Substituting: c^2 = 5^2 + 12^2 = 25 + 144 = 169. Therefore c = sqrt(169) = 13. The 5-12-13 is a classic Pythagorean triple, along with 3-4-5 and 8-15-17.

Question 5: What is the simplified form of the square root of 72?

6 times square root of 2 (Correct answer)
8 times square root of 3
9 times square root of 8
4 times square root of 18

Correct answer: 6 times square root of 2

sqrt(72) = sqrt(36 times 2) = sqrt(36) times sqrt(2) = 6*sqrt(2).

To simplify sqrt(72), find the largest perfect square that divides 72. 36 times 2 = 72, and 36 is a perfect square. So sqrt(72) = sqrt(36 times 2) = sqrt(36) times sqrt(2) = 6*sqrt(2). You can check: (6*sqrt(2))^2 = 36 times 2 = 72.

Question 6: The graph of y = x squared is shifted 3 units up and 2 units to the right. What is the new equation?

y = (x-2)^2 + 3 (Correct answer)
y = (x+2)^2 + 3
y = (x-2)^2 - 3
y = (x+3)^2 + 2

Correct answer: y = (x-2)^2 + 3

Shifting right by 2 replaces x with (x-2). Shifting up by 3 adds 3. New equation: y = (x-2)^2 + 3.

Transformations of y = x^2: A shift right by 2 units replaces x with (x-2), giving y = (x-2)^2. A shift up by 3 units adds 3 to the function, giving y = (x-2)^2 + 3. Note that horizontal shifts work in the opposite direction you might expect: shifting right uses (x-2), not (x+2).

MAP HS Math 2

What are the solutions to x squared minus 5x plus 6 = 0?