MAP Math (Grades 8-12) 2 — Questions and Answers

Question 1: Which of the following is the quadratic formula used to solve ax squared + bx + c = 0?

x = -b plus or minus square root of (b squared - 4ac) all over a
x = (-b plus or minus square root of (b squared - 4ac)) all over 2a (Correct answer)
x = (b plus or minus square root of (b squared + 4ac)) all over 2a
x = -b over 2a

Correct answer: x = (-b plus or minus square root of (b squared - 4ac)) all over 2a

The quadratic formula is x = (-b plus or minus sqrt(b^2 - 4ac)) divided by 2a. The entire numerator is divided by 2a.

The quadratic formula x = (-b plus or minus sqrt(b^2 - 4ac)) / (2a) solves any quadratic equation ax^2+bx+c=0. The expression under the radical, b^2-4ac, is called the discriminant. If the discriminant is positive: two real solutions. If zero: one real solution. If negative: no real solutions. This is a fundamental formula in MAP Growth high school mathematics.

Question 2: A right triangle has one leg of 8 and a hypotenuse of 17. What is the length of the other leg?

9
13
15 (Correct answer)
square root of 353

Correct answer: 15

a^2 + 8^2 = 17^2, so a^2 = 289 - 64 = 225, meaning a = 15. This is the 8-15-17 Pythagorean triple.

Using the Pythagorean theorem: a^2 + b^2 = c^2, where c is the hypotenuse. Substituting: a^2 + 8^2 = 17^2, which gives a^2 + 64 = 289, so a^2 = 225, and a = 15. The 8-15-17 triple is one of the classic Pythagorean triples worth memorizing alongside 3-4-5 and 5-12-13.

Question 3: What is the y-intercept of the equation 4x - 2y = 8?

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

Correct answer: y = -4

Set x=0: 4(0) - 2y = 8, so -2y = 8, meaning y = -4. The y-intercept is -4.

To find the y-intercept, set x = 0 and solve for y: 4(0) - 2y = 8 gives -2y = 8, so y = -4. The y-intercept is the point (0, -4). Alternatively, convert to slope-intercept form: -2y = -4x + 8, so y = 2x - 4. The constant -4 is the y-intercept.

Question 4: The volume of a cylinder is V = pi times r squared times h. If r = 3 and h = 5, what is the volume?

15 pi
30 pi
45 pi (Correct answer)
90 pi

Correct answer: 45 pi

V = pi times (3 squared) times 5 = pi times 9 times 5 = 45 pi.

Using V = pi times r^2 times h: Substitute r=3 and h=5: V = pi times (3^2) times 5 = pi times 9 times 5 = 45 pi. In decimal form, 45 pi is approximately 141.37 cubic units. Always remember to square the radius first — a common error is forgetting to apply the exponent.

Question 5: Which expression is equivalent to (2x cubed) to the 4th power?

8x to the 12th
16x to the 12th (Correct answer)
2x to the 12th
16x to the 7th

Correct answer: 16x to the 12th

(2x^3)^4 = 2^4 times (x^3)^4 = 16 times x^(3 times 4) = 16x^12.

The power of a product rule states (ab)^n = a^n times b^n. The power of a power rule states (a^m)^n = a^(m times n). Applying both: (2x^3)^4 = 2^4 times (x^3)^4 = 16 times x^(3 times 4) = 16x^12. A common mistake is only applying the exponent to the variable and forgetting to raise the coefficient as well.

Question 6: If a data set is {4, 7, 7, 9, 13}, what is the median?

7 (Correct answer)
8
9
13

Correct answer: 7

The data set is already ordered. With 5 values, the median is the 3rd value: 7.

To find the median: first order the data set from least to greatest (already done: 4, 7, 7, 9, 13). Then find the middle value. With 5 data points, the middle is the 3rd value: 7. If there were an even number of values, the median would be the average of the two middle values.

MAP Math (Grades 8-12) 2

Which of the following is the quadratic formula used to solve ax squared + bx + c = 0?