If $$p(x)=\frac{1}{4}x^2$$ , at what points do the graphs of $$y=p(x)$$ and $$y=p^{-1}(x)$$ intersect?

(4,0) and $$\left(4,\tfrac{1}{4}\right)$$

(0,0) and $$\left(\tfrac{1}{4},0\right)$$

Which best describes the number and type of roots of the quadratic polynomial $$x^2-3x+5$$ ?

one distinct real root and one distinct complex root

Three county high schools are planning to build a sports complex that is the same distance from all three schools. If each school is treated as the vertex of a triangle, where should the sports complex be built?

at the triangle’s circumcenter

at the triangle’s orthocenter

A two-column proof about the circle with a center at $$O$$ is shown. Given: $$\overline{ON}\cong\overline{OP}$$ . Prove: $$\overline{SP}\cong\overline{RN}$$ . Statements and Reasons include: (1) $$\overline{ON}\cong\overline{OP}$$ — Given; (2) $$\angle MOR\cong\angle QOS$$ — ?; (3) $$\overline{OS}\cong\overline{OR}$$ — ?; (4) $$\triangle OPS\cong\triangle ONR$$ — ?; (5) $$\overline{SP}\cong\overline{RN}$$ — CPCTC. Which of the following reasons will not be used as justification for Statements 2, 3, or 4?

Alternate interior angles formed by parallel lines are congruent.

All radii of the same circle are congruent.

Two trigonometric functions are given: • $$f(x)$$ is a tangent function with a period of $$\pi/3$$ . • $$g(x)=-2\cos(3x)+1$$ . Which of the following statements is true?

The period of $$f(x)$$ is half the period of $$g(x)$$ .

The period of $$f(x)$$ is the same as the period of $$g(x)$$ .

The period of $$f(x)$$ is one-third of the period of $$g(x)$$ .

The period of $$f(x)$$ is twice the period of $$g(x)$$ .

Marta is writing a paragraph proof to justify why the opposite sides of a parallelogram must be congruent. She begins with parallelogram ABCD and one diagonal drawn, as shown in the diagram. She outlines her proof with the following statements: 1) ABCD is a parallelogram. 2) AB ∥ DC and AD ∥ BC. 3) ∠ABD ≅ ∠CDB and ∠ADB ≅ ∠CBD. 4) DB ≅ DB. 5) ΔDAB ≅ ΔBCD. 6) AB ≅ DC and AD ≅ BC (concluding that opposite sides of a parallelogram are congruent.) Which reason should Marta give for stating that the triangles are congruent in Statement 5?

Diagonals of a parallelogram bisect each other.

Corresponding parts of congruent triangles are congruent.

The planning committee for a large housing development wants to find out what curbside trash pickup schedule would be most convenient for the people who live in the development. Which method is most likely to produce a random sample of their preferences?

poll one person from every set of 5 houses after they have been opportunity to get feedback from neighbors

invite everyone in the neighborhood to submit their preferences by email

place surveys in the first two mailboxes on each street in the development with directions about where to drop them off

place a flyer asking for a schedule preference on the windshield of each car parked outside in the development one Saturday morning

Consider the exponential equation below. $$10\cdot\left(\frac{2}{7}\right)^{(4x+2)}=3$$ . If an equivalent equation is written in the form $$\log_b m = n$$ , which of the following are possible values of b, m, and n?

$$b=\frac{2}{7}$$ , $$m=\frac{3}{10}$$ , $n=4x+2

$$b=4x+2$$ , $$m=\frac{10}{3}$$ , $$n=\frac{2}{7}$$

$$b=\frac{2}{7}$$ , $$m=30$$ , $n=4x+2

$$b=3$$ , $$m=10(4x+2)$$ , $$n=\frac{2}{7}$$

A tax preparation company wants to see how satisfied its customers are with their services. Which of the following would give them the best unbiased sample?

surveying a random sample of customers from a list of all of their current and previous customers

looking at customer reviews on their social media page

questioning the first 25 people that call the company

asking the last 25 people on an alphabetical list of all of their current customers

NC Math 3 Practice End of Course Test

Authored by Joackim Sikazwe

Mathematics

12th Grade

CCSS covered

Used 2+ times

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MULTIPLE CHOICE QUESTION

45 sec • 1 pt

-2

-1

Tags

CCSS.HSA.APR.B.2

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The population of North Carolina was approximately 9.5 million in 2010. The population has increased by about 1.3% per year. If the population continues to grow at this rate, in what year will North Carolina’s population reach 12 million?

2030

2028

2024

2019

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The graph of a function, f(x), has zeros at -2/3, 3, and 5. Which of the following is a factor of f(x)?

Tags

CCSS.HSF-IF.C.7C

MULTIPLE CHOICE QUESTION

1 min • 1 pt

A landscape architect is creating a plan in which a circular flower garden will have the same area as a triangle-shaped stone terrace. The base and height of the terrace are represented with the variables b and h, respectively. If r represents the radius of the flower garden, which equation gives r in terms of b and h?

Tags

CCSS.HSA.CED.A.4

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Tags

CCSS.HSA.APR.D.6

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Tags

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Tags

CCSS.HSA.APR.D.6

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NC Math 3 Practice End of Course Test

The population of North Carolina was approximately 9.5 million in 2010. The population has increased by about 1.3% per year. If the population continues to grow at this rate, in what year will North Carolina’s population reach 12 million?

The graph of a function, f(x), has zeros at -2/3, 3, and 5. Which of the following is a factor of f(x)?

What is the equation represented by the graph below?

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