北京师大附中2020-2021学年上学期高二年级期末考试数学试卷（AP）

本试卷有三道大题，考试时长90分钟，满分100分。

一、填空题
共30小题，每小题2分，共30分。

1. If=k and k=3，what is the value of x?

A. 2 B. 4 C. 9 D. 10

2. If y=kx，where k is a constant，and y=24 when x=6，what is the value of y when x=5?

A. 6 B. 15 C. 20 D. 23

In the figure above，lines l and m are parallel and lines s and t are parallel. If the measure of ∠1 is 35°，what is the measure of ∠2?

A. 35° B. 55° C. 70° D. 145°

4. If 16 + 4x is 10 more than 14，what is the value of 8x ?

A. 2 B. 6 C. 16 D. 80

Which of the following is equivalent to the expression above?

A. B.

C. D.

h = 3a + 28.6

A pediatrician uses the model above to estimate the height h of a boy，in inches，in terms of the boy’s age a，in years，between the ages of 2 and 5. Based on the model，what is the estimated increase，in inches，of a boy’s height each year?

A. 3 B. 5.7 C. 9.5 D. 14.3

The equation above represents a parabola in the xy-plane. Which of the following equivalent forms of the equation displays the x-intercepts of the parabola as constants or coefficients?

A. B.

C. D.

8. In a video game，each player starts the game with k points and loses 2 points each time a task is not completed. If a player who gains no additional points and fails to complete 100 tasks has a score of 200 points，what is the value of k ?

A. 0 B. 150 C. 250 D. 400

9. The graph of a line in the xy-piane has slope 2 and contains the point （1，8）. The graph of a second line passes through the points （1，2） and （2，1）. If the two lines intersect at the point （a，b），what is the value of a+ b ?

A. 4 B. 3 C. -1 D. -4

10. A function f satisfies f（2） = 3 and f
（3） = 5. A function g satisfies g（3） = 2 and g（5） = 6. What is the value of f（g（3）） ?

A. 2 B. 3 C. 5 D. 6

11. Which of the following complex numbers is equivalent to ? （Note: i=）

A. B.

C. D.

12.

A website uses the formula above to calculate a seller’s rating，R，based on the number of favorable reviews，F，and unfavorable reviews，N. Which of the following expresses the number of favorable reviews in terms of the other variables?

A. B.

C. D.

13. What is the sum of all values of m that satisfy 2m²-16m+8 =0?

A. -8 B. – C. D. 8

14. Miles Traveled by Air Passengers in Country X，1960 to 2005

According to the line of best fit in the scatterplot above，which of the following best approximates the year in which the number of miles traveled by air passengers in Country X was estimated to be 550 billion?

A. 1997 B. 2000 C. 2003 D. 2008

15. The distance traveled by Earth in one orbit around the Sun is about 580，000，000 miles. Earth makes one complete orbit around the Sun in one year. Of the following，which is closest to the average speed of Earth，in miles per hour，as it orbits the Sun?

A. 66，000 B. 93，000 C. 210，000 D. 420，000

16. Results on the Bar Exam of Law School Graduates

Passed

bar exam

Did not pass bar exam

Took review course

Did not take

review course

The table above summarizes the results of 200 law school graduates who took the bar exam. If one of the surveyed graduates who passed the bar exam is chosen at random for an interview

，what is the probability that the person chosen did not take the review course?

A. B. C. D.

Questions 17 and 18 refer to the following information.

The quantity of a product supplied and the quantity of the product demanded in an economic market are functions of the price of the product. The functions above are the estimated supply and demand functions for a certain product. The function S（P） gives the quantity of the product supplied to the market when the price is P dollars，and the function D（P） gives the quantity of the product demanded by the market when the price is P dollars.

17. How will the quantity of the product supplied to the market change if the price of the product is increased by $10?

A. The quantity supplied will decrease by 5 units.

B. The quantity supplied will increase by 5 units.

C. The quantity supplied will increase by 10 units.

D. The quantity supplied will increase by 50 units.

18. At what price will the quantity of the product supplied to the market equal the quantity of the product demanded by the market?

A. ＄90 B. ＄ 120 C. ＄133 D. ＄155

19. Graphene，which is used in the manufacture of integrated circuits，is so thin that a sheet weighing one ounce can cover up to 7 football fields. If a football field has an area of approximately 1 acres，about how many acres could 48 ounces of graphene cover?

A. 250 B. 350 C. 450 D. 1350

20.

The figure on the left above shows a wheel with a mark on its rim. The wheel is rolling on the ground at a constant rate along a level straight path from a starting point to an ending point. The graph of y = d（t） on the right could represent which of the following as a function of time from when the wheel began to roll?

A. The speed at which the wheel is rolling

B. The distance of the wheel from its starting point

C. The distance of the mark on the rim from the center of the wheel

D. The distance of the mark on the rim from the ground

21. In the equation above，if a is negative and b is positive，which of the following must be true?

A. c>1 B. c=1 C. c=-1 D. c<-1

22. In State X，Mr. Camp’s eighth-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth-grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighth-grade classes and there are 1，800 eighth-grade classes in the state，which of the following best estimates the number of eighth-grade students in the state who have fewer than two siblings?

A. 16，200 B. 23，400 C. 30，600 D. 46，800

Questions 23 and 24 refer to the following information.

Townsend Realty Group Investments
Property address	Purchase price （dollars）	Monthly rental price （dollars）
Clearwater Lane	128，000	950
Driftwood Drive	176，000	1，310
Edgemont Street	70，000	515
Glenview Street	140，000	1，040
Hamilton Circle	450，000	3，365

The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount，in dollars，the company paid for each property and the corresponding monthly rental price，in dollars，the company charges for the property at each of the five locations.

23. The relationship between the monthly rental price r，in dollars，and the property’s purchase price p，in thousands of dollars，can be represented by a linear function. Which of the following functions represents the relationship?

A. r（p）=2.5p-870

B. r（p）=5p+165

C. r（p）=6.5p+440

D. r（p）=7.5p-10

24. Townsend Realty purchased the Glenview Street property and received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Which of the following best approximates the original price，in dollars，of the Glenview Street property?

A. $ 350，000

B. $ 291，700

C. $ 233，300

D. $ 175，000

25.

The polynomials f（x） and g（x） are defined above. Which of the following polynomials is divisible by 2x+3?

A. h（x）=f（x）+g（x）

B. p（x） =f（x） + 3g（x）

C. r（x）= 2f（x）+ 3g（x）

D. s（x）= 3f（x）+ 2g（x）

26. Let x and y be numbers such that -y<x<y. Which of the following must be true?

I. |x|<y

II. x>0

III. y>0

A. I only B. I and II only C. I and III only D. I，II，and III

27. A rectangle was altered by increasing its length by 10 percent and decreasing its width by p percent. If these alterations decreased the area of the rectangle by 12 percent，what is the value of p?

A. 12 B. 15 C. 20 D. 22

28. In planning maintenance for a city’s infrastructure，a civil engineer estimates that，starting from the present，the population of the city will decrease by 10 percent every 20 years. If the present population of the city is 50，000，which of the following expressions represents the engineer’s estimate of the population of the city t years from now?

A. 50，000（0.1） B. 50，000（0.1）

C. 50，000（0.9） D. 50，000（0.9）

29.

In the system of equations above，a and b are constants. For which of the following values of a and b does the system of equations have exactly two real solutions?

A. a=-2，b=2 B. a=-2，b=4

C. a=2，b=4 D. a=4，b=3

30.

The figure above shows a regular hexagon with sides of length a and a square with sides of length a. If the area of the hexagon is 384 square inches，what is the area，in square inches，of the square?