Manchester High School Math Department SAT Warm-ups: Quarter 2 Directions: The attached 8 warm-ups must be completed in the first quarter. Each warm-up includes three Multiple Choice questions and one Student Produced Response. For timing purposes please follow the guide: If you would like to break up the warm-ups into two, use the multiple choice questions on day one and the student response on day two. In that case, adjust the time allowed as appropriate.
Class Level Time for Completing Time for Reviewing Answers Questions Post-Secondary Prep 10 minutes 5 minutes College Prep 8 minutes 4 minutes Honors 6 minutes 4 minutes Quarter 2 SAT Warm-Up 1: Multiple Choice Problems
1) If , where x and k are integers, which of the following could be the value of k?
a. 3 b. 6 c. 9 d. 12 e. 15
2) In a certain game, each of 5 players received a score between 0 and 100, inclusive. If their average (arithmetic mean) score was 80, what is the greatest possible number of the 5 players who could have received a score of 50?
a. None b. One c. Two d. Three e. Four
Region M
Region N
Region O
Region P
3) If the four regions shown in the graph below are the only regions in Town T, the total of which two regions accounts for exactly 70 percent of all cable television subscribers in Town T?
a. M and N b. M and O c. N and O d. N and P e. O and P Quarter 2 SAT Warm-Up 1: Student Produced Response
4) In the figure above, if O is the center of the circle, what is the value of x? Quarter 2 SAT Warm-Up 2: Multiple Choice Problems
1) The sum of four consecutive odd integers w, x, y, and z is 24. What is the median of the set ?
a. 3 b. 5 c. 7 d. 9 e. 24
2) For which of the following graphs of f does for all values of x shown?
INSERT GRAPH CHOICES PAGE 367 a. b. c. d. e.
3) In the figure above, the four circles have the same center and their radii are 1, 2, 3, and 4, respectively. What is the ratio of the area of the small shaded ring to the area of the large shaded ring?
a. 1:2 b. 1:4 c. 3:5 d. 3:7 e. 5:7 Quarter 2 SAT Warm-Up 2: Student Produced Response
4) For what integer value of x is and ? Quarter 2 SAT Warm-Up 3: Multiple Choice Problems
1) A class has twice as many boys as girls. The students in the class stand in one line, with a girl at the front of the line. Which of the following must be true?
a. The last person in line is a girl.
b. The last person in line is a boy.
c. There are more girls than boys in the class.
d. There are at least two girls standing next to each other.
e. There are at least two boys standing next to each other.
2) On the staircase shown above, both the depth and the height of each step are s, and each step forms a right angle. What is the value of t in terms of s?
a. b. c. d. e.
3) Which of the following is an equation of the line that has y-intercept of 2 and an x-intercept of 3?
a. b. c. d. e. Quarter 2 SAT Warm-Up 3: Student Produced Response
4) In 2 weeks, 550 cartons of juice were sold in the school cafeteria. At this rate, how many cartons of juice would one expect to be sold in 5 weeks? Quarter 2 SAT Warm-Up 4: Multiple Choice Problems
1) The pattern shown above is composed of rectangles. This pattern is used repeatedly to completely cover a rectangular region 12L units long and 10L units wide. How many rectangles of dimension L by W are needed?
a. 30 b. 36 c. 100 d. 150 e. 180
2) The figure above shows a portion of the graph of the function f. If for all values of x, then for how many different values of x between 0 and 12?
a. Eight b. Nine c. Ten d. Eleven e. Twelve
3) In a certain school, there are k classes with n students in each class. If a total of p pencils are distributed equally among these students, how many pencils are there for each student?
a. b. c. d. e.
Quarter 2 SAT Warm-Up 4: Student Produced Response 4) Exactly 4 actors try out for the 4 parts in a play. If each actor can perform any one part and no one will perform more than one part, how many different assignments of actors are possible?
Quarter 2 SAT Warm-Up 5: Multiple Choice Problems
x f(x) g(x) 0 5 2 1 0 4 2 2 3 3 4 1 4 1 5 5 3 0
1) According to the table above, if , then what is the value of ?
a. 1 b. 2 c. 3 d. 4 e. 5
2) The odometer of a new automobile functions improperly and registers only 2 miles for every 3 miles driven. If the odometer indicates 48 miles, how many miles has the automobile actually been driven?
a. 144 b. 72 c. 64 d. 32 e. 24
3) Carlos delivered n packages on Monday, 4 times as many packages on Tuesday as on Monday, and 3 more packages on Wednesday than on Monday. What is the average (arithmetic mean) number of packages he delivered per day over the three days?
a. b. c. d. e.
Quarter 2 SAT Warm-Up 5: Student Produced Response 4) Each angle of above has the same measure as an angle in (not shown). If the length of one side of is 24, what is one possible perimeter of ?
Quarter 2 SAT Warm-Up 6: Multiple Choice Problems
1) On the number line above, what number is the coordinate of point R?
a. b. c. d. e. 2) For the function f, defined above, what are all the values of x for which is a real number?
a. All real numbers b. c. d. e.
3) In the figure above, is a radius of the circle with center O. Which of the following triangles has the least area?
a. b. c. d. e. Quarter 2 SAT Warm-Up 6: Student Produced Response
4) A line l with a slope of passes through the points and . What is the value of y? Quarter 2 SAT Warm-Up 7: Multiple Choice Problems
1) A list of numbers consists of positive and n negative numbers. If a number is picked at random from this list, the probability that the number is positive is. What is the value of ?
a. b. c. d. e.
2) In the figure above, line l is parallel to line m. What is the value of x?
a. b. c. d. e.
3) If a>b and a(b-a) = 0, which of the following must be true? I a = 0 II b<0 III a-b>0
a. I only b. II only c. III only d. I and II only e. I, II and III Quarter 2 SAT Warm-Up 7: Student Produced Response
4) If of is subtracted from 2, what is the resulting value? Quarter 2 SAT Warm-Up 8: Multiple Choice Problems
1) In the figure above, ∆XYZ is equilateral, with side of length 2. If WY is a diameter of the circle with center O, then the area of the circle is
a. b. c. d. e.
2) The graph above is a parabola that is symmetric about the x-axis. Which of the following could be an equation of the parabola?
a. b. c. d. e.
3) When 15 is divided by the positive integer k, the remainder is 3. For how many different values of k is this true?
a. One b. Two c. Three d. Four e. Five
Quarter 2 SAT Warm-Up 8: Student Produced Response 4) Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning?
SAT Warm-ups: Quarter 2 SOLUTIONS Warm-Up 1 1) C 2) C Warm-Up 4 3) A 1) E 4) 55 2) A 3) A 4) 24
Warm-Up 2 1) C Warm-Up 5 2) C 1) E 3) D 2) B 4) 3 3) C 4) 52 or 78 or 104
Warm-Up 3 1) E Warm-Up 6 2) C 1) C 3) D 2) B 4) 1375 3) A 4) 3/2 or 1.5 Warm-Up 7 1) C Warm-Up 8 2) A 1) C 3) E 2) A 4) 5/3 or 1.66 or 1.67 3) C 4) 18