B) The mild temperature was lowered by a heavy rain in the morning, and the temperature dropped lower by evening. 3 page

(A) 10

(B) 15

(C) 20

(D) 25

(E) 30

11. Point S is the point with the greatest y -coordinate on the semicircle shown below. What is the x –coordinate of point R?

(A) – 5.5

(B) - 4

(C) – 3.5

(D) - 3

(E) – 2.5

12. For 12 bottles of shampoo of various brands, the cost and volume of each are displayed in the scatter plot below, and the line of best fit for the data is shown. Of the following, which is closest to the average (arithmetic mean) cost per ounce for the 12 bottles?

(A) $0.06

(B) $0.09

(C) $0.12

(D) $0.15

(E) $0.18

13. The graph of a quadratic function and the graph of a linear function in the xy -plane can intersect in at most how many points?

(A) One

(B) Two

(C) Three

(D) Four

(E) More than four

14. In the figure below, if AB = 6 and BC = 12, what is the area of the shaded region?

(A) 9

(B) 12

(C) 16

(D) 18

(E) 20

15. If a and b are positive integers and 9(3^{a}) = 3^{b}, what is a in terms of b?

(A) b - 2

(B) b - 1

(C) b

(D) b + 1

(E) b + 2

16. The tin can in the figure below is a cylinder that is 8 inches high and has a base of radius 3 inches. Of 5 pencils with lengths 6 inches, 8.5 inches, 9 inches, 10.5 inches, and 12 inches, how many cannot fit entirely inside the can?

(A) One

(B) Two

(C) Three

(D) Four

(E) Five

17. When the number k is multiplied by 5, the result is the same as when 5 is added to k. What is the value of 4k?

(A) _{ }

(B) 1

(C) _{ }

(D) 4

(E) 5

18. A circle (not drawn) passes through point A in the figure below. What could be the total number of points of intersection of this circle and _{ }?

I. 1

II. 3

III. 4

(A) I only

(B) II only

(C) I and II only

(D) II and III only

(E) I, II, and III

19. The function f graphed below is defined for -3 _{ }x_{ }6. For which of the following values of x is f(x) < |f(x)|?

(A) - 3

(B) - 2

(C) - 1

(D) 1

(E) 5

20. If x and y are numbers such that (x + 9)(y – 9) = 0, what is the smallest possible value of x^{2} + y^{2}?

(A) 0

(B) 9

(C) 18

(D) 81

(E) 162

21. A new roll of film has p pictures. After t pictures are taken, there are k pictures left. What is t in terms of p and k?

(A) p + k

(B) p - k

(C) k – p

(D) kp

(E) _{ }

22. The prime number p is a factor of 30 and is also a factor of 42. How many possible values are there for p?

(A) One

(B) Two

(C) Three

(D) Four

(E) Five

23. According to the graph below, for which month was sales minus cost greatest?

(A) June

(B) July

(C) August

(D) September

(E) October

24. In the figure below, O is the center of the circle and segment _{ }is tangent to the circle at point B. If the measure of ∠ABO is x°, how many possible values are there for x?

(A) One

(B) Two

(C) Three

(D) Four

(E) More than four

25. The bus fare from city A to city B is $5 more for adults than for children. If a group of 5 adults and 6 children pay a total of $124 to travel by bus from city A to city B, what is the cost of the ticket for one adult?

(A) $11

(B) $12

(C) $14

(D) $16

(E) $17

26. The smallest squares in Figure A and Figure B are all equal in size. If the area of Figure A is 33 square centimeters, what is the area, in square centimeters, of Figure B?

(A) 15

(B) 18

(C) 21

(D) 24

(E) 28

27. If the steps below are followed in order, which of the following is a simplified expression for the result?

1. Add 4y to x.

2. Multiply the sum by 3.

3. Subtract y – 3x from the product.

(A) 11y

(B) 13y

(C) 2x + 11y

(D) 4x + 13y

(E) 6x + 11y

28. In triangle XYZ below, XW = 2, WZ = 8, and XY = 6. What is the area of triangle WYZ?

(A) 6

(B) 12

(C) 18

(D) 24

(E) 30

29. Differentiate the function in the below.

_{ }

(A) _{ }

(B) _{ }

(C) _{ }

(D) _{ }

(E) _{ }

30. Find the integral of the function in the below.

_{ }

(A) _{ }

(B) _{ }

(C) _{ }

(D) _{ }

(E) _{ }

TEST 06

1. Which of the following triples (x, y, z) does not satisfy _{ }21?

(A) (4, 5, 1)

(B) (5, 4, 1)

(C) (2, 10, 2)

(D) (7, 3, 0)

(E) (3, 3, 12)

2. Susan had 60 trading cards. After giving away g cards and receiving r cards, she had 70 cards. What is the value of r - g?

(A) 10

(B) 20

(C) 30

(D) 40

(E) 50

3. If k is a positive integer divisible by 7, and if k < 90, what is the greatest possible value of k?

(A) 83

(B) 84

(C) 87

(D) 88

(E) 89

4. The graph below shows the monthly sales for Company A and Company B for the second half of 2004. What was the largest one-month decrease in sales for Company B during this period of time?

(A) $45,000

(B) $30,000

(C) $25,000

(D) $20,000

(E) $15,000

5. For parties, the number of cases of juice a caterer orders is directly proportional to the number of people attending. If the caterer orders 3 cases for a party with 40 people attending, how many cases would she order for a party with 280 people attending?

(A) 7

(B) 10

(C) 14

(D) 18

(E) 21

6. Which of the following is an element of both the set of positive odd integers and the set of prime numbers?

(A) 2

(B) 5

(C) 9

(D) 12

(E) 21

7. The length of a rectangular garden is 3 feet more than its width. If the length of the garden is 9 feet, what is the area of the garden in square feet?

(A) 27

(B) 36

(C) 54

(D) 81

(E) 108

8. On the number line below, the tick marks are equally spaced. What is the value of b - a?

(A) _{ }

(B) _{ }

(C) _{ }

(D) _{ }

(E) _{ }

9. Jamal has some coins in his pocket. Some of these coins are quarters, and none of the quarters in his pocket are dated earlier than 2000. Which of the following must be true?

(A) None of the coins in Jamal’s pocket are dated earlier than 2000.

(B) Some of the coins in Jamal’s pocket are dated earlier than 2000.

(C) Some of the coins in Jamal’s pocket are dated 2000 or later.

(D) Most of the coins in Jamal’s pocket are either quarters or dated earlier than 2000.

(E) Most of the coins in Jamal’s pocket are not quarters.

10. The circumference of the circle with center O shown bellow is 2π. What is the area of the shaded region?

(A) _{ }

(B) _{ }

(C) 1

(D) 0.5

(E) 0.25

11. If a, b, and c are positive integers, and if (a – c)b = 0, which of the following must be true?

(A) a < b

(B) b < c

(C) a = b

(D) a = c

(E) b = c

12. In the figure below, regular pentagon ABCDE is divided into three nonoverlapping triangles. Which of the following is true about the three triangles?

(A) They have equal areas.

(B) They have equal perimeters.

(C) They are similar.

(D) They are isosceles.

(E) They each have at least one angle of measure _{ }.

13. If p < -5 or p > 5, which of the following must be true?

I. p^{2} > 5

II. |p| > 5

III. p^{3} > 5

(A) III only

(B) I and II only

(C) I and III only

(D) II and III only

(E) I, II, and III

14. In the figure below, a < 40 and b = c + 1. If c is an integer, what is the least possible value of b?

(A) 30

(B) 39

(C) 50

(D) 61

(E) 71

15. For all positive integers a and b, let ▲ be defined by a▲b = a^{2} + b^{2} – 2. If c and d are positive integers, which of the following cannot be the value of c▲d?

(A) 0

(B) 2

(C) 3

(D) 6

(E) 8

16. The functions r and t are defined below. For how many values of a is it true that r(a) = t(a)?

r(x) = x^{2}

t(x) = x – 2

(A) None

(B) One

(C) Two

(D) Three

(E) More than three

17. The function y = f(x) defined for - 5_{ }6, is graphed below. Which of the following gives all values of x for which f(x) is positive?

(A) 0 < x_{ }6

(B) 5 < x_{ }6

(C) – 5 _{ }x < 2

(D) – 4 < x < 1 and 5 < x_{ }6

(E) – 5 < x < - 4 and 1 < x < 5

18. In the xy -plane, an equation of line _{ }is y = 3x – 1. If line m is the reflection of line _{ }in the y -axis, what is an equation of line m?

(A) y = - 3x - 1

(B) y = - 3x + 1

(C) y = 3x + 1

(D) y = -_{ }- 1

(E) y = -_{ }+ 1

19. For which of the following values for k will the system of equations below have no solution?

3x + 7y = 12

6x – ky = 6

(A) - 14

(B) - 7

(C) 0

(D) 7

(E) 14

20. The table below shows the number of items 100 customers purchased from a hardware store over a 4 -hour period. Which of the following can be determined from the information in the table?

I. The average (arithmetic mean) number of items purchased per customer

II. The median number of items purchased per customer

III. The mode of the number of items purchased per customer

(A) None

(B) I and II only

(C) I and III only

(D) II and III only

(E) I, II, and III

21. There are 6 bookcases in a house. Each bookcase contains at least 125 books but not more than 160 books. Which of the following could be the total number of books in all 6 bookcases?

(A) 500

(B) 625

(C) 725

(D) 925

(E) 1,000

22. In the figure below, lines k, _{ }and m are parallel. If y = 125, what is the value of x + z?

(A) 90

(B) 95

(C) 100

(D) 105

(E) 110

23. Graphed below is the amount that a computer shop charges for a repair job as a function of the number of hours required to do the job. Which of the following is most consistent with the information in the graph?

(A) The shop charges the same amount for any job of any length.

(B) The shop charges at an hourly rate for work with no fixed initial amount.

(C) The shop charges a fixed initial amount plus an hourly rate for work, starting at the beginning of the first hour.

(D) The shop charges a fixed amount for the first 2 hours or less of work. The shop charges at an hourly rate for work beyond 2 hours.

(E) The shop charges at an hourly rate for work beginning at the start of the first hour. This rate decreases after 2 hours of work.

24. For how many values of t is the equation below true?

|t – 9| = 0

(A) Three

(B) Two

(C) One

(D) None

(E) More than three

25. An amusement park awards tickets that can be exchanged for prizes to reward high scores at an arcade game. Some scores and the corresponding number of prize tickets awarded are shown in the table below. For scores from 100 up to 200, the number of tickets awarded increases by a constant amount for each 10 -point score increase. How many tickets would be awarded for a score of 180?

(A) _{ }

(B) _{ }

(C) _{ }

(D) 5

(E) _{ }

26. There are k students in a class, only one of whom is a junior. If 5 seniors are added to the class, how many students in the class will not be juniors?

(A) k + 1

(B) k + 2

(C) k + 3

(D) k + 4

(E) k + 5

27. The quadratic function graphed below has equation f(x) = a – x^{2}. Which of the following must be true?

(A) a > 0

(B) a < 0

(C) a is even

(D) a is odd

(E) a is the square of an integer.

28. Which of the following inequalities is true about the lengths a and b of the sides of the triangle below?

(A) 0_{ }(a + b)^{2} < 20

(B) 20_{ }(a + b)^{2} < 40

(C) 40_{ }(a + b)^{2} < 100

(D) 100_{ }(a + b)^{2} < 400

(E) 400_{ }(a + b)^{2}

29. Differentiate the function in the below.

_{ }

(A) _{ }

(B) _{ }

(C) _{ }

(D) _{ }

(E) _{ }

30. Find the integral of the function in the below.

_{ }

(A) _{ }

(B) _{ }

(C) _{ }

(D) _{ }

(E) _{ }

TEST 07

1. If x^{2} – 36 = 0, which of the following could be a value of x?

(A) - 6

(B) - 4

(C) 0

(D) 3

(E) 12

2. The length of a rectangular rug is 2 feet more than its width. If the length of the rug is 8 feet, what is the area of the rug in square feet?

(A) 16

(B) 48

(C) 66

(D) 80

(E) 96

3. If r = 2t and t = 3, what is the value of 2r?

(A) 2

(B) 4

(C) 6

(D) 8

(E) 12

4. If the statement below is true, which of the following must also be true?

Some integers in set X are even.

(A) If an integer is even, it is in set X.

(B) If an integer is odd, it is in set X.

(C) All integers in set X are even.

(D) All integers in set X are odd.

(E) Not all integers in set X are odd.

5. A triangle has a perimeter of 13 and one side of length 3. If the lengths of the other two sides are equal, what is the length of each of them?

(A) 4

(B) 5

(C) 6

(D) 7

(E) 8

6. The grid below shows the number of hours worked last week by 12 students of various ages at after-school jobs. Which of the following is true, according to this grid?

(A) Half of the students worked more than 12 hours each.

(B) One student worked exactly 15 hours.

(C) One 16 year old worked more than 11 hours.

(D) More 18 year olds than 17 year olds worked at least 13 hours each.

(E) Most of the students were under 16 years old.

7. Squaring the product of z and 5 gives the same result as squaring the sum of z and 5. Which of the following equations could be used to find all possible values of z?

(A) 5z^{2} = (z + 5)^{2}

(B) (5z)^{2} = z^{2} + 5^{2}

(C) 5^{2}z = z^{2} + 5^{2}

(D) (5z)^{2 }= (z + 5)^{2}

(E) 5z^{2 }= z^{2} + 5^{2}

8. If as many 7-inch pieces of wire as possible are cut from a wire that is 3 feet long, what is the total length of the wire that is left over? (12 inches = 1 foot)

(A) 1 inch

(B) 2 inches

(C) 3 inches

(D) 4 inches

(E) 5 inches

9. Which of the lettered points in the figure below has coordinates (x, y) such that |x| + |y| = 5?

(A) A

(B) B

(C) C

(D) D

(E) E

10. If n is a member of both set A and set B bellow, which of the following must be true?

I. n is an integer.

II. 4n is an integer.

III. n = 4

(A) None

(B) II only

(C) I and II only

(D) I and III only

(E) I, II, and III only

11. If y is directly proportional to x and if y = 20 when x = 6, what is the value of y when x = 9?

(A)

(B)

(C) 23

(D) 27

(E) 30

12. The nth term of a sequence is defined to be 4n + 3. The 50th term is how much greater than the 45th term?

(A) 5

(B) 16

(C) 20

(D) 23

(E) 24

13. Which of the rectangular solids shown below has a volume closest to the volume of a right circular cylinder with radius 2 and height 4?

(A) A

(B) B

(C) C

(D) D

(E) E

14. If x is a negative integer, what is the ordering of j, k, and m from least to greatest?

(A) j < k < m

(B) j < m < k

(C) k < j < m

(D) m < j < k

(E) m < k < j

15. Flour, water, and salt are mixed by weight in the ratio of 5:4:1, respectively, to produce a certain type of dough. In order to make 5 pounds of this dough, what weight of salt, in pounds, is required?

(A)

(B)

(C)

(D) 1

(E) 2

16. In rectangle ABCD below, the area of the shaded region is given by . If the area of the shaded region is 7 , what is the total area, to the nearest whole number, of the unshaded regions of rectangle ABCD?