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6 . The expression (4z + 3)(z – 2) is equivalent to: - F. 4z 2 – 5 -G. 4z 2 – 6

FOIL METHOD. 6 . The expression (4z + 3)(z – 2) is equivalent to: - F. 4z 2 – 5 -G. 4z 2 – 6 -H. 4z 2 – 3z – 5 -J. 4z 2 – 5z – 6 -K. 4z 2 + 5z – 6. PRETEST. midpoints.

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6 . The expression (4z + 3)(z – 2) is equivalent to: - F. 4z 2 – 5 -G. 4z 2 – 6

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  1. FOIL METHOD 6. The expression (4z + 3)(z – 2) is equivalent to: -F. 4z2 – 5 -G. 4z2 – 6 -H. 4z2 – 3z – 5 -J. 4z2 – 5z – 6 -K. 4z2 + 5z – 6 PRETEST

  2. midpoints 9. In the standard (x,y) coordinate plane, point M with coordinates (5,4) is the midpoint of AB, and B has coordinates (7,3). What are the coordinates of A. -A. (17, 11) -B. (9, 2) -C. (6, 3.5) -D. (3, 5) -E. (-3, -5) PRETEST

  3. AREAS 16. In square ABCE shown below, D is the midpoint of CE. Which of the following is the ratio of the area of ADE to the area or ADB. -F. 1:1 -G. 1:2 -H. 1:3 -J. 1:4 -K. 1:8 D E C A B PRETEST

  4. RATIOS 18. Janelle cut a board 30 feet long into 2 pieces. The ratio of the lengths of the 2 pieces is 2:3. What is the length, to the nearest foot, of the shorter piece. -F. 5 -G. 6 -H. 12 -J. 15 -K. 18 PRETEST

  5. EXPONENTS. 3a6 22. For all a > 1, the expression 3a4equals: -F. 1/2 -G. –a2 -H. a2 -J. -1/a2 -K. 1/a2 PRETEST

  6. RADICALS 7 a√7 26. If 3√7 = 3√7 is true, then a = ? -F. 1 -G. √7 -H. 7 -J. 21 -K. 49 PRETEST

  7. PATTERNS 27. A hot-air balloon 70 meters above the ground is falling at a constant rate of 6 meters per second while another hot-air balloon 10 meters above the ground is rising at a constant rate of 15 meters per second. To the nearest tenth of a second, after how many seconds will the 2 balloons be the same height above the ground? -A. 8.9 -B. 6.7 -C. 2.9 -D. 0.4 -E. 0.2 PRETEST

  8. PROBABILITIES 28. A hiking group will go from a certain town to a certain village by van on 1 of 4 roads, from the village to a waterfall by riding bicycles on 1 of 2 bicycle paths, and then from the waterfall to their campsite by hiking on 1 of 6 trails. How many routes are possible for the hiking group to go from the town to the village to the waterfall to their campsite? -F. 6 -G. 12 -H. 24 -J. 48 -K. 220 PRETEST

  9. RATIOS. 29. Cube A has an edge length of 2 inches. Cube B has an edge length double that of Cube A. What is the volume, in cubic inches, of Cube B? -A. 4 -B. 8 -C. 16 -D. 32 -E. 64 PRETEST

  10. AREA 31. A right circular cylinder is shown in the figure below, with dimensions given in centimeters. What is the total surface area of this cylinder, in square centimeters. (Note: The total surface area of a cylinder is given by 2r2 + 2rh where r is the radius and h is the height.) -A. 300 -B. 400 -C. 500 -D. 600 -E. 1,600 20 20 PRETEST

  11. FUNCTIONS 32. Given f(x) = 4x + 1 and g(x) = x2 - 2, which of the following is an expression for f(g(x))? -F. -x2 + 4x + 1 -G. x2 + 4x - 1 -H. 4x2 - 7 -J. 4x2 - 1 -K. 16x2 + 8x - 1 PRETEST

  12. ANGLES 34. Lines a, b, c, and d are shown below and a ll b. Which of the following is the set of all angles that must be supplementary to <x ? -F. {1, 2} -G. {1, 2, 5, 6} -H. {1, 2, 9, 10} -J. {1, 2, 5, 6, 9, 10} -K. {1, 2, 5, 6, 9, 10, 13, 14} b a x 1 9 8 c 2 3 10 11 13 12 d 5 4 15 14 7 6 PRETEST

  13. EXPONENTS. 35. (3x3)3 is equivalent to: -A. x -B. 9x6 -C. 9x9 -D. 27x6 -E. 27x9 PRETEST

  14. TRIG RATIOS. K 38. For right triangle KLM below, what is sin <M ? -F. 10 / 12 -G. 12 / 10 -H.√44 / 10 -J. 10 / √44 -K.√44 / 12 12 cm L M 10 cm PRETEST

  15. MIDPOINTS 3 5 42. What rational number is halfway between 1 and 1 ? -F. 1 / 2 -G. 1 / 4 -H. 2 / 15 -J. 4 / 15 -K. 8 / 15 PRETEST

  16. .TOTAL PIES 47. Tom has taken 5 of the 8 equally weighted tests in his U.S. History class this semester, and he has an average score of exactly 78.0 points. How many points does he need to earn on the 6th test to bring his average score up to exactly 80.0 points? -A. 90 -B. 88 -C. 82 -D. 80 -E. 79 PRETEST

  17. EXPONENTS 2.1) 3x3∙2x2y∙ 4x2y is equivalent to: -F. 9x7y2 -G. 9x12y2 -H. 24x7y2 -J. 24x12y -K. 24x12y2 PRETEST

  18. .PROBLEM SOLVING 3.1) Mr. Dietz is a teacher whose salary is $22,570 for this school year, which has 185 days. In Mr. Dietz’s school district, substitute teachers are paid $80 per day. If Mr. Dietz takes a day off without pay and a substitute teacher is paid to teach Mr. Dietz’s classes, how much less does the school district pay in salary by paying a substitute teacher instead of paying Mr. Dietz for that day? -A. $42 -B. $80 -C. $97 -D. $105 -E. $122 PRETEST

  19. TOTAL PIE 4.1) So far, a student has earned the following scores on four 100-point tests this grading period: 65, 73, 81, and 82. What score must the student earn on the fifth test of the grading period to earn an average test grade of 80 for the 5 tests? -F. 75 -G. 76 -H. 78 -J. 99 -K. The student cannot earn an average of 80. PRETEST

  20. CONSECUTIVE INTEGERS 9.1) What 2 numbers should be placed in the blanks below so that the difference between consecutive numbers is the same? 17, ___ , ___ , 41 -A. 23, 29 -B. 24, 34 -C. 25, 33 -D. 26, 35 -E. 27, 31 PRETEST

  21. SQUARE AND SQUARE ROOTS 10.1) If x is a real number such that x3 = 64, then x2 + √x = ? -F. 4 -G. 10 -H. 18 -J. 20 -K. 47 PRETEST

  22. VOLUME 11.1) A formula for the volume V of a sphere with radius r is V = 4/3r3. If the radius of a spherical rubber ball is 1 ¼ inches, what is its volume to the nearest cubic inch? -A. 5 -B. 7 -C. 8 -D. 16 -E. 65 PRETEST

  23. MATRIXES 13.1) The number of students participating in fall sports at a certain high school can be shown by the following matrix. Tennis Soccer Cross-Country Football [ 40 60 80 80 ] The athletic director estimates the ratio of the number of sports awards that will be earned to the number of students participating with the following matrix. Given these matrices, what is the athletic director’s estimate for the number of sports awards that will be earned for these fall sports? -A. 80 -B. 88 -C. 91 -D. 92 -E. 99 Tennis Soccer Cross-Country Football 0.3 0.4 0.2 0.5 PRETEST

  24. LIKE EXPRESSIONS 16.1)What expression must the center cell of the table below contain so that the sums of each row, each column, and each diagonal are equivalent? -F. 6x -G. 4x -H. 2x -J. -2x -K. -4x PRETEST

  25. .RATIOS 19.1) At a refinery, 100,000 tons of sand are required to produce each 60,000 barrels of a tarry material. How many tons of sand are required to produce 3,000 barrels of this tarry material? -A. 5,000 -B. 18,000 -C. 20,000 -D. 40,000 -E. 50,000 PRETEST

  26. .RATIOS 21.1) For all positive integers x, y, and z, which of the following expressions is equivalent to x ? -A. -B. -C. -D. -E. y x∙ z y ∙ z x∙ x y ∙ y y ∙ x x∙ y x - z y - z PRETEST x + z y + z

  27. TRIG RATIOS 28.1) The hypotenuse of the right triangle PQR shown below is 16 feet long. The sine of <P is 3/5. About how many feet long is QR ? -F. 8.0 -G. 9.6 -H. 12.4 -J. 14.3 -K. 15.4 P 16 PRETEST Q R

  28. EQUIVALENT EXPRESSIONS 31.1) What is the x-coordinate of the point in the standard (x,y) coordinate plane at which the 2 lines y = 2x + 6 and y = 3x + 4 intersect? -A. 1 -B. 2 -C. 4 -D. 6 -E. 10 PRETEST

  29. EQUIVALENT EXPRESSIONS 32.1) For all pairs of real numbers M and V where M = 3V + 6, V = ? -F. M/3 - 6 -G. M/3 + 6 -H. 3M - 6 -J. M – 6 -K. M + 6 3 PRETEST 3

  30. EQUIVALENT EXPRESSIONS. 34.1) If a = b + 2, then (b - a)4 = ? -F. -16 -G. -8 -H. 1 PRETEST -J. 8 -K. 16

  31. RIGHT ANGLES 37.1) Members of the fire department lean a 30-foot ladder against a building. The side of the building is perpendicular to the level ground so that the base of the ladder is 10 feet away from the base of the building. To the nearest foot, how far up the building does the ladder reach? -A. 10 -B. 20 -C. 28 -D. 31 -E. 40 PRETEST

  32. ANGLES. 40.1) In the figure below, ABCD is a trapezoid, E lies on AD, and angle measures are as marked. What is the measure of < BDC ? -F. 15 -G. 25 -H. 30 -J. 35 -K. 45 B C 30 ? 105 60 A E D PRETEST

  33. .RATIOS 42.1) Of the 804 graduating seniors in a certain high school, approximately 2/5 are going to college and approximately 1/4 of those going to college are going to a state university. Which of the following is the closest estimate for how many of the graduating seniors are going to a state university? -F. 80 -G. 90 -H. 160 -J. 200 -K. 320 PRETEST

  34. EQUIVALENT EXPRESSIONS 1 + i 1 - i 48.1) In the complex numbers, where i2 = -1, 1 ∙1 - i = ? -F. i - 1 -G. 1 + i -H. 1 – i -J. 1 – i 2 -K. 1 + i 2 PRETEST

  35. RATIOS 53.1) Douglas wants to draw a circle graph showing the favorite colors of his friends. When he polled his friends asking each their favorite color, 25% of his friends said red; 30% of his friends said blue; 20% of his friends said green; 10% of his friends said purple; and the remaining friends said colors other than red, blue, green, and purple. The colors other than red, blue, green, and purple will be grouped together in an Other sector. What will be the degree measure of the Other sector? -A. 108˚ -B. 54˚ -C. 27˚ -D. 15˚ -E. 10˚ PRETEST

  36. .CO-ORDINATE GEOMETRY 58.1) A triangle, ABC, is reflected across the x-axis to have the image A’B’C’ in the standard (x, y) coordinate plane; thus, A reflects to A’.The coordinates of point A are (c,d). What are the coordinates of point A’? -F. (c , -d) -G. (-c , d) -H. (-c , - d) -J. (d, c ) -K. Cannot be determined from the given information PRETEST

  37. .EQUIVALENT EXPRESSIONS 59.1) If x = 2t – 9 and y = 5 – t, which of the following expresses y in terms of x ? -A. y = (1 – x) / 2 -B. y = (19 – x) / 2 -C. y = 14 – 2x -D. y = 5 - x -E. y = 1 - x PRETEST

  38. .RATIOS A poll of 200 registered voters was taken before the election for mayor of Springdale. All 200 voters indicated which 1 of the 4 candidates for whom they would vote. The results of the poll are given in the table below. 13. What percent of the voters polled chose Whitney in the poll? -A. 15% -B. 20% -C. 25% -D. 30% -E. 40% PRETEST

  39. RATIOS A poll of 200 registered voters was taken before the election for mayor of Springdale. All 200 voters indicated which 1 of the 4 candidates for whom they would vote. The results of the poll are given in the table below. 14. If the poll is indicative of how the 10,000 registered voters of Springdale will actually vote in the election, which of the following is the best estimate of the number of votes Lue will receive in the election. -F. 1,500 -G. 2,500 -H. 4,000 -J. 5,000 -K. 8,000 PRETEST

  40. RATIOS A poll of 200 registered voters was taken before the election for mayor of Springdale. All 200 voters indicated which 1 of the 4 candidates for whom they would vote. The results of the poll are given in the table below. 15. If the information in the table were converted into a circle graph (pie chart), then the central angle of the sector for Gomez would measure how many degrees? -A. 54˚ -B. 72˚ -C. 90˚ -D. 108˚ -E. 144˚

  41. RATIOS 33. The table below shows the total number of goals scored in each of 43 soccer matches in a regional tournament. What is the average number of goals scored per match, to the nearest 0.1 goal? -A. 1.0 -B. 2.8 -C. 3.0 -D. 6.1 -E. 17.1

  42. ANGLES 39. In the figure below, B lies on AC, BD bisects <ABE, and BE bisects <CBD. What is the measure of <DBE ? -A. 90˚ -B. 60˚ -C. 45˚ -D. 30˚ -E. Cannot be determined from the given information D E B A C PRETEST

  43. ANGLES 43. In isosceles trapezoid ABCD, AB is parallel to DC, <BDC measures 25˚, and <BCA measures 35˚. What is the measure of <DBC ? -A. 85˚ -B. 95˚ -C. 105˚ -D. 115˚ -E. 125˚ A B 35˚ 25˚ D C

  44. .CO-ORDINATE GEOMETRY 59. In the figure below, the vertices of ABC have (x,y) coordinates (4,5), (5,3), and (1,3), respectively. What is the area of ABC? -A. 4 -B. 4√2 -C. 4√3 -D. 8 -E. 8√2 NEED PICTURE PRETEST

  45. A -PROBABILITIES • A deck of cards for a children’s game contains 10 red cards, 10 blue cards, and 10 yellow cards. The players take turns, each drawing a card at random from the deck and placing the card on the table. When it is the fourth player’s turn, there are 3 yellow cards on the table. What is the probability that the fourth player will draw a yellow card? • A) 7/30 • B) 7/27 • C) 1/3 • D) 4/10 • E) 7/10 LOOK ALSO FOR FRACTIONS WHICH COULD OF BEN REDUCED PRETEST

  46. .A- PROBABILITY • What is the probability of drawing a heart from a well-shuffled standard deck of playing cards. • A) 1/4 • B) 1/52 • C) 1/13 • D) 4/13 • E) 1 4 DIFFERENT TYPES OF SUITS

  47. 16.9 A- Probability • WHAT IS THE PROBABILITY OF GETTING A SUM OF 8 ON ONE ROLL OF A FAIR PAIR OF DICE: • A) 1/4 • B) 1/6 • C) 8/36 • D) 5/36 • E) None of the above If I rolled three Dice , how many Different possibilities ? PRETEST

  48. B -SLOPES • What is the slope of the line whose equation is x+2y=5 - (x+y)? • A) 5/3 • B) -2 • C) -2/3 • D) -3/2 • E) -1 PRETEST

  49. 19.2% C- Averages • THE AVERAGE OF A SET OF 7 INTEGERS IS 24. WHEN AN 8TH NUMBER IS INCLUDED IN THE SET THE AVERAGE OF SET INCREASES TO 31. WHAT IS THE 8TH NUMBER: • A) 31 • B) 62 • C) 56 • D) 80 • E) 168 PRETEST

  50. D-Y INTERCEPT CAN WE MAKE A REASONABLE GUESS ? • What is the y-intercept of the line in the standard (x,y) coordinate plane that goes through the points (-3,6) and (3,2)? • A) 0 • B) 2 • C) 4 • D) 6 • E) 8 -3 AND 3 =ZERO PRETEST

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