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**PRETEST -F. 4z2 – 5 -G. 4z2 – 6 -H. 4z2 – 3z – 5 -J. 4z2 – 5z – 6**

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

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**-A. (17, 11) -B. (9, 2) -C. (6, 3.5) -D. (3, 5) -E. (-3, -5) PRETEST**

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

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**E D C A B -F. 1:1 -G. 1:2 -H. 1:3 -J. 1:4 -K. 1:8**

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 E D C A B PRETEST

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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

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**3a6 -F. 1/2 -G. –a2 -H. a2 -J. -1/a2 -K. 1/a2**

EXPONENTS. 22. For all a > 1, the expression 3a4 equals: -F. 1/2 -G. –a2 -H. a2 -J. -1/a2 -K. 1/a2 3a6 PRETEST

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**PRETEST a√7 7 -F. 1 -G. √7 -H. 7 -J. 21 -K. 49**

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

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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

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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

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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

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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 2𝜋r2 + 2𝜋rh where r is the radius and h is the height.) -A. 300𝜋 -B. 400𝜋 -C. 500𝜋 -D. 600𝜋 -E. 1,600𝜋 20 20 PRETEST

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**g(x) = x2 - 2, which of the following is an expression for f(g(x))?**

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

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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} a b x 1 8 9 c 2 3 10 11 13 12 d 4 5 14 15 6 7 PRETEST

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

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

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TRIG RATIOS. 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 K 12 cm M L 10 cm PRETEST

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MIDPOINTS 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 5 3 PRETEST

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.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

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**-F. 9x7y2 -G. 9x12y2 -H. 24x7y2 -J. 24x12y -K. 24x12y2 PRETEST**

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

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.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

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**-K. The student cannot earn an average of 80.**

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

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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

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**x3 = 64, then x2 + √x = ? -F. 4 -G. 10 -H. 18 -J. 20 -K. 47**

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

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VOLUME 11.1) A formula for the volume V of a sphere with radius r is V = 4/3 𝜋r3. 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

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**Tennis Soccer Cross-Country Football**

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 [ ] 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

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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 x 8x -3x -2x ? 6x 7x -4x 3x PRETEST

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.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

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**PRETEST equivalent to x ? -A. y -B. -C. -D. -E.**

.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

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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 P 16 PRETEST Q R

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**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

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**32.1) For all pairs of real numbers M and V where M = 3V + 6, V = ?**

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

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**EQUIVALENT EXPRESSIONS.**

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

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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

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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 D E PRETEST

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.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

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**where i2 = -1, 1 ∙ 1 - i = ? -F. i - 1 -G. 1 + i -H. 1 – i -J. 1 – i 2**

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

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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

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**-K. Cannot be determined from the given information**

.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

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**-A. y = (1 – x) / 2 -B. y = (19 – x) / 2 -C. y = 14 – 2x -D. y = 5 - x**

.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

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.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% Candidate Number of voters Blackcloud Lue Gomez Whitney 50 80 40 30 PRETEST

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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 Candidate Number of voters Blackcloud Lue Gomez Whitney 50 80 40 30 PRETEST

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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˚ Candidate Number of voters Blackcloud Lue Gomez Whitney 50 80 40 30

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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 B C D E. 17.1 Total number of goals in a match Number of matches with this total 1 2 3 4 5 6 7 10 9

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**PRETEST -A. 90˚ -B. 60˚ -C. 45˚ -D. 30˚ -E. Cannot be determined D E**

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

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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

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**-A. 4 -B. 4√2 -C. 4√3 -D. 8 -E. 8√2 PRETEST**

.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

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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

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.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

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16.9 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 A- Probability If I rolled three Dice , how many Different possibilities ? PRETEST

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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

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19.2% 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 C- Averages PRETEST

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**CAN WE MAKE A REASONABLE GUESS ?**

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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E -PERIMETER If the length of a rectangle is 1 foot less than twice its width and its perimeter is 34 feet, what is the length of the rectangle in feet? A) 6 B) 11 C) 11 2/3 D) 22 1/3 E) None of these PRETEST

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**PRETEST E-AREA OF SQUARE**

Shannon is planning to tile a rectangular kitchen countertop that is 24 inches wide and 64 inches long. She determined that 1 tile will be needed for each 4-inch-by-4-inch region. What is the minimum number of tiles that will be needed to completely cover the countertop to its edges? A) 44 B) 88 C) 96 D) 176 E) 384 PRETEST

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6.9% .E - Perimeter A CIRCULAR RUNNING TRACK IS BEING BUILT IN A FENCED-IN ATHLETIC FIELD 100 FEET WIDE AND 150 FEET LONG. IF A BORDER OF 10 FEET IS NEEDED BETWEEN THE OUTSIDE EDGE OF THE TRACK AND BOTH FENCES, WHICH IS THE RADIUS OF THE LARGEST TRACK THAT CAN BE BUILT? A) 40 B) 45 C) 65 D) 90 E) 110 PRETEST

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G 3,4, TRIANGLE 5,12,13 TRIANGLE A ramp for loading trucks is 13 feet long and covers 12 feet along the level ground. How many feet high is the highest point on the ramp? A) 1 B) 2 C) 4 D) 5 E) 6¼ PRETEST

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54.6% .G- 3,4,5 Triangle THE LENGTHS OF THE SIDES OF A TRIANGLE ARE 3,4,5 INCHES. WHAT IS THE LENGTH IN INCHES OF THE SHORTEST SIDE OF A SIMILAR TRIANGLE THAT HAS A PERIMETER OF 36 INCHES: A. 9 B. 12 C. 13 D. 15 E. 18 PRETEST

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H- AREA OF SQUARES The diagonal of a square quilt is 4√2 feet long. What is the area of the quilt in square feet? A) 16√2 B) 16 C) 4√2 D) 4 E) √2 PRETEST

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H -TRIANGLES Points A(1,0), B(8,0), and C(3,4) are the vertices of a triangle. What is the area of this triangle? A) 5 B) 10.5 C) 14 D) 16 E) 28 PRETEST TIP—SAME VALUES FOR Y AXIS

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H –TRIANGLES. On level ground, a vertical rod 12 feet tall casts a shadow 4 feet long, and at the same time a nearby vertical flagpole casts a shadow 12 feet long. How many feet tall is the flagpole? A) 4 B) 8 C) 12 D) 20 E) 36

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I -MIDPOINTS What is the distance, in coordinate units, between the points (-3,5) and (4,-1) in the standard (x,y) coordinate plane? A) √13 B) √17 C) √85 D) 13 E) 85 PRETEST

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**PRETEST IN HOW MANY ORDERS CAN 6 DIFFERENT BOOKS BE PLACED ON A SHELF:**

MADE EASY IN HOW MANY ORDERS CAN 6 DIFFERENT BOOKS BE PLACED ON A SHELF: A. 21 B. 30 C. 720 D E. NONE OF THE ABOVE PRETEST

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