Summer Math
Pre and Post Tests
for
Post Geometry
(for students who have completed non-honors Geometry this past year)
________________________________________ Name Please read the directions (separate document) completely before starting your packet! Print out the packet so you can record your work. This will be turned in to your teacher in August. REMEMBER – ALL ANSWERS (letter choice or student generated response) MUST BE INPUTTED ONLINE AT THE WEBSITE www.classmarker.com. If you lose or forget your username and password, email Mr. Toth at ttoth@communityschoolnaples.org. Even though you will be inputting your answers online we have included a blank “answer sheet” to help organize your answers. You can write your letter choice (or numeric value for student generated responses) in the blank next to each problem number as you work out your solutions. When you actually log in to input answers, this should make the process much smoother and less prone to error. Obviously, it is of utmost importance to make sure you are entering answers in the correct tests. *Please make notes and comments about the problems that caused difficulty so that you can recall the process you undertook when we go over the packets in the fall. *If you encounter any typos or errors, please email me with the problem and the issue at ttoth@communityschoolnaples.org
Answer Sheet for Post non-­‐honors Geometry Pretest Test 1 Section 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Test 1 Section 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Test 1 Section 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Answer Sheet for Post non-­‐honors Geometry Post Tests Test 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Test 3 Section 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Test 3 Section 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Test 3 Section 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Diagnostic Model SAT Geometry and Measurement: Test 1, Section 1 1. For the intersecting lines above, which of the following must be true? I.
b = 2c II. !
a= III. !
a + 120 = b + c (a) I only (b) II only (c) I and II only (d) II and III only (e) I, II, and III 2. On the line segment, above, RT = 10 and RM = 8. What is the length of the line segment joining the midpoints of 𝑅𝑇 and 𝑅𝑀 (a) 1 (b) 3 (c) 5 (d) 7 (e) 9 3. If each edge of cube M with a unit length of 3 is increased by 50%, creating a second cube B, then what is the volume of cube B? (a) 20.5 (b) 36 (c) 64 (d) 91.125 (e) 216 4. In the figure above, square ABCD is inscribed in a circle with area 18𝜋. What is the area of the shaded region? (a) 9 (b) 9π (c) 18 -­‐ 9π (d) 18π -­‐ 9 (e) 18π – 36 5. In the figure above, if side RS = ST, and x = 115⁰, what is the measure of angle y? (a) 65 (b) 75 (c) 85 (d) 115 (e) 130 6. In circle O above, 𝑃𝑄 is the diameter and the circumference is 24π . If ∠POR + 60⁰, what is the length of arc 𝑅𝑄? (a) 4π (b) 6π (c) 8π (d) 12π (e) 16π 7. The perimeter of rectangle MATH in the figure is 48. What is the area of each square? (a) 24 (b) 32 (c) 64 (d) 128 (e) 256 8. If the unequal sides of a triangle are 3, x, and 7, where 3< x < 7, then what is the smallest integer value of x? (a) 3 (b) 4 (c) 5 (d) 6 (e) 10 Note: Figure not drawn to scale. 9. If AB = 12 and the circumference of circle A is 3 times the circumference of circle B, what is the length of 𝐶𝐵? !
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10. If the points (2,3) and (5,y) lie on a line whose slope is − , what does y equal? !
a) -­‐6.5 b) -­‐0.5 c) 0 d) 0.5 e) 6.5 11. In the figure, if 90 < a + c < 180, which of the following describes all possible values of b +d? (a) 0 <b + d < 90 (b) 90 < b + d < 180 (c) 180 < b + d < 270 (d) 180 < b + d < 360 (e) 270 < b + d < 360 Questions 12 and 13 refer to the figure below. ∠DAB = 15° and ∠ABC = 45⁰. 12. What is the length of 𝐴𝐵? (a) 10 (b) 10 2 (c) 10 3 (d) 20 2 -­‐ 10 (e) 20 3 – 10 13. What is the length of 𝐷𝐵? (a) 20 – 10 3 (b) 20 – 10 2 (c) 10 3 -­‐ 10 (d) 10 2 -­‐ 10 (e) 10 3 14. What is the perimeter of the triangle formed by joining the vertices A, B, and C of the cube above, with an edge of 1? (a) 1.5 2 (b) 3 (c) 4 (d) 3 2 (e) 6 15. In the figure above, find the value of x. (a) 2 (b) 4 (c) 8 (d) 12 (e) 16 16. If the wheels of a train make 16 revolutions when it rolls a distance of 60 feet, what is the radius of the wheel? (a) !
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17. Each of the four outside walls of the large wooden box shown above is to be covered with a waterproof plastic that comes in 3-­‐foof-­‐wide-­‐rolls. The plastic does not overlap. What is the total length, in feet, of plastic, needed to cover the four walls? (a) 21 𝑓𝑡. (b) 42 ft. (c) 63 𝑓𝑡. (d) 84 𝑓𝑡. (e) 126 𝑓𝑡. 18. If the diagonal of the square inscribed in the circle is 8, what is the sum of the shaded areas? (a) 𝜋 !"
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+ 2𝜋 19. In the figure above, if b = 54 and c = 75, what is the value of a? (a) 111 (b) 119 (c) 121 (d) 129 (e) 131 20. The surface areas of the rectangular prism above are given. If the lengths of the edges are integers, what is the volume in cubic feet? (a) 94 (b) 168 (c) 188 (d) 1,152 (e) 1,176 Test 1, Section 2 1. If the angles of a triangle are in the ratio of 2 : 3 : 5, what kind of triangle is it? (a) 𝐴𝑐𝑢𝑡𝑒 (b) Obtuse (c)Equilateral (d) 𝐼𝑠𝑜𝑐𝑒𝑙𝑒𝑠 (e) 𝑅𝑖𝑔ℎ𝑡 2. If the diameter of circle A is twice as large as the diameter of circle B, what is the ratio of the area of the larger circle to the area of the smaller circle? (a) 8: 1 (b) 6:1 (c) 4: 1 (d) 2: 1 (e) 3: 2 3. If x = 60 in the scalene triangle above, then which of the following must be true? (a) 𝑥 > 𝑦 > 𝑧 (b) 𝑥 > 𝑧 > 𝑦 (c) 𝑦 > 𝑥 > 𝑧 (d) 𝑦 > 𝑧 > 𝑥 (e) 𝑧 > 𝑦 > 𝑥 4. Which of the following could be the graph of 𝑥 ! + 8𝑥 + 12 = 𝑦? 5. If the diameter of the circle is 10, what is the ratio of the area of the small square to the area of the large square? (a) 1: 4 (b) 1: 𝜋 (c) 1: 3 (d) 1: 2 (e) 3: 5 6. In the figure above, point M has the greatest y-­‐coordinate on the semi-­‐circle. What is the x-­‐coordinate of point P? (a) −1.5 (b) -­‐2 (c) −2.5 (d) −3 (e) −3.5 7. In the figure above, if the radius of the inscribed circle is 8, then the perimeter of the shaded region is… (a) 2𝜋 + 8 (b) 2𝜋 + 16 (c) 4𝜋 + 8 (d) 4𝜋 + 16 (e) 16𝜋 + 16 8. In rectangle OEAD in the figure above is inscribed in the circle OBC, which of the following statements must be true? I.
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(c) 𝐼𝐼 𝑎𝑛𝑑 𝐼𝐼𝐼 (d) 𝐼 𝑎𝑛𝑑 𝐼𝐼𝐼 𝑂𝑛𝑙𝑦 (e) 𝐼 , 𝐼𝐼, 𝑎𝑛𝑑 𝐼𝐼𝐼 Free Response: 9. In the figure above, S is parallel to T, 𝑎 = 48! . 𝑎𝑛𝑑 𝑏 = 107! . What is the measure of ∠𝑐? 10. What is the average of the marked angles 1, 2, and 3 in the figure above? 11. If the area of triangle T, sides 5, 12, and 13, equals the area of rectangle R, width 8, then what is the perimeter of rectangle R? 12. In the figure above, what is the value of altitude x? 13. If Jack’s house is 7.1 miles due north of the Senior Citizen Center and Belinda’s house is 6.3 miles due west of it, then to the nearest tenth, what is the shortest distance between their houses? 14. In the figure above, what is the coordinate of point N? 15. To the nearest tenth, what is the circumference of a circle with an area of 49𝜋? !
16. If a line 𝑙 with a slope of − passes through the points (5, 0) and (x, -­‐2), then what is the value of x? !
17. In the figure above, the radius of the small circle A is one-­‐half the radius of the large circle B. What is the ratio of the area of the small circle to the area of the large circle? 18. On circle O above, what is the value of x? Test 1 Section 3 1. Four equal squares are arranged to form one larger square. If the perimeter of each of the smaller squares is 36, what is the area of the larger square? (a) 72 (b) 81 (c) 144 (d) 324 (e) 1,296 2. If triangle A and triangle B are each equilateral, which of the following much be true about these triangle? I. 𝑇ℎ𝑒𝑖𝑟 𝑎𝑟𝑒𝑎𝑠 𝑎𝑟𝑒 𝑒𝑞𝑢𝑎𝑙 II. 𝑇ℎ𝑒𝑖𝑟 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟𝑠 𝑎𝑟𝑒 𝑒𝑞𝑢𝑎𝑙 III. 𝑇ℎ𝑒𝑦 𝑎𝑟𝑒 𝑠𝑖𝑚𝑖𝑙𝑎𝑟 (a) 𝐼 𝑂𝑛𝑙𝑦 (b) II Only (c) 𝐼𝐼𝐼 𝑂𝑛𝑙𝑦 (d) 𝐼 𝑎𝑛𝑑 𝐼𝐼 𝑂𝑛𝑙𝑦 (e) 𝐼 , 𝐼𝐼, 𝑎𝑛𝑑 𝐼𝐼𝐼 3. In triangle ABC, AB = BC = CA = s. In terms of s, what is the height of the triangle? (a) ! !
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4. The area of triangle T is 625 square inches. If the length of the base b is half the length of the altitude drawn to that base, then what is the length of the altitude? (a) 15 (b) 20 (c) 25 (d) 50 (e) 100 5. In the isosceles triangle ACB, if side AC is decreased by 4 and side BC is increased by 4, a new triangle ECD is formed. What is the difference in the areas of the two right triangles? (a) 0 (b) 2 (c) 4 (d) 8 (e) 12 6. If the area of the circle above is 36𝜋 and AB = BC, then what is the area of ∆𝐴𝐵𝐶? (a) 9 (b) 18 (c)36 (d) 72 (e) 81 7. In the two concentric circles with center O, the radius of the large circle is twice the radius of the small circle. What is the ratio of the area of the small circle to the area of the large circle? !
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8. In the figure above, what is the perimeter of ∆𝑊𝐼𝑁? (a) 2 (b) 12 (c) 3 2 + 3 (d) 3 2 + 6 (e) 6 2 + 6 9. A square is inscribed in a circle with a radius of 2𝜋. What is the perimeter of the square? (a)2𝜋 2 (b) 4𝜋 2 (c) 6𝜋 2 (d) 8𝜋 2 (e) 10𝜋 2 10. Which of the following points (when plotted) will be three times as far from A (7, 10) as from B (3, 4)? (a) (1, 1) (b) (2, 4) (c) (3, 4) (d) (3, 5) (e) (9, 13) 11. In the figure above, if tan 𝜙 = 1, the x = !
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(c) 5 (d) 4 2 (e) 8 12. In the figure above, the radius of circle B is 12 and the tangent segments AD and DC are each 16. What is the value of x? (a) 5 (b) 5.32 (c) 7 (d) 8 (e) 20 13. In the figure above, with line 𝑙 parallel to line m, which of the following statements must be true? I. 𝐴𝑟𝑒𝑎 𝑜𝑓 ∆𝐴𝐵𝐶 = 𝐴𝑟𝑒𝑎 𝑜𝑓 ∆𝐴𝐸𝐶 II. ∠𝐸𝐴𝐶 = ∠𝐸𝐶𝐹 III. ∠𝐷𝐸𝐴 = ∠𝐸𝐴𝐶 (a) 𝐼 𝑂𝑛𝑙𝑦 (b) III Only (c) 𝐼 𝑎𝑛𝑑 𝐼𝐼 𝑂𝑛𝑙𝑦 (d) 𝐼 𝑎𝑛𝑑 𝐼𝐼𝐼 𝑂𝑛𝑙𝑦 (e) 𝐼𝐼 𝑎𝑛𝑑 𝐼𝐼𝐼 𝑂𝑛𝑙𝑦 14. In the cube drawn above, which statement is NOT true? (a) 𝐵𝐷 = 𝐴𝐶 (b) 𝐴𝐶 = 𝐴𝐹 (c) 𝐶𝐷 = 𝐴𝐵 (d) 𝐴𝐷 = 𝐵𝐹 (e) 𝐵𝐷 = 𝐵𝐹 15. In the figure above, circle O has a radius of 4 and ∆𝑂𝐴𝐵 is an isosceles right triangle. What is the area of the shaded region? (a) 𝜋 (b) 1.5 𝜋 (c) 2 𝜋 (d) 4 𝜋 (e) 8 𝜋 1st Post Test Test 2 Student-­‐produced Response Questions 1. What is the diameter of a circle whose area is 64𝜋? 2. A triangle has sides that measure 3, 8, and n. If 3 < 𝑛 < 8 and n is an integer, how many different triangles are possible? 3. If the area of triangle A, with sides of 6, 8, and 10, equals the area of rectangle B, with width of 4, what is the perimeter of the rectangle? 4. How many degrees are there in the angle formed by the hand of a close at 8:30? (do not grid in the degree symbol) 5. Claudia has a cylindrical telescope with a circular base of area 12𝜋. What is the length of the telescope if the space it occupies (the volume) is 6,096𝜋? 6. In the figure above, two 7 X 7 squares overlap to form a 7 X 11 rectangle. What is the area of the shaded region? 7. If the area of square S is the same as the area of triangle T, with base equal to 12 and altitude equal to 9, then, to the nearest tenth, what is the length of a side of the square? 8. If the area of the circle is 36𝜋, what is the length of a side of the inscribed square, to the nearest hundredth? 9. In the figure above, the radius of the inner circle of the tire is twice the width of the tire itself. To the nearest integer, what percent of the entire area is the area of the tire? (Do not grid in the percent sign) !
10. Given a rectangle ABCD with length 10 and width 4. If 𝐸𝐹 ∥ 𝐶𝐷 and the area of ECDF is the area of rectangle !
ABCD, what is the measure of FD? 11. In the figure above, the three concentric circles have radii lengths of 3, 7, and 12. What is the shortest line segment that can be drawn containing exactly one point on each of the three circles? 12. In the figure above, circle P is inscribed in half of the circle N, which is inscribed in half of circle M. What is the ratio of the area of circle P to the area of circle M? 13. In the figure above, hat is the value of x? 14. The three sides of a triangle are 4, 5, and 8. If the length of one side of a similar triangle is 16, what is the least possible perimeter of the larger triangle? 15. In the figure, H is the midpoint of side DE of rectangle DEFG. If GH is 12, to the nearest tenth, what is the area of triangle GDH? 16. What is the largest number of 3-­‐inch by 5-­‐inch cards that can be cut from a sheet of construction paper 17 inches by 22 inches? 17. In the circle above, the center is B, the diameter AC= 18, and ∠𝐷𝐵𝐸 is a right angle. Find the area of the shaded region to the nearest integer? 18. In the figure above, if point A is (-­‐3, -­‐2) and point B is (5, 5), then what is the length of AB, to the nearest tenth? 19. A rectangular planting field, 50 yards by 100 yards, is surrounded on all sides by a concrete pedestrian walk 6 feet wide. What is the number of square feet in the surface of the walk? 20. In the circle above, he diameter is 15 and the inscribed angle has a length of 12. What is the width of the rectangle? 21. What is the sum of the root of the quadratic equation 𝑥 ! − 11𝑥 + 10 = 0? 22. In the figure above, if tan 𝑎 ! = tan 𝑏 ! , then the measure of ∠𝐴𝐵𝐶 in degrees is… 23. If the radius of circle O in the figure above is 12 and AB is tangent to the circle at point B, with AC = 8, what is the value of x? 24. If the length of a side of an equilateral triangle is 10 inches, what is the length of an altitude of the triangle to the nearest hundredth? !
25. What is the smallest value in the range for the parabola 𝑦 = 𝑥 ! − 3𝑥 + 6? !
2nd Post Test Test 3 Section 1 !
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1. If 𝑎 = , and is the value of 𝑎 − 𝑎? !
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(e) 1 2. If the endpoint of a line segment AB is (-­‐5, 2) and the midpoint is (2, -­‐5), what is the other endpoint? !
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(c) (0, 0) (d) (5, −8) (e) (9, −12) (d) 63 (e) 189 3. If + + = 9, what is the value of x? 𝑎 3 (b) 7 (c) 21 !!!!!!!!!
4. If v, w, x, y, and z are consecutive odd integers, what is the value of 𝑎 0 (b) 2 (c) 3 (d) 5 !
? (e) 10 5. If the length of one side of a regular polygon is 25% of its perimeter, then polygon has how many sides? 𝑎 3 (b) 4 (c) 5 (d) 8 (e) 25 6. If 𝑎 < 0 < 𝑏, which of the following inequalities much be true? 𝑎 𝑎 ! < 𝑏 ! (b) 𝑎 ! < 𝑏 ! !
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7. If x – y = -­‐5 and x + y = 11, what is the value of 𝑥 ! − 𝑦 ! ? 𝑎 − 96 (b)−55 (c) -­‐16 (d) 16 !
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(e) 55 8. In the figure above, if ∆𝐴𝐵𝐶 is equilateral and AD = AB what is the value of x? 𝑎 30 (b)45 (c) 60 (d) 90 (e) 120 9. If 2 ! = 16, then 𝑥 !!! =_____ 𝑎 1 (b) 4 (c) 5 (d) 125 (e) 256 10. If set S consists of all odd multiples of 3, that is, S = (…,-­‐9, -­‐3, 3, 9,…). If the integers x and y are in S, which of the following must also be in S? 𝑎 𝑥𝑦 (b) 𝑥 + 𝑦 (c) 𝑥 − 𝑦 (d) 𝑥 ÷ 𝑦 (e) −𝑥 − 𝑦 11. A square with a side of 𝜋 is equal in area to a circle. What is the diameter of the circle? 𝑎 2𝜋 !
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12. In the figure above, 3PR = PS. What is the value of ? !
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13. If the shaded area in the figure above is 4𝜋, what is the circumference of the circle? 𝑎 4 (b) 8 (c) 4𝜋 (d) 4𝜋 ! (e) 8𝜋 !
14. If the average of an integer N and its reciprocal is , what is that integer? 𝑎
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(b) 3 (c) 5 (d) 6 (e) 7 15. If x books cost d dollars, how much will m books cost at the same rate? 𝑎 𝑚𝑥𝑑 !"
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16. If the surface area of a cube is 54𝑒 ! , what is the volume of the cube? 𝑎 3𝑒 (b) 9𝑒 ! (c) 9𝑒 ! (d) 27𝑒 ! (e) 27𝑒 ! 17. In the figure above, three lines intersect. What is the sum of the degree measures of the marked angles? 𝑎 510 (b) 590 (c) 720 (d) 1,050 (e) 𝐶𝑎𝑛𝑛𝑜𝑡 𝑏𝑒 𝑑𝑒𝑡𝑒𝑟𝑖𝑛𝑒𝑑 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑖𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 18. If the sum of 3 unequal positive integers equals 20, what is the largest possible value of the smallest number? 𝑎 3 (b) 5 (c) 6 (d) 17 (e) 18 !
19. If 𝑚!" = 20 𝑎𝑛𝑑 𝑚 ! = , what is the value of x in terms of m? !
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(d) 2𝑚 (e) 4𝑚 20. In the figure above, if AD is extended to the right to point B (not shown) so that D is the midpoint of ADB, and if the length of AB is 2y, what is the length of CD in terms of y? 𝑎 𝑦 2 (b) 𝑦 3 (c) 𝑦 5 !
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(e) 2𝑦 Test 3 Section 2 1. The vaue of [7 − 2(3 − 2)!! ]!! is 𝑎 − 5 !
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(e) 5 2. What graph on the number line represent the solution to 𝑥 ≥ −1 ∪ (𝑥 ≥ 3)? !
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3. If 𝑘 ≠ 0, which one of the following is the solution for + 𝑎 (2, 16) (b) (4, 6) (c) (4, 8) (d) (4, −6) = ? !
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(e) !
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5. In the graph above, two linear functions are shown. Which of the following are true for these functions? I. 𝑔 𝑖𝑠 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑥 II. 𝑔 𝑥 > ℎ 𝑥 𝑓𝑜𝑟 𝑠𝑜𝑚𝑒 𝑥 III. 𝑇ℎ𝑒𝑟𝑒 𝑖𝑠 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 𝑜𝑛𝑒 𝑥 𝑓𝑜𝑟 𝑤ℎ𝑖𝑐ℎ 𝑔 𝑥 = ℎ(𝑥) (a) 𝐼 𝑂𝑛𝑙𝑦 (b) 𝐼 𝑎𝑛𝑑 𝐼𝐼 𝑂𝑛𝑙𝑦 (c) 𝐼 𝑎𝑛𝑑 𝐼𝐼𝐼 𝑂𝑛𝑙𝑦 (d) 𝐼𝐼 𝑎𝑛𝑑 𝐼𝐼𝐼 𝑂𝑛𝑙𝑦 (e) 𝐼 , 𝐼𝐼, 𝑎𝑛𝑑 𝐼𝐼𝐼 6. If 𝑎 𝑟 ! − 𝑟𝑥 = 0, then an expression for x in terms of a, n, and r is… 𝑎 𝑥 = 𝑎𝑟 ! (b) 𝑥 = 𝑎𝑟 !!! (c) 𝑥 = 𝑎𝑟 !!! (d) 𝑥 = 𝑎𝑟 !! (e) 𝑥 = 𝑎𝑟 ! − 1 7. In the figure above, a wheel with center O rolls in a straight line (without slipping) along a level track. Two spots of red dye on the wheel leave measuring marks on the track as indicated by the dots on the rack above. What is the degree measure of x? 𝑎 120 (b) 144 (c) 216 (d) 240 (e) 𝐶𝑎𝑛𝑛𝑜𝑡 𝑏𝑒 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒𝑑 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑖𝑛𝑓𝑟𝑜𝑚𝑎𝑡𝑖𝑜𝑛 𝑝𝑟𝑜𝑣𝑖𝑑𝑒𝑑 8. In the figure above, if the slope of the line m is , what is the area of the shaded region? !
!
𝑎 900 (b) 1,000 (c) 1,050 (d) 1,150 (e) 1,200 Student-­‐produced Response Questions 9. If 2x + 1 = 10, then 4x + 1 = !
10. If the average of and its reciprocal is N, what is the value of N? !
11. In the figure above, if x + y =100, what is the average of a + b? 12. If the perimeter of a right triangle is 60 and the sides are x, 2x + 4, and 3x – 4, what is the area of the triangle? 13. If 3!" + 3!" + 3!" = 3 ! , what is the value of x? 14. As square, as shown in the figure above, is inscribed in a circle. If the circumference of the circle is 𝜋 2, what is the area of the square? 15. In the addition problem above, A, B, and C are different digitis from 1 to 5, inclusive. What digit does C represent? 16. If the operations * is defined as 𝑎 ∗ 𝑏 =
!"
!!!
, then what does 6 ∗ (6 ∗ 6) equal? 17. If a rectangular solid has two faces the same size and shape as Figure I and four faces the same size and shape as Figure II, what is the volume of the solid? 18. If 𝑥 𝑥 = 8, then what is the value of x? Test 3 Section 3 1. If rectangle A and isosceles triangle B shown above have the same perimeter, what is the value of x? 𝑎 5.5 (b) 7.5 (c) 10 (d) 11 (e) 12 2. For which of the following values of N is 3N – 1 not a prime number? 𝑎 1 (b) 2 (c) 3 (d) 4 (e) 6 3. If the area of a lawn is 360 square meters, and Dave cuts the lawn at the rate of 12 square meters a minute, what fraction of an hour does it take to cut his lawn? !
𝑎 !
!
(b) !
!
(c) !
!
(d) !
!
(e) !
4. If 713!" is multiplied out completely, what is the units digit of the resulting number? 𝑎 0 (b) 1 (c) 3 (d) 7 (e) 9 !
5. A circle is inscribed in a square as shown above. If a side of the square is , what is the ratio of the perimeter of !
the square to the circumference of the circle? 𝑎 !
!!
!
(b) !
!
(c) !
!
(d) !
!
(e) !
6. If k >0 and 25𝑥 ! + 𝑏𝑥 + 16 = (5𝑥 − 𝑘)! , for all values of x, what is the value of k – b? 𝑎 − 44 (b)−36 (c) 14 (d) 36 (e) 44 7. If AB = AC and 𝑙! ∥ 𝑙! , what is the value of x? 𝑎 40 (b) 80 (c) 100 (d) 140 (e) 𝐶𝑎𝑛𝑛𝑜𝑡 𝑏𝑒 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒𝑑 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑖𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 8. A perfect square is the result of squaring an integer. If K is a perfect square, then which of the following must represent the next consecutive perfect square? 𝑎 𝐾 + 1 (b) 𝐾 + 𝐾 (c) 𝐾 + 𝐾 + 1 (d) 𝐾 + 2 𝐾 + 1 (e) 2𝐾 + 2 𝐾 + 1 !
!
!
!"
9. What percent of 𝑖𝑠 !
𝑎 12 % !
? (b) 25% (c) 50% !
(d) 66 % !
(e) 75% 10. Leo rested a ladder against his house to repair a window. The ladder just reached the bottom of the window. The base of the ladder was 4.5 feet from the house. At a horizontal distance of 1.5 feet from the base of the ladder toward the house, the vertical rise was 5 feet. What is the distance from the bottom of Leo’s window to the ground? 𝑎 7.5 𝑓𝑡 (b) 10 𝑓𝑡 (c) 12.5 𝑓𝑡 (d) 15 𝑓𝑡 (e) 17.5 𝑓𝑡 11. If x = -­‐2, what is the value of −2𝑥 ! + 2𝑥 !! ? 𝑎 16
!
!"
!
(b) 8 !
(c) 0 !
(d) −8 !
(e) −16
!
!"
12. All of the following equations are examples of a direct variation except for… 𝑎 𝑦 = 13𝑥 !
(b) 𝑦 = !
(c) 2𝑦 = 𝑚𝑥 !
(d) = 𝑘 !
(e) 𝑥𝑦 = 𝑘 13. In the figure above, if the real numbers, a, b, and c are related as shown on the number line, which of the following is false? 𝑎 𝑐 = 𝑐 (b) 𝑎 > 𝑏 (c) 𝑎 > 1 (d) 𝑏 < 1 (e) 𝑎 − 𝑏 > 𝑏 − 𝑎 !"
14. If (𝑎 ! 𝑎 ! ) ! = 𝑎!"# and (𝑎 ! ) ! = 𝑎 !" , where x > 1 and y > 0, what is the product of x and y? 𝑎
!
!
(b) 4 (c) 8 (d) 16 (e) 20 15. In the figure above, BC is the tangent to circle O. If AO = x and OB = y, then (𝐶𝐵)! equals… 𝑎 𝑦 ! − 𝑥𝑦 (b) 𝑥𝑦 − 𝑥 ! (c) 𝑦 ! − 𝑥 ! (d) 𝑥 ! − 𝑦 ! (e) 𝑥𝑦