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Practice Test Unit 3 Geometry

Practice Test Unit 3 Geometry. Which of the following points is the greatest distance from the y-axis?. 1. . A. A. (1,10) B. (2,7) C. (3,5) D. (4,3) E. (5,1). . B. . C. . D. . E.

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Practice Test Unit 3 Geometry

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  1. Practice TestUnit 3Geometry

  2. Which of the following points is the greatest distance from the y-axis? 1  A A. (1,10) B. (2,7) C. (3,5) D. (4,3) E. (5,1)  B  C  D  E

  3. Points P, Q, R, and S lie on a line in that order. If QR = RS, PQ = 10, and PS = 38, what does QR equal? 2 38 – 10 = 28 10     P Q R S 38 QR = 28 ÷ 2 = 14

  4. Find the midpoint between the points (3,–6) and (7,13). 3

  5. In the figure below, is a straight line. What is the value of x? 4 x + x + 44 = 180 Straight Line 180 2x + 44 = 180 –44 –44 2x = 136 x = 68

  6. Find the area of ABC. 5 h 8 b Side Note: The y-coordinates are the same. 7 – (–1) = 7 + 1 = 8 Subtract x-coordinates.

  7. Find the area of ABC. 5  5 h  8 b = 20

  8. Find the length of the line segment AB. 6 Find the length by finding the distance between the points. A(–3,4)   B(2,1)

  9. Find the length of the line segment AB. 6 Find the length by finding the distance between the points. A(–3,4)   B(2,1) d ≈ 5.83

  10. Solve for x. 7 Congruent Angles 4 = 8 m || n m (x+80) x + 80 = 5x n –x –x (5x) 80 = 4x 20 = x 1 2 m || n m 1 = 3 = 5 = 7 4 3 6 5 n 2 = 4 = 6 = 8 7 8

  11. Find the value of x. 8 5y 9x + 8 80 9x + 8 = 80 Vertical Angles – 8 – 8 9x = 72 x = 8

  12. 9 If PRQ is an isosceles triangle with PQ = PR, find the measure of QPX. ∆PRQ: Isosceles Triangle The base angles are equal. QPX: Exterior Angle 60 ?

  13. In the figure, if x = 2z and y = 70, what is the value of z? 10 70 2z 2z = 70 + z Exterior Angles Rule – z – z z = 70

  14. 11 If the ratio of the angles of a triangle is 2:3:4, what is the degree measure of the largest angle? Largest Angle 4x 4(20) = 80

  15. In the isosceles right triangle ABC, leg equals 6. What is the length of ? 12 3x = 6 x = 2 6 = 5x = 5(2) = 10

  16. 13

  17. In ABC, the measure of A is 80° and the measure of B is 50°. If the length of AB is 2x – 12 and the length of AC is x – 3, what is the length of AB? 14 A C = 180° – 80° – 50° = 50° 80° AB = AC 2x – 12 = x – 3 –x –x x – 12 = –3 50° 50° x = 9 B C AB = 2(9)–12 = 18 –12 = 6

  18. In the right ABC, the length of leg is and D is the midpoint of . Find the length of . 15 x= = 3 30° C = 180° – A – B = 180° – 60° – 90° = 30°

  19. Find the length of JK. 16 L 34.6 mm 18 K J 1  x= .9511  34.6 x x= 32.91 cos 18 = .9511

  20. Two angles of a hexagon measure 140° each. The other four angles are equal in measure. What is the measure of each of the other four equal angles, in degrees? 17 Step 1: Find the sum of interior angles in a hexagon. x x  Number of sides = 6 140 140  Number of sides – 2 = 6 – 2 = 4 x x  Multiply 4 by 180 = 4(180) = 720

  21. Two angles of a hexagon measure 140° each. The other four angles are equal in measure. What is the measure of each of the other four equal angles, in degrees? 17 Step 1: Find the sum of interior angles in a hexagon. x x 720 Step 2: Set up equation by letting sum of angles equal 720. 140 140 x + x + x + x + 140 + 140 = 720 4x + 280 = 720 x x – 280 – 280 4x = 440 Measure of each the four equal angles is 110 x = 110

  22. 18 A regular octagon is shown. What is the measure, in degrees, of X? Step 1: Find sum of the interior angles in the regular octagon.  Number of sides = 8 X  Number of sides – 2 = 8 – 2 = 6  Multiply 6 by 180 = 6(180) = 1080 Step 2: Find value of each interior angle, X. Divide sum by number of sides, 8. 1080  8 = 135

  23. In the figure, right triangle ABC is contained within right triangle AED. What is the ratio of the area of AED to the area of ABC? 19 ∆ABC is Isosceles 45 ∆AED Big Triangle 45 A = 45 D = 90 E = 45 ∆AED is Isosceles 45 8

  24. In the figure, right triangle ABC is contained within right triangle AED. What is the ratio of the area of AED to the area of ABC? 19 Area of ∆ABC Small Triangle 45 = 18 45 Area of ∆AED Big Triangle = 32 45 8

  25. The figure above shows a square region divided into four rectangular regions, three of which have areas 5x, 5x, and x2, respectively. If the area of MNOP is 64, what is the area of square QROS? 20 x 5 Area of square QROS 5 5 Length  Width = 5  5 = 25 x x x 5

  26. All the dimensions of a certain rectangular solid are integers greater than 1. If the volume is 126 cubic inches and the height is 6 inches, what is the perimeter of the base? 21 Perimeter of Base V = Volume V = lwh 2l + 2w 126 = l  w  6 = 2(7) + 2(3) h = 14 + 6 w 6 = 20 21 = l  w (Base) l Base l = 3 or 7 w = 3 or 7

  27. 22 In trapezoid ABCD, AB = CD. What is the value of x? Method #1 Isosceles Trapezoid AandB supplementary 75° + x = 180° –75 –75 x = 105°

  28. 22 In trapezoid ABCD, AB = CD. What is the value of x? Method #2 Sum of all angles = 360° x + x + 75 + 75 = 360 2x + 150 = 360 –150 –150 2x = 210 x = 105

  29. Cube A has an edge of 2. Each edge of cube A is increased by 50%, creating a second cube B. The surface area of cube B is how much greater than the surface area of cube A? 23 Cube A Cube B 2 3 2 2 3 3 50% of 2 = .50  2 = 1 2 + 1 = 3 50% increase =

  30. Cube A has an edge of 2. Each edge of cube A is increased by 50%, creating a second cube B. The surface area of cube B is how much greater than the surface area of cube A? 23 SA = Surface Area Cube A Cube B 2 SA = 6s2 SA = 6s2 3 = 622 = 632 2 2 = 64 = 69 3 = 24 = 54 3 – SA Cube B SA Cube A 54 – 24 = 30

  31. 24 In the figure, VW = WX = VX = XY = YZ = XZ. If VZ = 12, what is the perimeter of the triangle VWX? VZ = 12 VX = 6 VW = 6 WX = 6 Perimeter VWX = 6 + 6 + 6 = 18

  32. 25 If the diameter of circle is 8, what is the ratio between the circle’s area and its circumference? d: diameter r: radius d = 2r Step 1: Find the radius, given diameter is 8. d = 8 r = 4 Step 3 Find area of circle. Step 2 Find circumference of circle. C = 2πr A = πr2 = 2π4 = 8π = π16 = 16π = π42

  33. 25 If the diameter of circle is 8, what is the ratio between the circle’s area and its circumference? Step 3 Find area of circle. Step 2 Find circumference of circle. C = 2πr A = πr2 = 2π4 = 8π = π16 = 16π = π42 Step 4: Find ratio. = 2 = 2:1

  34. 26 Find the circumference of a circle with area π. C = 2πr C: Circumference A: Area Find the radius A = πr2 C: Circumference A = π π = πr2 C = 2πr C = 2π 1 C = 2π 1 = r2 1 = r

  35. If a circle with an area of 4 is inscribed in a square , what is the perimeter of the square? 27 A: Area 4 P: Perimeter A = 4π P = 4s A = πr2 P = 4(4) d = 4  4π= πr2 r = 2 P = 16 (Find radius) 4 = r2 2 = r

  36. In the figure, the circle inscribed inside the square has a radius of 3. What is the area of the shaded region? 28 6 Circle Area Square Area A = πr2 A = s2 A = π·32 A = 62 d = 6  A = 36 3 A = π·9 A = 9π Area of shaded region = Square Area – Circle Area = 36 – 9π

  37. The circle has a diameter of 12. What is the length of ? 29 Length of major arc 6 C = 2πr = 9π C = 2π 6 = 12π

  38. If the circumference of the circle is 8, what is the area of the shaded region? 30 Circumference Area of circle C = 2πr A = πr2 C = 8π A = π42 8π= 2πr A = π 16 4 = r A = 16π Central Angle = 90° Area of sector = 4π

  39. ABC = 48°. Find the measure of the major arc . 31 Major Arc in red 48 48 Major Arc = 360 – 48 = 312

  40. If , find the measure of CDE. 32 = 60

  41. In the figure, if the slope of line m is , what is the value of y ? 33 Use the slope formula. 4(y – 8) = –8  3 4y – 32 = –24 +32 +32 y = 2 4y = 8

  42. 34 If a straight line intersects the x-axis at 5 and the y-axis at 3, what is the slope of the line? –5  3 

  43. Which line is parallel to the line 2y = 3x + 4 ? 35 Note: Parallel lines have the same slope. Step 1: Find the slope of 2y = 3x + 4 by rewriting in slope-intercept form, y = mx + b • 6y = 3x– 4 • 2y = x + 2 C. 4y = 6x– 1 • y = 3x + 4 E. 2y = –2x– 1 2y = 3x + 4

  44. Which line is parallel to the line 2y = 3x + 4 ? 35 Note: Parallel lines have the same slope. Step 2: Find the slope of each answer by rewriting in slope-intercept form, y = mx + b 2y = 3x + 4 6y = 3x – 4 NO Slopes not equal

  45. Which line is parallel to the line 2y = 3x + 4 ? 35 Note: Parallel lines have the same slope. Step 2: Find the slope of each answer by rewriting in slope-intercept form, y = mx + b 2y = 3x + 4 B. 2y = x + 2 NO Slopes not equal

  46. Which line is parallel to the line 2y = 3x + 4 ? 35 Note: Parallel lines have the same slope. Step 2: Find the slope of each answer by rewriting in slope-intercept form, y = mx + b 2y = 3x + 4 C. 4y = 6x – 1 Slopes are equal

  47. 36 A, B, C, and D are points in the coordinate system. Segments AB, BC, CD, and DA form a rectangle. The slope of line AB is . What is the slope of line BC. B B C A C A D D

  48. A, B, C, and D are points in the coordinate system. Segments AB, BC, CD, and DA form a rectangle. The slope of line AB is . What is the slope of line BC. 36 B Perpendicular Lines have slopes that are negative reciprocals A C D

  49. Which line segment in the figure has a slope of ? 37 Use to find the slope for each line segment.  Segments and have positive slopes.   They rise as you trace them from left to right. Thus, they can not be the answer. 

  50. Which line segment in the figure has a slope of ? 37 Use to find the slope for each line segment. –5  4 

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