Review for Grade 9 Math Exam - Unit 7 - Similarity and Transformations
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1 Review for Grade 9 Math Exam - Unit 7 - Similarity and Transformations Name: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the scale factor for this scale diagram. Original diagram Scale diagram a. 32 b. 8 c. d rectangle has length 6 cm and width cm. The rectangle is to be enlarged by a scale factor of 8. Calculate the length of the enlargement. a. 80 cm b. 8 cm c. 32 cm d. 1 cm 3. Determine the scale factor for this scale diagram. Original diagram Scale diagram a. 10 b. 1 c. d. 1
2 . Which of parallelograms, B, C, and D are scale diagrams of parallelogram O? O B C D a. Parallelogram D b. Parallelogram C c. Parallelogram B d. Parallelogram. Determine the scale factor for this reduction. Reduction Original a. 8 b. c. 1 d wheel has diameter 6 cm. Determine the diameter on a scale diagram if the scale factor is a. 71 cm b. 3.9 cm c. 108 cm d. 39 cm 7. Determine the scale factor for this reduction. Original Reduction a. 3 b. c. d.
3 8. Identify similar quadrilaterals. Q P S R a. P and Q b. P and R c. R and S d. Q and S 9. Identify similar rectangles. Y 7 cm 6 cm X cm Z 22 cm 10 cm W 6 cm 12 cm 11 cm a. Y and Z b. X and Z c. Y and W d. W and Z 10. Calculate the value of r in this proportion: a. 6 b. 10 c. 16 d. 6.
4 11. These two pentagons are similar. Determine the value of x. a cm b. 20. cm c cm d. 18 cm 12. Determine the length of EB in this pair of similar triangles. B E C D a b. 10 c. 8 d. 13. When the shadow of a flagpole is 33.6 m long, a 1.8-m fencepost casts a shadow 2.8 m long. How tall is the flagpole? a. 2.3 m b m c m d m 1. How many lines of symmetry does this tessellation have? a. 6 b. 2 c. d. 1
5 1. Which example shows a reflection of triangle X in the dotted line? Example i Example ii X X Example iii Example iv X X a. Example iii b. Example i c. Example ii d. Example iv 16. Which figure shows the rotation image of circle after a 13 counterclockwise rotation about its centre? Circle Figure i Figure ii Figure iii Figure iv a. Figure iv b. Figure i c. Figure iii d. Figure ii 17. Describe the rotational symmetry and line symmetry of this parallelogram. a. Rotational symmetry of order 2 about the centre; no line symmetry b. Rotational symmetry of order 2 about the centre; 1 line of symmetry through the centre c. Rotational symmetry of order 1 about the centre; 1 line of symmetry through the centre d. No rotational symmetry; no line symmetry
6 Short nswer 18. Determine the scale factor for this scale drawing. Original diagram Scale diagram 19. These quadrilaterals are similar. Determine the values of x and y x y 20. These parallelograms are similar. Determine the values of x and y. B D 12 C E F x 8 H G y 21. Determine the length of BD in these similar triangles. B C 1 7. D E
7 22. Determine the lengths of CD and CE in these similar triangles. B D 11. C 9 E 23. When the shadow of an electrical tower is 11.7 m long, a.-m lamp post casts a shadow 6. m long. How tall is the electrical tower? 2. Draw the lines of symmetry in this tessellation. 2. This polygon is one-half of a shape. Use the dotted line as a line of symmetry to complete the shape by drawing its other half. y x
8 26. This design was created by reflecting quadrilateral to create quadrilaterals B, C, and D. Describe the reflections y B D C x 27. This polygon is one-half of a shape. Use a vertical line through on the x-axis as a line of symmetry to complete the shape by drawing its other half. Write the coordinates of the larger shape formed by PQRS and its image y P S R Q x 28. Describe the rotational symmetry and line symmetry of this diagram.
9 29. Quadrilateral P is rotated 90 clockwise about vertex, then 270 counterclockwise about vertex. Which quadrilateral shows the final position of quadrilateral P? Q R P S Problem 30. Draw a scale diagram of parallelogram BCD with scale factor 3. D C B
10 31. These three rectangles are similar. a) Determine the values of x and y. b) Griswald draws another similar rectangle with width 7.6 cm. What is its length? 90 cm cm 36 cm x 18 cm y
11 Review for Grade 9 Math Exam - Unit 7 - Similarity and Transformations nswer Section MULTIPLE CHOICE 1. NS: C PTS: 1 DIF: Easy REF: 7.1 Scale Diagrams and Enlargements LOC: 9.SS TOP: Shape and Space (Transformations) 2. NS: B PTS: 1 DIF: Easy REF: 7.1 Scale Diagrams and Enlargements LOC: 9.SS TOP: Shape and Space (Transformations) 3. NS: C PTS: 1 DIF: Easy REF: 7.1 Scale Diagrams and Enlargements LOC: 9.SS TOP: Shape and Space (Transformations). NS: B PTS: 1 DIF: Moderate REF: 7.1 Scale Diagrams and Enlargements LOC: 9.SS TOP: Shape and Space (Transformations). NS: C PTS: 1 DIF: Easy REF: 7.2 Scale Diagrams and Reductions LOC: 9.SS TOP: Shape and Space (Transformations) 6. NS: B PTS: 1 DIF: Easy REF: 7.2 Scale Diagrams and Reductions LOC: 9.SS TOP: Shape and Space (Transformations) 7. NS: D PTS: 1 DIF: Easy REF: 7.2 Scale Diagrams and Reductions LOC: 9.SS TOP: Shape and Space (Transformations) 8. NS: B PTS: 1 DIF: Easy REF: 7.3 Similar Polygons 9. NS: D PTS: 1 DIF: Easy REF: 7.3 Similar Polygons 10. NS: D PTS: 1 DIF: Easy REF: 7.3 Similar Polygons 11. NS: C PTS: 1 DIF: Moderate REF: 7.3 Similar Polygons 12. NS: C PTS: 1 DIF: Moderate REF: 7. Similar Triangles 13. NS: B PTS: 1 DIF: Moderate REF: 7. Similar Triangles 1. NS: B PTS: 1 DIF: Easy REF: 7. Reflections and Line Symmetry LOC: 9.SS TOP: Shape and Space (Transformations) KEY: Conceptual Understanding
12 1. NS: D PTS: 1 DIF: Easy REF: 7. Reflections and Line Symmetry LOC: 9.SS TOP: Shape and Space (Transformations) 16. NS: D PTS: 1 DIF: Moderate REF: 7.6 Rotations and Rotational Symmetry LOC: 9.SS TOP: Shape and Space (Transformations) 17. NS: PTS: 1 DIF: Easy REF: 7.7 Identifying Types of Symmetry on the Cartesian Plane LOC: 9.SS TOP: Shape and Space (Transformations) SHORT NSWER 18. NS: The scale factor is 3.. PTS: 1 DIF: Moderate REF: 7.1 Scale Diagrams and Enlargements LOC: 9.SS TOP: Shape and Space (Transformations) 19. NS: x = 20. y = 31 PTS: 1 DIF: Moderate REF: 7.3 Similar Polygons KEY: Conceptual Understanding Procedural Knowledge 20. NS: y = 6 x = 66 PTS: 1 DIF: Moderate REF: 7.3 Similar Polygons KEY: Conceptual Understanding Procedural Knowledge 21. NS: BD = 6 PTS: 1 DIF: Moderate REF: 7. Similar Triangles 22. NS: CD =. CE = 2. PTS: 1 DIF: Moderate REF: 7. Similar Triangles
13 23. NS: 8.1 m PTS: 1 DIF: Moderate REF: 7. Similar Triangles 2. NS: PTS: 1 DIF: Easy REF: 7. Reflections and Line Symmetry LOC: 9.SS TOP: Shape and Space (Transformations) KEY: Conceptual Understanding 2. NS: y x PTS: 1 DIF: Easy REF: 7. Reflections and Line Symmetry LOC: 9.SS TOP: Shape and Space (Transformations) 26. NS: Quadrilateral B is the reflection image of quadrilateral in the oblique line through (0, 8) and (8, 0). Quadrilateral C is the reflection image of quadrilateral in the vertical line through on the x-axis. Quadrilateral D is the reflection image of quadrilateral in the oblique line through (0, 0) and (8, 8). PTS: 1 DIF: Moderate REF: 7. Reflections and Line Symmetry LOC: 9.SS TOP: Shape and Space (Transformations) KEY: Conceptual Understanding Communication
14 27. NS: y 6 S R S' 3 2 Q 1 P P' x The shape PSS'P'Q has coordinates: P(0,1), S(2,), S'(8, ), P'(10, 1), Q(, 3) PTS: 1 DIF: Moderate REF: 7. Reflections and Line Symmetry LOC: 9.SS TOP: Shape and Space (Transformations) 28. NS: Rotational symmetry of order 2 about the centre; no line symmetry PTS: 1 DIF: Easy REF: 7.7 Identifying Types of Symmetry on the Cartesian Plane LOC: 9.SS TOP: Shape and Space (Transformations) 29. NS: R PTS: 1 DIF: Moderate REF: 7.6 Rotations and Rotational Symmetry LOC: 9.SS TOP: Shape and Space (Transformations) PROBLEM 30. NS: PTS: 1 DIF: Moderate REF: 7.1 Scale Diagrams and Enlargements LOC: 9.SS TOP: Shape and Space (Transformations)
15 31. NS: a) Solve for x. Solve for y. So, x = 27 cm. So, y = cm. b) Let z represent the length. The length is 11.2 cm. PTS: 1 DIF: Moderate REF: 7.3 Similar Polygons KEY: Problem-Solving Skills Procedural Knowledge
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