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1. In geometry, which of the 1. In geometry, which of the following must be true? following must be true? I. A point is circular. I. A point is circular. II. The width of a line II. The width of a line is is very small. very small. III. A plane has no III. A plane has no thickness. thickness. A. I only B. III only A. I only C. I and II only B. III only D. I, II and III C. I and II only D. I, II and III B In geometry, a point has no shape or size. 1. B A line has no thickness In geometry, a point has no shape or width, only length. or size. A plane has no A line has no thickness or width, thickness, but it has shape and only length. size. A plane has no thickness, but it Only III is true. has shape and size. Only III is true. 2. How many round angles does 420° equal? 2. How many round angles 5 does 420° equal? A. 6 of a round angle A. B. C. D. 1 of a round angle 6 1 of a round angle 1 1 round angles 6 2 round angles A 1 round angle 360° 420 420 round 360 1 1 round angles 6 B. C. D. C 1 angle 360° 2. 3. 630° = A. 1 of a round angle. 7 round angles. 4 5 round angles. 4 2 round angles. B. C. D. 1 6 of a round angle 1 1 6 round angles 1 1 3 round angles angle 420 round 420 360 round 1 1 angles 6 round angles 3. How many round angles does 630° equal? A. B. C. 4 7 of a round angle 7 4 round angles 5 4 round angles 3. B 1 round angle 360° 630 7 630 round angles 360 4 4. A. B. C. D. How many right angles does 292.5° equal? 2 right angles 3 2 right angles 4 1 3 right angles 2 1 3 right angles 4 D. B 1 angle 360° 630 D 1 right angle 90° 292.5 292.5 right angles 90 13 1 3 right angles 4 4 5. What type of angle is the sum of two angles of 135°? A. Straight angle B. Reflex angle C. Obtuse angle D. Acute angle round 630 360 round angles 7 4 round angles 4. How many right angles does 292.5° equal? A. 3 right angles 3 4 right angles 1 3 2 right angles 1 3 4 right angles 2 B. 4. 9 8 round angles C. D. D 1 right angle 90° 292.5 90 right angles 13 4 right angles 1 3 4 right angles 292.5 5. What type of angle is 5. B the sum of two angles of 135°? Two angles of135°=2135°=270° A. Straight angle 180° < 270° < 360° B. Reflex angle 270° is a reflex angle. C. Obtuse angle The sum of two angles of D. Acute angle 135° is a reflex angle. 6. A. B. C. D. B Two angles of 135° What is the sum of ABC = 2 135° and reflex angle ABC? = 270° 0 90 180° < 270° < 360° 180 270° is a reflex 360 angle. The sum of two angles of 135° is a reflex angle. 6. D 6. What is the sum of 1 round angle equals 360. ABC and reflex angle ABC form a ABC and reflex angle ABC? round angle. A. 0 Therefore, the sum of ABC B. 90 and reflex angle ABC equals C. 180 360. D. 360 D At 7 o’clock, what is the size 1 round angle equals of the reflex angle between 360. ABC and reflex angle the hour-hand and the ABC form a round angle. minute-hand? Therefore, the sum of 7. A. B. C. D. 70 150 210 290 7. C ABC and reflex angle ABC equals 360. 7. At 7 o’clock, what is the size of the reflex angle between the hour-hand and the minute-hand? A. 70 B. 150 C. 210 D. 290 12 9 3 6 Required angle 7 360 210 12 C 12 8. In the figure, which angle is a right angle? R 70 80 90 6 100 80 100 Required 70 7 360 12 210 20 10 10 17 0 0 180 0 20 180 17 0 1 60 angle T A 3 S Q P 9 B O 8. In the figure, which angle is a right angle? R 8. C According to the figure, only AOR, QOT and BOR are right angles. S Q 70 P 80 90 100 80 100 70 10 10 0 180 O 17 0 A 20 20 T 0 SOQ POS QOT TOP 180 17 0 1 60 A. B. C. D. B A. B. C. D. In the figure, COD 9. C 70 80 90 20 10 10 17 0 0 180 0 180 17 0 1 60 70 20 B D 100 80 100 A O A. B. C. D. 50 60 70 130 SOQ POS QOT TOP C According to the figure, only AOR, QOT and BOR are right angles. In the figure, COD 9. C 9. C COD BOD BOC 70 80 90 D 100 80 100 70 0 180 20 10 0 10 With 3 interior angles With 5 interior angles With 3 sides Sum of interior angles 180 17 0 A. B. C. D. B 20 10. Which of the following is not a characteristic of a triangle? 180 17 0 1 60 130 60 70 A O A. B. C. D. 50 60 70 130 C COD BOD BOC 130 60 70 10. B 10. Which of the following is A triangle has 3 interior not a characteristic of a triangle? angles only. A. With 3 interior B is not a characteristic of a angles triangle. B. With 5 interior angles C. With 3 sides 11. Which of the following must D. Sum of interior be true? angles 180 I. There is at most 1 right angle in a right-angled B triangle. A triangle has 3 II. Interior angles of a interior angles only. triangle can all be B is not a acute. III. A triangle can have characteristic of a triangle. more than 1 obtuse angle. 11. Which of the following must be true? A. I only I. There is at most 1 B. III only right angle in a right-angled C. I and II only triangle. D. II and III only II. Interior angles of a 11. C A right-angled triangle has only 1 right angle. There is at most 1 obtuse angle (or 1 right angle) in a triangle, where all other angles must be acute. I and II must be true. triangle can all be acute. III. A triangle can have more than 1 obtuse angle. A. I only B. III only C. I and II only D. II and III only C A right-angled triangle has only 1 right angle. 12. Which one of the following There is at most 1 cannot be the three interior obtuse angle (or 1 right angle) in angles of a triangle? a triangle, where all other angles must be acute. A. 30°, 50°, 100° I and II must be B. 35°, 45°, 65° true. C. 25°, 55°, 100° 12. Which one of the D. 38°, 60°, 82° following cannot be the three interior angles of a triangle? A. 30°, 50°, 100° 12. B B. 35°, 45°, 65° For B, 35 45 65 145 C. 25°, 55°, 100° The sum of all interior angles of a D. 38°, 60°, 82° triangle must be 180. 35, 45, 65 cannot be the B three interior angles of a For B, triangle. 35 45 65 145 The sum of all interior angles of a triangle must be 180. 13. In the figure, if BAC = 60°, 35, 45, 65 find the sum of the three cannot be the three interior angles interior angles. of a triangle. A B A. B. C. D. C 60° 120° 150° 180° 13. In the figure, if BAC = 60°, find the sum of the three interior angles. A B 13. D The sum of all interior angles of a triangle must be 180. A. B. C. D. C 60° 120° 150° 180° D The sum of all interior angles of a triangle must be 180. 14. In the figure, y 49°. Find x. 14. In the figure, y 49°. Find x. A A y 2y x 2y x B A. B. C. D. y C B 82° 43° 33° 28° A. B. C. D. C 82° 43° 33° 28° C y x 2 y 180 x 3 y 180 y 49 14. C y x 2 y 180 x 3 y 180 y 49 x 3(49) 180 x 3(49) 180 x 147 180 33 15. The figure shows ABC. Find x y. B y A x 180 147 33 15. The figure ABC. Find x y. B y x 77 A x 77 C A. B. C. D. shows 103° 167° 51.5° 283° C A. B. C. D. 15. A x y 77 180 x y 103 103° 167° 51.5° 283° A x y 77 180 x y 180 77 103 16. The figure shows ABC. 16. The figure shows Express y in terms of x. ABC. Express y in terms of x. A A 76 76 y x C A. B. C. D. y 104° x y 76° x y 104° x y 76° x B y x B C B. C. D. A. y 104° x y 76° x y 104° x y 76° x 16. C C 76 x y 180 y 104 x 76 x y 180 y 104 x 17. In the figure, find y. 17. In the figure, find y. A y y y y B A B 70 70 C C A. B. C. D. 70 65 55 50 B. C. D. A. 70 65 55 50 C y y 70 180 2 y 70 180 17. C y y 70 180 2 y 70 180 y 55 2 y 180 70 2 y 110 y 55 18. Which of the following 18. Which of the following is an is an obtuse-angled triangle? obtuse-angled triangle? A. 50 50 50 A. 50 B. B. 40 40 40 70 C. D. 40 70 60 C. D. 30 18. B For B, unknown interior angle 180 40 40 100 One of the interior angles of the triangle is obtuse. This is an obtuse-angled triangle. 60 30 B For B, unknown interior angle 180 40 40 100 One of the interior 19. Which of the following are angles of the triangle is obtuse. concave polygons? This is an obtuse-angled triangle. I. 19. Which of the following are concave polygons? II. A. B. C. D. III. I and II only I and III only II and III only I, II and III I. II. III. 19. B A concave polygon is a polygon with at least one interior angle greater than 180. I and III are concave polygons. A. B. C. D. I and II only I and III only II and III only I, II and III B A concave polygon 20. Which of the following is a polygon with at least one polygons must not be interior angle greater than 180. convex? I and III are concave polygons. I. 20. Which of the following polygons must not be convex? II. I. A. B. C. D. II. III. I only III only I and II only I and III only 20. C A convex polygon is a polygon whose interior angles are all less than 180. III is a convex polygon, I and II are not. III. A. B. C. D. C I only III only I and II only I and III only 1. A convex polygon Which of the following are is a polygon whose interior angles polygons? are all less than 180. III is a convex polygon, I and II are not. I. 21. Which of the following are polygons? II. III. I. II. IV. III. A. B. C. D. I and III only II and III only II and IV only I, II, III and IV IV. 1. C A polygon is a plane figure enclosed by three or more line segments. II and IV are polygons. 2. How many diagonals does a square have? A. B. C. D. 1 2 4 6 B square has Diagonal 2. A 2 A. B. C. D. I and III only II and III only II and IV only I, II, III and IV C A polygon is a plane figure enclosed by three or more line segments. II and IV are polygons. 22. How many diagonals does a square have? A. 1 diagonals. B. 2 C. 4 D. 6 B A diagonals. 3. B A regular polygon is a polygon which is both equilateral and equiangular. II is a regular polygon. square has 2 3. Which of the following must be regular polygon? Diagonal I. 23. Which of the following must be regular polygon? II. I. II. III. A. B. C. D. I only II only III only I and II only 4. If a cuboid is cut vertically from the top as shown, the cross-section obtained is III. A. B. C. D. I only II only III only I and II only B A regular polygon is a polygon which is both equilateral and equiangular. II is a regular polygon. 24. If a cuboid is cut vertically from the top as shown, the cross-section obtained is A. B. C. D. 5. B 4. A A. B. According to the figure, the cross-section obtained is a rectangle. 5. The following shows a cube. If the cube is cut along the dotted lines, the plane figure obtained is A. C. D. A According to the figure, the cross-section obtained is a rectangle. B. C. 25. The following shows a cube. If the cube is cut along the dotted lines, the plane figure obtained is D. 7. B All faces of a regular hexahedron are squares. All faces of a regular octahedron are equilateral triangles. All faces of a regular icosahedron are equilateral triangles. Only II is true. 8. A Euler’s formula is V E F 2 . A. B. C. D. B 6. Which of the following have uniform cross-section? 26. Which of the following have uniform cross-section? I. I. II. II. III. III. IV. IV. A. B. C. D. IV only I and III only II and IV only I, II and III 6. C 7. Which of the following must be true? I. All faces of a regular hexahedron are regular hexagons. II. All faces of a regular octahedron are equilateral triangles. III. All faces of a regular icosahedron are regular pentagons. A. B. C. D. I only II only III only I, II and III A. B. C. D. IV only I and III only II and IV only I, II and III C 27. Which of the following must be true? I. All faces of a regular hexahedron are regular hexagons. II. All faces of a regular octahedron are equilateral triangles. III. All faces of a regular icosahedron are regular pentagons. A. I only B. II only C. III only D. I, II and III B All faces of a regular hexahedron are squares. All faces of a regular octahedron are equilateral triangles. All faces of a regular icosahedron are equilateral triangles. 8. The number of vertices, edges and faces of a polyhedron are V, E and F respectively. Which of the following is Euler’s formula? A. B. C. D. 9. V EF 2 V FE2 E F V 2 V EF Only II is true. 28. The number of vertices, edges and faces of a polyhedron are V, E and F respectively. Which of the following is Euler’s formula? A. V E F 2 B. V F E 2 C. E F V 2 D. V E F A Euler’s formula is V E F 2. Which of the following are 29. Which of the following regular polyhedra? are regular polyhedra? I. I. II. II. III. III. A. B. C. D. I and II only I and III only II and III only I, II and III A. B. C. D. I and II only I and III only II and III only I, II and III B All faces of a regular 9. B polyhedron are the same regular All faces of a regular polyhedron polygon. are the same regular polygon. I and III are I and III are regular regular polyhedra. polyhedra. 30. Which of the following is not a polyhedron? A. 10. Which of the following is not a polyhedron? B. A. C. B. D. C. A All faces of polyhedron are polygons. A is not polyhedron. a a D. 31. How many vertices does a pentagonal prism have? A. 10 10. A B. 8 All faces of a polyhedron are C. 7 polygons. D. 6 A is not a polyhedron. A In a pentagonal 11. How many vertices does a prism, there are 5 vertices at the pentagonal prism have? top and 5 vertices at the base. It has altogether 10 A. 10 vertices. B. 8 C. 7 D. 6 32. In the solid shown, number of vertices number of edges number of faces equals 11. A In a pentagonal prism, there are 5 vertices at the top and 5 vertices at the base. It has altogether 10 vertices. A. B. C. 0. 1. 2. D. 3. 12. In the solid shown, number of vertices number of C edges number of faces According to the figure, equals the number of vertices is 10, the number of edges is 15 and the number of faces is 7. Number of vertices number of edges number of faces A. 0. 10 15 7 B. 1. 2 C. 2. D. 3. 33. In a square pyramid as 12. C shown, number of According to the figure, the vertices number of number of vertices is 10, the faces number of edges equals number of edges is 15 and the number of faces is 7. Number of vertices number of edges number of faces 10 15 7 2 A. B. C. D. 13. In a square pyramid as shown, number of vertices number of faces number of edges equals A. B. C. D. 1. 2. 3. 4. 1. 2. 3. 4. B According to the figure, a square pyramid has 5 vertices, 8 edges and 5 faces. Number of vertices number of faces number of edges 558 2 13. B 34. Which of the following According to the figure, a square pyramid has 5 vertices, 8 edges is an isometric grid? and 5 faces. Number of vertices number of faces number of edges 5 58 2 A. 14. D In an isometric grid, the grid lines form equilateral triangles. 14. Which of the following is an isometric grid? B. A. C. B. C. D. D In an isometric grid, the grid lines form equilateral triangles. D. 15. When the given solid is drawn on an isometric grid, A is treated as the lowest point of the solid. Which of the following drawings is correct? 4 2 35. When the given solid is drawn on an isometric grid, A is treated as the lowest point of the solid. Which of the following drawings is correct? (The numbers in the figure are lengths of sides.) 4 2 A 4 2 4 2 A. A. B. C. B. D. A 15. B 16. When the given solid is drawn on an isometric grid, A is treated as the lowest point of the solid. Which of the following drawings is correct? (The numbers in the figure are lengths of sides.) C. 2 2 D. 4 B 2 6 2 A. A 36. When the given solid is drawn on an isometric grid, A is treated as the lowest point of the solid. Which of the following drawings is correct? (The numbers in the figure are lengths of sides.) 2 2 4 B. 2 6 2 A. C. D. B. 16. B 17. C C. 18. C A 17. When the given solid is drawn on an oblique grid, the shaded surface is treated as the front surface of the solid. Which of the following drawings is correct? 2 D. 2 4 2 2 4 A. B. B 37. When the given solid is drawn on an oblique grid, the shaded surface is treated as the front surface of the solid. Which of the following drawings is correct? (The numbers in the figure are lengths of sides.) C. D. 18. When the given solid is drawn on an oblique grid, the shaded surface is treated as the front surface of the solid. Which of the following drawings is correct? 2 2 4 2 4 2 2 2 2 2 6 2 A. A. B. B. C. D. 2 C. D. 2 1 19. How many cuboids 2 are used to form the solid as shown? A. B. C. D. C 38. When the given solid is drawn on an oblique grid, the shaded surface is treated as the front surface of the solid. Which of the following drawings is correct? (The numbers in the figure are lengths of sides.) 3 4 5 6 2 2 2 2 2 6 19. A According to the figure, 3 cuboids are used to form the solid. 1 3 2 A. 2 B. 20. Which of the following are the shapes of set squares? 30 C. 60 I. 60 D. II. 60 60 C 45 A. B. C. D. III. I and II only I and III only II and III only I, II and III 45 39. How many 2 2 1 cuboids are used to form the solid as shown? A. B. 3 4 C. D. 5 6 20. B There are two types of set squares. The interior angles of A one of them are 45, 45 and 90, and those of the other one are According to the figure, 30, 60 and 90. 3 cuboids are used to form the I and III are the shapes of solid. set squares. 1 3 2 40. Which of the following are the shapes of set squares? 30 60 I. II. 60 60 45 A. B. C. D. 60 III. 45 I and II only I and III only II and III only I, II and III B There are two types of set squares. The interior angles of one of them are 45, 45 and 90, and those of the other one are 30, 60 and 90. I and III are the shapes of set squares.
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