PLC Papers. Created For:

Transcription

1 PLC Papers Created For:

2 3D shapes 2 Grade 4 Objective: Identify the properties of 3-D shapes Question 1. The diagram shows four 3-D solid shapes. (a) What is the name of shape B.. (1) (b) Write down the number of vertices of shape C.. (1) (c) Write down the number of edges of shape A.. (1) (d) Write down the number of faces of shape D.. (1) (e) Write down the name of the solid shape below.. (1) (Total 5 marks)

3 Question 2. Write in the correct word or number to complete these sentences a) A triangular based prism has 3 faces that are...and. faces that are triangles (2) b) A. pyramid has 7 faces, 12 edges and 7 vertices 6 faces are and 1 face is a.. (3) (Total 5 marks) Total /10

4 Alternate & corresponding angles 2 Grade 4 Objective: Apply the properties of angles and a point, angles on a straight line, vertically opposite angles, alternate angles and corresponding angles Question 1 D 57 º y º E F 69 º G DE is parallel to FG. Diagram NOT accurately drawn (i) Find the size of the angle marked y. (ii) Give a reason for your answer (Total 2 marks)

5 Question 2

6 Question 3

7 Question 4 Total /10

8 Area of Triangles, Trapezia and Parallelograms 2 Grade 4 Objective: Know and apply formulae to calculate areas of triangles, trapezia and parallelograms. Question 1. Find the areas of the following 2D shapes. (a) cm 2 (2) (b) m 2 (2) (c) cm 2 (2)

9 (d) cm 2 (2) (e) cm 2 (2) Total /10

10 Area of a Circle 2 Grade 4 Objective: Calculate the area of a circle. Question 1. (a) A circular dinner plate has a radius of 15cm. Calculate the area of the dinner plate, giving your answer to 2 decimal places. (2) (b) A clock has a diameter of 20cm. Calculate the area of the clock face. Give your answer to 1 decimal place. (2) (Total 4 marks)

11 Question 2 Find the area of the semi-circle shown. The diagram is not to scale and has a diameter of 70cm. Give your answer to 1 decimal place. (Total 3 marks) Question 3. Find the area of the shaded area shown. Leave your answer in terms of. 5cm 12cm (Total 3 marks) Total /10

12 Area of Composite Shapes 2 Grade 4 Objective: Calculate the area of composite shapes including circles. Question 1. Find the area of the following composite shapes: (a) m 2 (3) (b) (4) (Total 7 marks)

13 Question 2. Find the area of the shaded region. Give your answer to 2 decimal places. m 2 (3) Total /10

14 Bearings 2 Grade 4 Objective: Measure and use bearings (including the 8 compass point bearings). Question 1. On what bearing are the following directions? (a) North East (b) South West (c) North (d) South East (Total 4 marks) Question 2. What angles are between the following compass points? (a) North West to South (b) South to North West (c) South to South West (Total 3 marks) Question 3. The diagram shows the position of two boats, B and C. Boat T is on a bearing of 060 from boat B. Boat T is on a bearing of 285 from boat C. In the space above, draw an accurate diagram to show the position of boat T. Mark the position of boat T with a cross ( ). Label it T. (Total 3 marks) Total /10

15 Circle terminology 2 Grade 3 Objective: Describe the parts of a circle, including tangent, arc, sector, segment, centre, radius, chord, diameter, circumference Question 1. Measure the radius of this circle. cm. (1) Question 2. Here is a circle with the centre marked O. Write C on the circumference of the circle. (1) Write D on the diameter of the circle. (1) Draw a radius on the circle. (1) (Total 3 marks)

16 Question 3. In the space below draw accurately, a circle of diameter 8 cm. Use the point C as the centre of your circle. C (1)

17 Question 4 O is the centre of the circle below. Here are five words. Circumference chord tangent diameter radius Choose a word to complete each of these sentences BE is a Pint P lies on the CD is a AE is a (Total 4 marks)

18 Question 5 Complete the sentence below. The circle has a.. of 6cm. (1) Total /10

19 Circumference of a Circle 2 Grade 4 Objective: Calculate the circumference of a circle Question 1. (a) Calculate the circumference of a circle with radius 8cm. Give your answer to 1 decimal place.... (2) (b) Calculate the circumference of a circle with a diameter of 5 cm. Give your answer to 2 decimal places.... (3) (Total 5 marks) Question 2. A circle has circumference 20.6cm. Calculate the radius of the circle, giving your answer to 1 decimal place.... (2)

20 Question 3. The circumference of a circle is 60cm. Find the area of the circle, giving your answer to 2 decimal places.... (Total 3 marks) Total /10

21 Congruency 2 Grade 3 Objective: Consider transformations when describing congruent and similar shapes, including on a coordinate axis Question 1 Here are 8 polygons. (a) Write down the mathematical name for shape A.... (1) (b) Write down the letter of the shape that is an octagon. (c) Write down the letters of the pair of congruent shapes.... (1)... and... (1) (Total 3 marks)

22 Question 2 On the grid below, draw a shape that is congruent to shape A. Question 3 (Total 2 marks) Circle the figure that is congruent to C (Total1 mark) Question 4 Write down what the term congruency means? (Total1 mark)

23 Question 5 Circle from the list of transformations from below which DO NOT allow congruent shapes? Reflection Translation Enlargement Rotation (Total 1 mark) Question 6 Circle the transformations from below which gives congruent shapes? Rotation Enlargement Reflection (Total 2 marks) Total Marks / 10

24 Congruent triangles 2 Grade 4 Objective: Question 1 Use basic congruency criteria for triangles These triangles are congruent. Use the letters a, b and c to show which angles are equal. Not drawn accurately (2) Question 2 Here are four triangles Not drawn accurately a) Draw circles round the two triangles that are congruent. (1) b) State the congruency rule you used... (1) (Total 2 marks)

25 Question 3 Are these pairs of triangles congruent? If they are state the congruency rule you used. If they are not explain why they are not congruent. a) Are the triangles congruent? Reason..... (2) b) Are the triangles congruent? Reason... c).. (2) Are the triangles congruent? Reason..... (2) (Total 6 marks) Total Marks / 10

26 Enlargements Fractional scale factors 2 Grade 4 Objective: Identify and construct enlargements using fractional scale factors Question 1. A photograph is 6.5cm wide and 4.5cm high. An enlargement of the photograph is 5.2cm wide. (a) Find the scale factor of enlargement...(1) (b) Find the height of the enlarged photograph...(1) (c) A man on the enlarged photograph is 3.2cm tall, what was his height on the original photograph? Question 2. 1 Enlarge this shape by a scale factor of from the point (1, 2 ) 2...(2) (Total 4 marks) y x

27 (Total 3 marks) Question 3. Describe fully the enlargement that transforms shape A onto shape B y 10 5 B A x 5 (Total 3 marks)

28 Total /10

29 Perimeter of 2D shapes 2 Grade 4 Objective: Calculate the perimeter of 2D shapes including circles. Question 1. Find the perimeter of the following regular polygons, given the dimensions: (a) 5cm (1) (b) 6cm (1) (Total 2 marks) Question 2. (a) Find the side of a square which has a perimeter of 36cm. (1) (b) Find the missing side on a rectangle when other sides are 14cm, 14cm and 3cm. (1)

30 (c) Two of the sides of a rectangle are 6cm and 11cm. What is the perimeter? (2) (Total 4 marks) Question 3. Find the perimeter of a circle with a radius 5cm. Give your answer to 1 decimal place. (2) Question 4. A regular octagon has a perimeter of 120 cm. How long is each side? (2) Total /10

31 Plans and Elevations 2 Grade 4 Objective: Construct and use plans and elevations of 3D shapes Question 1 The diagram represents a solid made from 5 identical cubes.. On the grid below, draw the view of the solid from direction A On the grid below, draw the view of the solid from direction B. On the grid below, draw the view of the solid from direction C. (Total 3 marks)

32

33 Question 2 Here are the front elevation, side elevation and the plan of a 3-D shape In the space below, draw a sketch of the 3D shape

34 (Total 2 marks) Question 3 Ben is going to make a 3-D cuboid The 3-D shape is to be 2 cm high, 5 cm wide and 6 cm long. In the space below, draw a sketch of the 3-D shape. (Total 1 mark)

35 Question 4 The diagram shows a solid object made of 6 identical cubes (a) On the grid below, draw the side elevation of the solid object from the direction of the arrow (b) On the grid below, draw the plan of the solid object (2) (2) (Total 4 marks) Total / 10

36

37 Polygons 2 Grade 4 Objective: Derive and apply the properties of polygons Question 1. Look at the shapes below A B D F G J C E H a) Which shapes are regular?.. (3) b) Which shapes are hexagons?.. (2) c) Which shape is not a polygon?.. (1) Question 2. Draw a nonagon. (Total 6 marks) (Total 2 marks)

38 Question 3. This diagram shows a tessellation of regular hexagons. Explain how to use the diagram to calculate the interior angle of a regular octagon (Total 2 marks) Total /10

39 Vectors 2 Grade 4 Objective: Describe vectors as 2-D translations Add and subtract vectors and multiply by a scalar (using diagrammatic and column representations). Question 1. Describe each of the following vectors as 2-D translations as follows: Example: =2 right and 3 up (a) (b) (c) Question 2. Give the vector that describes each of these journeys: (Total 3 marks) (Total 3 marks)

40 Question 3. Write the vector sum and resultant vector for the following diagram: (Total 3 marks) Question 4. a=,find the value of 4a.. (Total 1 mark) Total /10

41 Volume of Prisms 2 Grade 4 Objective: Know and apply formulae to calculate volumes of cuboids and other right prisms (including cylinders). Question 1. Find the volumes of the following prisms: (a) (b) m 3 (2) (c) cm 3 (2) cm 3 (3)

42 (d) cm 3 (3) Total /10

43 PLC Papers Created For:

44 3D shapes 2 Grade 4 Solutions Objective: Identify the properties of 3-D shapes Question 1. The diagram shows four 3-D solid shapes. (a) What is the name of shape B Cylinder 1M (1) (b) Write down the number of vertices of shape C 5 vertices 1M (1) (c) Write down the number of edges of shape A 12 edges 1M (1) (d) Write down the number of faces of shape D 5 faces 1M (1) (e) Write down the name of the solid shape below Tetrahedron 1M (or triangular based pyramid) (1) (Total 5 marks)

45 Question 2. Write in the correct word or number to complete these sentences a) A triangular based prism has 3 faces that are rectangles and 2 faces that are triangles 1M for each word/number (2) b) A hexagonal based pyramid has 7 faces, 12 edges and 7 vertices 6 faces are triangles and 1 face is a hexagon (3) 1M for each word/number (Total 5 marks) Total /10

46 Alternate & corresponding angles 2 Grade 4 Solutions Objective: Question 1 Apply the properties of angles and a point, angles on a straight line, vertically opposite angles, alternate angles and corresponding angles D 57 º y º E F 69 º G DE is parallel to FG. Diagram NOT accurately drawn (i) (ii) Find the size of the angle marked y. Give a reason for your answer. 69 A1... Alternate angles are equal. =A1.... (Total 2 marks)

47 Question 2 46 Alternate angles are equal hence q = 59 Angles on a straight line adds up to 180 therefore r = = 46 No reasons required 59 A1 46 A1

48 Question A1 Angles on straight line adds up to = 120 A1 60 A1 Alternate angles are equal. A1

49 Question A1 Corresponding angles are equal A1 OR Accept: co-interior angles add up to 180 therefore = 110 A1 Total /10

50 Area of Triangles, Trapezia and Parallelograms 2 Grade 4 Solutions Objective: Know and apply formulae to calculate areas of triangles, trapezia and parallelograms. Question 1. Find the areas of the following 2D shapes. (a) Multiply perpendicular lengths 7x10 = 70cm 2 (M1 A1) cm 2 (2) (b) Multiply perpendicular lengths then half. 12x5/2=30 m 2 (M1 A1) m 2 (c) (2) Parallogram: 15x10 = 150 (M1 for both) 150x2 = 300cm 2 (A1) cm 2 (2)

51 (d) Add parallel sides, multiply by distance between and half. 0.5x4x(5+9) = 28cm 2 (M1A1) cm 2 (2) (e) Add parallel sides, multiply by distance between and half. 0.5x18x(40+16)=504cm 2 (M1A1) cm 2 (2) Total /10

52 Area of a Circle 2 Grade 4 Solutions Objective: Calculate the area of a circle. Question 1. (a) A circular dinner plate has a radius of 15cm. Calculate the area of the dinner plate, giving your answer to 2 decimal places. (M1) cm 2 (A1) (2) (b) A clock has a diameter of 20cm. Calculate the area of the clock face. Give your answer to 1 decimal place. 20/2=10 (M1) cm 2 (A1) (2) (Total 4 marks)

53 Question 2 Find the area of the semi-circle shown. The diagram is not to scale and has a diameter of 70cm. Give your answer to 1 decimal place. 70/2=35 (M1, M1) cm 2 (A1) (Total 3 marks) Question 3. Find the area of the shaded area shown. Leave your answer in terms of. 5cm 12cm (12 2 ) (5 2 ) (M1) cm 2 (A1) (A1) (Total 3 marks) Total /10

54 Area of Composite Shapes 2 Grade 4 Solutions Objective: Calculate the area of composite shapes including circles. Question 1. Find the area of the following composite shapes: (a) 18x12=216(M1) 4x4=16 (M1) =200m 2 (A1) m 2 (3) (b) 14x12x0.5=84 (M1) = (M1 M1) =160.97m 2 (A1) (4) (Total 7 marks)

55 Question 2. Find the area of the shaded region. Give your answer to 2 decimal places. 18x12=216 (M1) 4 2 = ( 1) =165.73m 2 (A1) m 2 (3) Total /10

56 Bearings 2 SOLUTIONS Grade 4 Objective: Measure and use bearings (including the 8 compass point bearings). Question 1. On what bearing are the following directions? (a) North East (b) South West (c) North 000 or (d) South East (Total 4 marks) Question 2. What angles are between the following compass points? (a) North West to South (b) South to North West (c) South to South West 45 0 (Total 3 marks) Question 3. The diagram shows the position of two boats, B and C. Boat T is on a bearing of 060 from boat B. Boat T is on a bearing of 285 from boat C. In the space above, draw an accurate diagram to show the position of boat T. Mark the position of boat T with a cross ( ). Label it T. T (Total 3 marks) Total /10

57 Circle terminology 2 Grade 3 Solutions Objective: Describe the parts of a circle, including tangent, arc, sector, segment, centre, radius, chord, diameter, circumference Question 1. Measure the radius of this circle. 4 cm. (1) Question 2. Here is a circle with the centre marked O. D C Write C on the circumference of the circle. (1) Write D on the diameter of the circle. (1) Draw a radius on the circle. (1) (Total 3 marks)

58 Question 3. In the space below draw accurately, a circle of diameter 8 cm. Use the point C as the centre of your circle. C Circle drawn compass opened to 4cm from point C (1)

59 Question 4 O is the centre of the circle below. Here are five words. Circumference chord tangent diameter radius Choose a word to complete each of these sentences BE is a Pint P lies on the CD is a AE is a diameter circumference tangent chord (Total 4 marks)

60 Question 5 Complete the sentence below. The circle has a radius of 6cm. radius (1) Total /10

61 Circumference of a Circle 2 Solutions Grade 4 Objective: Calculate the circumference of a circle Question 1. (a) Calculate the circumference of a circle with radius 5cm. Give your answer to 1 decimal place. 2 5 =31.4 (M1 A1)... (2) (b) Calculate the circumference of a circle with a diameter of 3.5 cm. Give your answer to 2 decimal places. 3.5 =11.00 (M1 A1, A1 - rounding)... (3) (Total 5 marks) Question 2. A circle has circumference 31.4cm. Calculate the radius of the circle, giving your answer to 1 decimal place =5.0 (M1 A1)... (2)

62 Question 3. The circumference of a circle is 60cm. Find the area of the circle, giving your answer to 2 decimal places = (M1) = (M1 A1)... (Total 3 marks) Total /10

63 Congruency 2 Grade D SOLUTIONS Objective: Consider transformations when describing congruent and similar shapes, including on a coordinate axis Question 1 Here are 8 polygons. (a) Write down the mathematical name for shape A. Hexagon A1... (1) (b) Write down the letter of the shape that is an octagon. (c) C A1... Write down the letters of the pair of congruent shapes. (1)... D and... G A1 if both correct (1) (Total 3 marks)

64 Question 2 On the grid below, draw a shape that is congruent to shape A. Question 3 M1 A1 if a congruent shape is seen Accept any rotated or reflected shape (Total 2 marks) Circle the figure that is congruent to C A1 for B circled correctly Question 4 Write down what the term congruency means? Congruency means the shape is in the same size but either rotated or.. reflected. A1 for similar explanation ( 1mark) ( 1mark) Question 5 Circle from the list of transformations from below which DO NOT allow congruent shapes? Reflection Translation Enlargement Rotation ( 1 mark) A1 for 1 circled correctly

65 Question 6 Circle the transformations from below which gives congruent shapes? ( 2 marks) Rotation Enlargement Reflection A1 A1 for all 2 circled correctly ; A1 for 1 circled correctly Total Marks / 10

66 Congruent triangles 2 Grade 4 Solutions Objective: Question 1 Use basic congruency criteria for triangles These triangles are congruent. Use the letters a, b and c to show which angles are equal. a c b a c b Not drawn accurately 1M for each correct triangle (2) Question 2 Here are four triangles Not drawn accurately a) Draw circles round the two triangles that are congruent. (1) b) State the congruency rule you used. RHS (1) (Total 2 marks)

67 Question 3 Are these pairs of triangles congruent? If they are state the congruency rule you used. If they are not explain why they are not congruent. a) Are the triangles congruent? No Reason 1M The angles that are equal are not between the two sides that are equal so you can t use SAS 1M (2) b) Are the triangles congruent? Yes 1M Reason SSS 1M c) Are the triangles congruent? No (2) 1M Reason You don t know anything about the length of the sides 1M (2) (Total 6 marks) Total Marks / 10

68 Enlargements Fractional scale factors 2 Grade 4 Solutions Objective: Identify and construct enlargements using fractional scale factors Question 1. A photograph is 6.5cm wide and 4.5cm high. An enlargement of the photograph is 5.2cm wide. (a) Find the scale factor of enlargement = 0.8 (1) (b) Find the height of the enlarged photograph = 3.6cm (1) (c) A man on the enlarged photograph is 3.2cm tall, what was his height on the original photograph? = 4cm (2) (Total 4 marks) Question 2. 1 Enlarge this shape by a scale factor of from the point (1, 2 ) 2 1 mark at least 2 construction lines 1mark correct centre 1 mark correct size (Total 3 marks)

69 Question 3. Describe fully the enlargement that transforms shape A onto shape B B A 1 mark at least 2 construction lines 1mark correct centre ( 3, 4) 1 mark correct SF ½ or 0.5 (Total 3 marks) Total /10

70 Perimeter of 2D shapes 2 Grade 4 Solutions Objective: Calculate the perimeter of 2D shapes including circles. Question 1. Find the perimeter of the following regular polygons, given the dimensions: (a) 5cm 7x5=35cm (A1) (1) (b) 6cm 6x6=36cm (A1) (1) (Total 2 marks) Question 2. (a) Find the side of a square which has a perimeter of 36cm. 36/4=9cm (A1) (1) (b) Find the missing side on a rectangle when other sides are 14cm, 14cm and 3cm. 3cm (B1) (1)

71 (c) Two of the sides of a rectangle are 6cm and 11cm. What is the perimeter? =34cm (M1 A1) (2) (Total 4 marks) Question 3. Find the perimeter of a circle with a radius 5cm. Give your answer to 1 decimal place. =. (M1 A1) (2) Question 4. A regular octagon has a perimeter of 120 cm. How long is each side? 120/8=15cm (M1 A1) (2) Total /10

72 Plans and Elevations 2 Grade 4 SOLUTIONS Objective: Construct and use plans and elevations of 3D shapes Question 1 The diagram represents a solid made from 5 identical cubes.. On the grid below, draw the view of the solid from direction A On the grid below, draw the view of the solid from direction B. On the grid below, draw the view of the solid from direction C. B1 B1 B1 (Total 3 marks)

73

74 Question 2 Here are the front elevation, side elevation and the plan of a 3-D shape In the space below, draw a sketch of the 3D shape B2 for a complete 3-D sketch (B1 for a partial 3-D sketch) (Total 2 marks)

75 Question 3 Ben is going to make a 3-D cuboid The 3-D shape is to be 2 cm high, 5 cm wide and 6 cm long. In the space below, draw a sketch of the 3-D shape. 6cm 5cm 2cm Correctly drawn cuboid as per Measurements B1 (Total 1 mark)

76 Question 4 The diagram shows a solid object made of 6 identical cubes (a) On the grid below, draw the side elevation of the solid object from the direction of the arrow B2 for 4 vertical squares only (B1 for 4 vertical squares with extra squares added) (b) On the grid below, draw the plan of the solid object (2) B2 for any 2x1 rectangle (B1 for a 2x1 rectangle with one added square) (2) (Total 4 marks)

77 Total / 10

78 Polygons 2 Grade 4 Solutions Objective: Derive and apply the properties of polygons Question 1. Look at the shapes below A B D F G J C E H a) Which shapes are regular? A, E and J 1 mark each, no extras (3) b) Which shapes are hexagons? B and F 1 mark each, no extras (2) c) Which shape is not a polygon? D 1 mark (1) (Total 6 marks) Question 2. Draw a nonagon. 1M shape with straight sides 1M shape with 9 sides (Total 2 marks)

79 Question 3. This diagram shows a tessellation of regular hexagons. Explain how to use the diagram to calculate the interior angle of a regular octagon = 270 1M = 135 The interior angle is M (Total 2 marks) Total /10

80 Vectors 2 Grade 4 SOLUTIONS Objective: Describe vectors as 2-D translations Add and subtract vectors and multiply by a scalar (using diagrammatic and column representations). Question 1. Describe each of the following vectors as 2-D translations as follows: Example: =2 right and 3 up (a) =2 left and 4 up (b) =2 left and 4 down (c) =4 left and 6 up (Total 3 marks) Question 2. Give the vector that describes each of these journeys: (Total 3 marks)

81 Question 3. Write the vector sum and resultant vector for the following diagram: = 3 3. M1 M1 A1 (Total 3 marks) Question 4. a=,find the value of 4a = 5 20 A1. (Total 1 mark) Total /10

82 Volume of Prisms 2 Grade 4 Solutions Objective: Know and apply formulae to calculate volumes of cuboids and other right prisms (including cylinders). Question 1. Find the volumes of the following prisms: (a) 5.2x9.3x4.1=198.3 cm 3 (M1 A1) m 3 (2) (b) ½ x base x width x depth ½ x 3 x 5 x 11=82.5cm 3 (M1 A1) cm 3 (2) (c) 2 h= (M1) = (M1 A1) cm 3 (3)

83 (d) Base x perpendicular height x depth= volume (M1) 12 x 8 x 14 = 1344 cm 3 (M1 A1) cm 3 (3) Total /10