Nets, Plans & Elevations 1kingslynnacademy.co.uk/wp-content/uploads/2015/10/... · PiXL PLC 2017...

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PLC Papers

Created For:

PiXL PLC 2017 Certification

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)

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

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

DE is parallel to FG.

(i) Find the size of the angle marked y°.

..........................°

(ii) Give a reason for your answer.

..........................................................................................................................

. (Total 2 marks)

57 º º

Diagram NOT accurately drawn

Question 2

Question 3

Question 4

Total /10

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.

………………………cm2

……………………… m2

……………………… cm2

Total /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.

(b) A clock has a diameter of 20cm.

Calculate the area of the clock face. Give your answer to 1 decimal place.

(Total 4 marks)

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 �.

(Total 3 marks)

Total /10

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:

……………………………m2

……………………………

(Total 7 marks)

Question 2.

Find the area of the shaded region.

Give your answer to 2 decimal places.

……………………………m2

Total /10

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

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.

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)

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

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)

Question 5

Complete the sentence below.

The circle has a …………………………………….. of 6cm.

Total /10

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.

..............................................

(b) Calculate the circumference of a circle with a diameter of 5 cm.

..............................................

(Total 5 marks)

Question 2.

A circle has circumference 20.6cm.

Calculate the radius of the circle, giving your answer to 1 decimal place.

..............................................

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

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.

..................................... (1)

(c) Write down the letters of the pair of congruent shapes.

..................................... and ..................................... (1)

(Total 3 marks)

Question 2

On the grid below, draw a shape that is congruent to shape A.

(Total 2 marks) Question 3

Circle the figure that is congruent to C

(Total1 mark)

Question 4 Write down what the term congruency means? …………………………………………………………………………(Total1 mark)

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

Congruent triangles 2 Grade 4 Objective: Use basic congruency criteria for triangles

Question 1 These triangles are congruent. Use the letters a, b and c to show which angles are equal.

(2) Question 2 Here are four triangles

a) Draw circles round the two triangles that are congruent. (1)

b) State the congruency rule you used. …………………………….. (1)

(Total 2 marks)

Not drawn accurately

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)

(2) b)

(2) c)

(Total 6 marks)

Total Marks / 10

Are the triangles congruent? …………………… Reason …………………………………………. ………………………………………………….. …………………………………………………..

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?

.........................................(2)

(Total 4 marks)

Question 2.

Enlarge this shape by a scale factor of from the point (1 , 2 )

10 5 – 5

(Total 3 marks)

Question 3.

Describe fully the enlargement that transforms shape A onto shape B

(Total 3 marks)

– 5 5 10 15

Total /10

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:

……………………………

(Total 2 marks)

Question 2.

(a) Find the side of a square which has a perimeter of 36cm.

……………………………

(b) Find the missing side on a rectangle when other sides are 14cm, 14cm and 3cm.

……………………………

(c) Two of the sides of a rectangle are 6cm and 11cm. What is the perimeter?

……………………………

(Total 4 marks)

Question 3.

Find the perimeter of a circle with a radius 5cm.

……………………………

Question 4.

A regular octagon has a perimeter of 120 cm.

How long is each side?

……………………………

Total /10

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.

(Total 3 marks)

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.

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

(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)

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

(2) (b) On the grid below, draw the plan of the solid object

(Total 4 marks)

Total / 10

Polygons 2 Grade 4

Objective: Derive and apply the properties of polygons Question 1. Look at the shapes below

a) Which shapes are regular?

………………………………………………………………………………………….. (3)

b) Which shapes are hexagons?

………………………………………………………………………………………….. (2)

c) Which shape is not a polygon?

………………………………………………………………………………………….. (1)

(Total 6 marks)

Question 2.

Draw a nonagon.

(Total 2 marks)

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

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

(Total 3 marks)

Question 2.

Give the vector that describes each of these journeys:

(Total 3 marks)

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

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:

………………………m3

………………………cm3

Total /10

PLC Papers

Created For:

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)

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

Alternate & corresponding angles 2 Grade 4 Solutions

Objective: Apply the properties of angles and a point, angles on a straight line, vertically opposite angles, alternate angles and corresponding angles

Question 1

DE is parallel to FG.

(i) Find the size of the angle marked y°.

..........................°

(ii) Give a reason for your answer.

..........................................................................................................................

. (Total 2 marks)

57 º º

Diagram NOT accurately drawn

69 ° A1

Alternate angles are equal. =A1

Question 2

• Alternate angles are equal hence q = 59°

• Angles on a straight line adds up to 180 therefore

r = 180- 134= 46 °

No reasons required

46 ° A1

59 ° A1

Question 3

120 ° A1

Angles on straight line adds up to 180° A1

180 – 60 = 120°

60 ° A1

Alternate angles are equal. A1

Question 4

Total /10

Corresponding angles are equal A1

Accept:

co-interior angles add up to 180 ° therefore 180 – 70 = 110 A1

110 ° A1

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.

Multiply perpendicular lengths

7x10 = 70cm2 (M1 A1)

………………………cm2

Multiply perpendicular lengths then half.

12x5/2=30 m2 (M1 A1)

……………………… m2

Parallogram: 15x10 = 150 (M1 for both)

150x2 = 300cm2 (A1)

……………………… cm2

Add parallel sides, multiply by distance between and half.

0.5x4x(5+9) = 28cm2 (M1A1)

……………………… cm2

(e) Add parallel sides, multiply by distance between and half.

0.5x18x(40+16)=504cm2 (M1A1)

……………………… cm2

Total /10

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)

705.86 cm2 (A1)

(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)

314.2 cm2 (A1)

(Total 4 marks)

Question 2

Find the area of the semi-circle shown.

The diagram is not to scale and has a diameter of 70cm.

70/2=35

��×�� (M1, M1)

1924.2 cm2 (A1)

(Total 3 marks)

Question 3.

Find the area of the shaded area shown.

Leave your answer in terms of �.

(122 × �) − (52 × �) (M1)

144� − 25� (A1)

119� cm2 (A1)

(Total 3 marks)

Total /10

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:

18x12=216(M1)

4x4=16 (M1)

216-16=200m2 (A1)

……………………………m2

14x12x0.5=84 (M1)

72 × � ÷ 2 = 76.97 (M1 M1)

84+76.97=160.97m2 (A1)

……………………………

(Total 7 marks)

Question 2.

Find the area of the shaded region.

18x12=216 (M1)

42 × � = 50.27 (�1)

216-50.27=165.73m2 (A1)

……………………………m2

Total /10

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 0450

(b) South West 2250

(c) North 000 or 3600

(d) South East 1350 (Total 4 marks)

Question 2.

What angles are between the following compass points?

(a) North West to South 2250

(b) South to North West 1350

(c) South to South West 450 (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

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.

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)

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

Circle drawn compass opened to 4cm from point C (1)

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 diameter

Pint P lies on the circumference

CD is a tangent

AE is a chord

(Total 4 marks)

Question 5

Complete the sentence below.

The circle has a radius of 6cm.

radius

Total /10

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)

..............................................

(b) Calculate the circumference of a circle with a diameter of 3.5 cm.

3.5 × � = 11.00�� (M1 A1, A1 - rounding)

..............................................

(Total 5 marks)

Question 2.

A circle has circumference 31.4cm.

Calculate the radius of the circle, giving your answer to 1 decimal place.

31.4 ÷ � ÷ 2 = 5.0�� (M1 A1)

..............................................

Question 3.

The circumference of a circle is 60cm.

Find the area of the circle, giving your answer to 2 decimal places.

60 ÷ 2� = 9.54929… .. (M1)

9.5492× � = 286.48��2 (M1 A1)

..............................................

(Total 3 marks)

Total /10

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.

..................................... (1)

(b) Write down the letter of the shape that is an octagon.

..................................... (1)

(c) Write down the letters of the pair of congruent shapes.

..................................... and ..................................... (1)

(Total 3 marks)

D G A1 if both correct

Hexagon A1

Question 2

On the grid below, draw a shape that is congruent to shape A.

(Total 2 marks) Question 3

Circle the figure that is congruent to C

( 1mark)

Question 4 Write down what the term congruency means? …………………………………………………………………………….. ( 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

Congruency means the shape is in the same size but either rotated or reflected. A1 for similar explanation

M1 A1 if a congruent shape is seen Accept any rotated or reflected shape

A1 for B circled correctly

Question 6

Circle the transformations from below which gives congruent shapes?

( 2 marks)

Rotation Enlargement

Reflection

Total Marks / 10

A1 A1 for all 2 circled correctly ; A1 for 1 circled correctly

Congruent triangles 2 Grade 4 Solutions Objective: Use basic congruency criteria for triangles

Question 1 These triangles are congruent. Use the letters a, b and c to show which angles are equal.

1M for each correct triangle (2)

Question 2 Here are four triangles

a) Draw circles round the two triangles that are congruent. (1)

b) State the congruency rule you used. RHS (1)

(Total 2 marks)

Not drawn accurately

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)

(2) b)

(2) c)

(Total 6 marks)

Total Marks / 10

Are the triangles congruent? No 1M Reason The angles that are equal are not between the two sides that are equal so you can’t use SAS 1M

Are the triangles congruent? Yes 1M Reason SSS 1M

Are the triangles congruent? No 1M Reason You don’t know anything about the length of the sides 1M

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 5.2 ÷ 6.5 = 0.8 (1)

(b) Find the height of the enlarged photograph

4.5 × 0.8 = 3.6cm (1)

(c) A man on the enlarged photograph is 3.2cm tall, what was his height on the original photograph?

3.2 ÷ 0.8 = 4cm (2)

(Total 4 marks)

Question 2.

Enlarge this shape by a scale factor of from the point (1 , 2 )

(Total 3 marks)

1 mark at least 2 construction lines

1mark correct centre

1 mark correct size

Question 3.

Describe fully the enlargement that transforms shape A onto shape B

(Total 3 marks)

Total /10

1 mark at least 2 construction lines

1mark correct centre (– 3 , 4) 1 mark correct SF ½ or 0.5

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:

5cm 7x5=35cm (A1) ……………………………

6cm 6x6=36cm (A1)

……………………………

(Total 2 marks)

Question 2.

(a) Find the side of a square which has a perimeter of 36cm.

36/4=9cm (A1) ……………………………

(b) Find the missing side on a rectangle when other sides are 14cm, 14cm and 3cm.

3cm (B1)

……………………………

(c) Two of the sides of a rectangle are 6cm and 11cm. What is the perimeter?

6+6+11+11=34cm (M1 A1) ……………………………

(Total 4 marks)

Question 3.

Find the perimeter of a circle with a radius 5cm.

Give your answer to 1 decimal place. � × � × � = ��.�� (M1 A1)

……………………………

Question 4.

A regular octagon has a perimeter of 120 cm.

How long is each side?

120/8=15cm (M1 A1) ……………………………

Total /10

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.

B1 B1 B1

(Total 3 marks)

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.

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)

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)

Correctly drawn cuboid as per Measurements B1

2cm 5cm

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

(2) 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)

(Total 4 marks)

Total / 10

Polygons 2 Grade 4 Solutions

Objective: Derive and apply the properties of polygons Question 1. Look at the shapes below

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)

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 360 – 90 = 270 1M 270 ÷ 2 = 135 The interior angle is 1350 1M

(Total 2 marks)

Total /10

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

=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:

� 3−3� �0

4� �−5

(Total 3 marks)

Question 3.

Write the vector sum and resultant vector for the following diagram:

�−6−2�

+ �35� =

�−3

3� .

M1 M1 A1

(Total 3 marks)

Question 4.

a= ,find the value of 4a.

4� 1−5� = � 4−20

� A1

. (Total 1 mark)

Total /10

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:

5.2x9.3x4.1=198.3 cm3(M1 A1)

………………………m3

½ x base x width x depth

½ x 3 x 5 x 11=82.5cm3 (M1 A1)

………………………cm3

��2ℎ = �� (M1)

� × 62 × 18 = 2036��3 (M1 A1)

………………………cm3

Base x perpendicular height x depth= volume (M1)

12 x 8 x 14 = 1344 cm3(M1 A1)

………………………cm3

Total /10

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