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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)
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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
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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)
D
F
E
G
57 º º
69 º
Diagram NOT accurately drawn
y
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Question 2
PiXL PLC 2017 Certification
Question 3
PiXL PLC 2017 Certification
Question 4
Total /10
PiXL PLC 2017 Certification
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)
………………………cm2
(2)
(b)
……………………… m2
(2)
(c)
……………………… cm2
(2)
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(d)
……………………… cm2
(2)
(e)
……………………… cm2
(2)
Total /10
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
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 �.
12cm
(Total 3 marks)
Total /10
5cm
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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)
……………………………m2
(3)
(b)
……………………………
(4)
(Total 7 marks)
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Question 2.
Find the area of the shaded region.
Give your answer to 2 decimal places.
……………………………m2
(3)
Total /10
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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)
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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)
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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)
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Question 5
Complete the sentence below.
The circle has a …………………………………….. of 6cm.
(1)
Total /10
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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)
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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
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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)
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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)
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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
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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
Not drawn accurately
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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)
(2)
(Total 6 marks)
Total Marks / 10
Are the triangles congruent? …………………… Reason …………………………………………. ………………………………………………….. …………………………………………………..
Are the triangles congruent? …………………… Reason …………………………………………. ………………………………………………….. …………………………………………………..
Are the triangles congruent? …………………… Reason …………………………………………. ………………………………………………….. …………………………………………………..
PiXL PLC 2017 Certification
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 )
1 2
10 5 – 5
5
x
y
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(Total 3 marks)
Question 3.
Describe fully the enlargement that transforms shape A onto shape B
(Total 3 marks)
A B
10
– 5 5 10 15
5
– 5
x
y
PiXL PLC 2017 Certification
Total /10
PiXL PLC 2017 Certification
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)
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(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
PiXL PLC 2017 Certification
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.
PiXL PLC 2017 Certification
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
(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)
PiXL PLC 2017 Certification
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
(2)
(Total 4 marks)
Total / 10
PiXL PLC 2017 Certification
PiXL PLC 2017 Certification
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)
A B
D
C
E
F G
H
J
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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
PiXL PLC 2017 Certification
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)
(Total 3 marks)
Question 2.
Give the vector that describes each of these journeys:
(Total 3 marks)
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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
PiXL PLC 2017 Certification
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)
………………………m3
(2)
(b)
………………………cm3
(2)
(c)
………………………cm3
(3)
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(d)
………………………cm3
(3)
Total /10
PLC Papers
Created For:
PiXL PLC 2017 Certification
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)
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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
PiXL PLC 2017 Certification
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)
D
F
E
G
57 º º
69 º
Diagram NOT accurately drawn
y
69 ° A1
Alternate angles are equal. =A1
PiXL PLC 2017 Certification
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°
46 ° A1
59 ° A1
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Question 3
120 ° A1
Angles on straight line adds up to 180° A1
180 – 60 = 120°
60 ° A1
Alternate angles are equal. A1
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Question 4
Total /10
Corresponding angles are equal A1
OR
Accept:
co-interior angles add up to 180 ° therefore 180 – 70 = 110 A1
110 ° A1
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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 = 70cm2 (M1 A1)
………………………cm2
(2)
(b)
Multiply perpendicular lengths then half.
12x5/2=30 m2 (M1 A1)
……………………… m2
(2)
(c)
Parallogram: 15x10 = 150 (M1 for both)
150x2 = 300cm2 (A1)
……………………… cm2
(2)
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(d)
Add parallel sides, multiply by distance between and half.
0.5x4x(5+9) = 28cm2 (M1A1)
……………………… cm2
(2)
(e) Add parallel sides, multiply by distance between and half.
0.5x18x(40+16)=504cm2 (M1A1)
……………………… cm2
(2)
Total /10
PiXL PLC 2017 Certification
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)
(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)
314.2 cm2 (A1)
(2)
(Total 4 marks)
PiXL PLC 2017 Certification
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)
1924.2 cm2 (A1)
(Total 3 marks)
Question 3.
Find the area of the shaded area shown.
Leave your answer in terms of �.
12cm
(122 × �) − (52 × �) (M1)
144� − 25� (A1)
119� cm2 (A1)
(Total 3 marks)
Total /10
5cm
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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)
216-16=200m2 (A1)
……………………………m2
(3)
(b)
14x12x0.5=84 (M1)
72 × � ÷ 2 = 76.97 (M1 M1)
84+76.97=160.97m2 (A1)
……………………………
(4)
(Total 7 marks)
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Question 2.
Find the area of the shaded region.
Give your answer to 2 decimal places.
18x12=216 (M1)
42 × � = 50.27 (�1)
216-50.27=165.73m2 (A1)
……………………………m2
(3)
Total /10
PiXL PLC 2017 Certification
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
T
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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.
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)
C
D
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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)
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
Question 5
Complete the sentence below.
The circle has a radius of 6cm.
radius
(1)
Total /10
PiXL PLC 2017 Certification
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.
31.4 ÷ � ÷ 2 = 5.0�� (M1 A1)
..............................................
(2)
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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
PiXL PLC 2017 Certification
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
C A1
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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
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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
PiXL PLC 2017 Certification
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
a
a b
c
c
b
Not drawn accurately
PiXL PLC 2017 Certification
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)
(2)
(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
PiXL PLC 2017 Certification
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 2
1 mark at least 2 construction lines
1mark correct centre
1 mark correct size
PiXL PLC 2017 Certification
Question 3.
Describe fully the enlargement that transforms shape A onto shape B
(Total 3 marks)
Total /10
A B
1 mark at least 2 construction lines
1mark correct centre (– 3 , 4) 1 mark correct SF ½ or 0.5
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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)
PiXL PLC 2017 Certification
(c) Two of the sides of a rectangle are 6cm and 11cm. What is the perimeter?
6+6+11+11=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
PiXL PLC 2017 Certification
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.
PiXL PLC 2017 Certification
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
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
6cm
2cm 5cm
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
Total / 10
PiXL PLC 2017 Certification
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)
A B
D
C
E
F G
H
J
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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
PiXL PLC 2017 Certification
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:
� 3−3� �0
4� �−5
0�
(Total 3 marks)
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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
PiXL PLC 2017 Certification
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 cm3(M1 A1)
………………………m3
(2)
(b)
½ x base x width x depth
½ x 3 x 5 x 11=82.5cm3 (M1 A1)
………………………cm3
(2)
(c)
��2ℎ = ������ (M1)
� × 62 × 18 = 2036��3 (M1 A1)
………………………cm3
(3)
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(d)
Base x perpendicular height x depth= volume (M1)
12 x 8 x 14 = 1344 cm3(M1 A1)
………………………cm3
(3)
Total /10