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PLC Papers

Created For:

PiXL PLC 2017 Certification

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


Question 2


Question 3


Question 4

Total /10


Arcs and Sectors 2 Grade 6

Objective: Calculate arc lengths and angles, and areas of sectors

Question 1.

PQ is an arc of a circle with radius 9.4cm.

Angle POQ = 143o

(a) Calculate the perimeter of sector POQ.

Give your answer to three significant figures.

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

(3)

(b) Calculate the area of sector POQ.


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

(2)

(Total 5 marks)


Question 2.

A sector has a radius of 8cm and an arc length of 5cm.

(a) What is the angle of the sector? Give your answer correct to 3 significant figures.

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

(3)

(b) Calculate the area of the sector. Give your answer to three significant figures.

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

(2)

(Total 5 marks)

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.

(a)

………………………cm2

(2)

(b)

……………………… m2

(2)

(c)

……………………… cm2

(2)


(d)

……………………… cm2

(2)

(e)

……………………… cm2

(2)

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.

(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)


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


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)


Question 2.

Find the area of the shaded region.

Give your answer to 2 decimal places.

……………………………m2

(3)

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.

(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)


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)


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.

(1)

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.

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

(2)

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


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

(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)


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


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)

(2)

(Total 6 marks)

Total Marks / 10

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




Derive triangle results 2 Grade 5

Objective: Derive results about triangle angles and sides using known angle facts, triangle congruence, similarity and properties of quadrilaterals, and use known results to obtain simple proofs. Include the fact that the base angles of an isosceles triangle are equal, and include derivation of Pythagoras' theorem.

Question 1

The diagram below shows two parallel lines, ABC and DEF cut by the line GH.

H

A B C

D E F

G

Show that corresponding angles are equal

(Total 4 marks)


Question 2

Show that the area of a triangle is equal to half the base area multiplied by the perpendicular height.

A

B C

(Total 6 marks)

Total /10


Enlargements and negative scale factors 2 Grade 5

Objective: Identify and construct enlargements including using negative scale factors

Question 1

Enlarge the triangle on the grid by a scale factor of ¼ using the origin as the centre of enlargement.

(3)

Question 2

Enlarge this shape by a scale factor of 3 from the point ( – 5 , – 2 )

(3)

– 5

10

5

– 5 10 5 15 x

y

– 5

10

5

– 5 10 5 15 x

y


Question 3

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

b) What is the image of the point ( 5 , 2 ) under this enlargement?

(4)

Total / 10

Total marks / 10

– 5

10

5

– 5 10 5

15 x

y



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


(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


Total /10


Loci 2 Grade 5

Objective: Use constructions to solve loci problems

Question 1.

Draw the locus of the points 30km from the line AB

Scale: 1 cm represents 10 km

(Total 2 marks)

Question 2. On the diagram, draw the locus of the points, outside the rectangle, that are 3cm from the edges of this rectangle.

(Total 3 marks)

B

A


Question 3. There is a lighthouse at A and B. To avoid the rocks, a ship must sail equidistant to both A and B. Draw a line that is equidistant to A and B on the diagram.

(Total 2 marks)

Question 4. The diagram represents a triangular garden ABC

The scale of the diagram is 1 cm represents 1 m.

A tree is to be planted in the garden so that it is Nearer to AB than to AC, Within 5m of point A. On the diagram, shade the region where the tree may be planted.

(Total 3 marks)

Total /10

A

B


Pythagoras 2 Grade 5

Objective: Know and use Pythagoras's theorem for right-angled triangles

Question 1

ABC is a right angled triangle. AB = 8 m, BC = 14 m Calculate the length of AC. Give your answer correct to 1 decimal place.

………………………. (3) (Total 3 marks) Question 2

ABC is a right angled triangle. AB = 10 cm, AC = 21 cm Calculate the length of BC. Give your answer correct to 1 decimal place.

………………………. (Total 3 marks) (3)


Question 3

ABCD is a rectangle. AB = 23 m, AD = 12 m Work out the length of the diagonal BD. Give your answer correct to 3 significant figures.

………………………. (4) (Total 4 marks)

Total marks / 10


Similarity and Congruence 2 Grade 5

Objective: Apply the concepts of congruence and similarity

Question 1

Which of the two shapes above are congruent?

……………………… (2) (Total 2 marks) Question 2

In this diagram AB and DE are parallel. Find the lengths of DE and BC.

…………………. (Total 4 marks) (4)

CA

FED

B


Question 3

The diagram shows a model of a post. It has a surface area of 290 cm2. The scale of the model is 1:30. What is the surface area of the real post?

…………..…………. (4) (Total 4 marks) Total /10

6 cm

10 cm

5 cm

5 cm

Diagram accurately drawn

NOT


Standard constructions 2 Grade 5

Objective: Use the standard ruler and compass constructions to construct a 60° angle, a perpendicular bisector of a line segment, a perpendicular to a given line from/at a given point, and an angle bisector

Question 1.

Bisect this angle

(Total 3 marks)

Question 2.

Construct an isosceles triangle with side length 5cm, 4cm, 4cm.

(Total 4 marks)


Question 3

Construct a perpendicular bisector on the line AB below

(Total 3 marks)

Total /10

B

A


Surface Area 2 Grade 5

Objective: Calculate the surface area of spheres, pyramids, cones and composite solids

Question 1

Find the surface area of this cone, including the base. Give you answer to the nearest square centimetre.

…………………. (3) (Total 3 marks) Question 2 A pyramid has a square base of side 8 cm. Each of the triangular faces are isosceles

triangles with a height of 10 cm from the apex to the middle of the base. Find the surface area of the pyramid in square centimetres.

…… ……………. (Total 3 marks) (3)


Question 3 Find the total surface area of

this box, which is a prism with an L shaped face.

…………….…. (4) (Total 4 marks) Total /10


Trigonometry 2 Grade 5

Objective: Know and use the trigonometric ratios for right-angled triangles

Question 1

ABC is a right angled triangle. AC = 11 cm and the angle ACB is 67o Calculate the length of AB. Give your answer to 1 decimal place.

…….………………. (3) (Total 3 marks) Question 2 ABC is a right angled triangle.

AB = 9 cm, BC = 12 cm Calculate the angle ACB. Give your answer correct to the nearest degree.

…………………. (Total 3 marks) (3)


Question 3 ABCD is a rectangle.

AD = 13 m and the diagonal BD makes an angle of 74o with BC. Work out the length of the diagonal BD. Give your answer correct to 3 significant figures

………………. (4) (Total 4 marks) Total /10


Volume 2 Grade 5

Objective: Calculate the volume of spheres, pyramids, cones and composite solids.

Question 1

Find the volume of this cone. Give you answer to the nearest cubic centimetre.

….………………. (3) (Total 3 marks) Question 2 A pyramid has a square base of side 8 cm. The height of the pyramid (measured

perpendicular to the base) is 9.2 cm. Find the volume of the pyramid to the nearest cubic centimetre.

…. ……………. (Total 3 marks) (3)


Question 3 Find the volume of this box,

which is a prism with an L shaped face.

………….…. (4) (Total 4 marks) Total /10

PLC Papers

Created For:


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


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


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

OR

Accept:

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

110 ° A1


Arcs and Sectors 2 Grade 6 Solutions

Objective: Calculate arc lengths and angles, and areas of sectors

Question 1.

PQ is an arc of a circle with radius 9.4cm.

Angle POQ = 143o

(a) Calculate the perimeter of sector POQ.


Arc length = 143360 x π x 2 x 9.4 (=23.4607.) (M1)

Perimeter = Arc length + 9.4 x 2 (M1)

Perimeter = 42.3cm (A1)

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

(3)

(b) Calculate the area of sector POQ.


Area = 143360 x π x 9.42 (M1)

Area = 110cm2 (A1)

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

(2)

(Total 5 marks)


Question 2.

A sector has a radius of 8cm and an arc length of 5cm.

(a) What is the angle of the sector? Give your answer correct to 3 significant figures.

Arc length = 5 = �360 x π x 2 x 8 (B1)

θ = 5 × 3602 × � ×8 (M1)

θ = 35.8o (A1)

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

(3)

(b) Calculate the area of the sector. Give your answer to three significant figures.

Area = 35.8360 x π x 82 (M1 ft their angle)

Area = 20.0cm2 (A1)

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

(2)

(Total 5 marks)

Total /10


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)


(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


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)


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


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)


Question 2.

Find the area of the shaded region.


18x12=216 (M1)

42 × � = 50.27 (�1)

216-50.27=165.73m2 (A1)

……………………………m2

(3)

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

T


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


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)


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

(1)

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)

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

(2)

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


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)


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


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)


a

a b

c

c

b



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


Derive triangle results 2 Grade 5 Solutions

Objective: Derive results about triangle angles and sides using known angle facts, triangle congruence, similarity and properties of quadrilaterals, and use known results to obtain simple proofs. Include the fact that the base angles of an isosceles triangle are equal, and include derivation of Pythagoras' theorem.

Question 1

The diagram below shows two parallel lines, ABC and DEF cut by the line GH.

H

A B C

D E F

G

Show that corresponding angles are equal

Angle HBC = Angle ABE (vertically opposite angles) M1

Angle ABE = Angle BEF (alternate angles) M1

Hence Angle HBC = Angle BEF (corresponding angles) C1

This argument can be repeated for any pair of corresponding angles C1

(Total 4 marks)


Question 2

Show that the area of a triangle is equal to half the base area multiplied by the perpendicular height.

X A Y

B N C

Add a line perpendicular to BC, from a point N on BC, that goes to A M1

Add two lines, the same length as and parallel to AN, from B to X and from C to Y. M1

Join XY M1

Area of triangle ABN = 1/2 area of rectangle XABN M1

Area of triangle ANC = 1/2 area of rectangle ANCY

Hence area of triangle ABC = 1/2 (area of rectangle XABN + area of rectangle ANCY) M1

= 1/2 area of rectangle XBCY

= 1/2 BC x CY

= 1/2 BC x AN

= 1/2 x base x perpendicular height C1

(Total 6 marks)

Total /10


Enlargements and negative scale factors 2 Grade 5 Solutions

Objective: Identify and construct enlargements including using negative scale factors

Question 1

Enlarge the triangle on the grid by a scale factor of ¼ using the origin as the centre of enlargement.

1M construction lines

(at least one in correct position)

1M using the origin

1M correct size

(3)

Question 2

Enlarge this shape by a scale factor of 3 from the point ( – 5 , – 2 )



1M using the correct point

1M correct size

(3)

– 5

10

5

– 5 10 5 15 x

y

– 5

10

5

– 5 10 5 15 x

y


Question 3



1M using the correct point

1M correct size

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

b) What is the image of the point ( 5 , 2 ) under this enlargement?

1M ( -4 , -1 )

(4)

Total / 10

– 5

10

5

– 5 10 5

15 x

y


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


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


Loci 2 Grade 5 Solutions

Objective: Use constructions to solve loci problems Question 1.

(Total 2 marks)

Question 2.

(Total 3 marks)


Question 3.

(Total 2 marks)

Question 4.

(Total 3 marks)

Total /10


Pythagoras 2 Grade 5 Solutions

Objective: Know and use Pythagoras's theorem for right-angled triangles

Question 1

ABC is a right angled triangle. AB = 8 m, BC = 14 m Calculate the length of AC. Give your answer correct to 1 decimal place. AC2 = 82 + 142 (M2 square, add)

= 64 + 196 = 260 AC = 16.1 (A1)

16.1 m………………. (3) (Total 3 marks) Question 2

ABC is a right angled triangle. AB = 10 cm, AC = 21 cm Calculate the length of BC. Give your answer correct to 1 decimal place.

BC2 = 212 - 102 (M2 square, subtract)

= 441 - 100 = 341 BC = 18.5 (A1)

18.5 cm……………. (Total 3 marks) (3)


Question 3

ABCD is a rectangle. AB = 23 m, AD = 12 m Work out the length of the diagonal BD. Give your answer correct to 3 significant figures. BD2 = 122 + 232 (M2 square, add)

= 144 + 529 = 673 BD = 25.9 (A2 correct, correct 3sf)

………25.9 m…. (4) (Total 4 marks) Total /10


Similarity and Congruence 2 Grade 5 Solutions

Objective: Apply the concepts of congruence and similarity

Question 1

Which of the two shapes above are congruent?

…A & C (B2)…………. (2) (Total 2 marks) Question 2

In this diagram AB and DE are parallel. Find the lengths of DE and BC.

Scale factor = 3 DE = SF x 2.5 = 7.5 (M1, A1) BC = 11 / SF = 3.7 (M1, A1)

………3.7 cm……. (Total 4 marks) (4)

CA

FED

B


Question 3

The diagram shows a model of a post. It has a surface area of 290 cm2. The scale of the model is 1:30. What is the surface area of the real post? Scale factor = 30 So Area factor = 302 = 900 (M1,A1) Surface area of real post = 900 x 290 = 261 000 (A1, A1)

……261 000 cm2…………. (4) (Total 4 marks) Total /10

6 cm

10 cm

5 cm

5 cm

Diagram accurately drawn

NOT


Standard constructions 2 Grade 5 Solutions

Objective: Use the standard ruler and compass constructions to construct a 60° angle, a perpendicular bisector of a line segment, a perpendicular to a given line from/at a given point, and an angle bisector

Question 1.

Bisect this angle

(Total 3 marks)

Question 2.

Construct an isosceles triangle with side length 5cm, 4cm, 4cm.

M1 for 5cm line drawn

B1 B1 for construction arcs drawn from each end

A1 for correct triangle

(Total 4 marks)


Question 3.

Construct a perpendicular bisector on the line AB below

(Total 3 marks)

Total /10


Surface Area 2 Grade 5 Solutions

Objective: Calculate the surface area of spheres, pyramids, cones and composite solids

Question 1

Find the surface area of this cone, including the base. Give you answer to the nearest square centimetre.

S. Area = Πrl + Πr2 = Πx4.1x9.3 + Πx4.12 (M2 sloping face, circle) = 119.8 + 52.8 = 172.6 (A1)

173 cm2………………. (3) (Total 3 marks) Question 2 A pyramid has a square base of side 8 cm. Each of the triangular faces are isosceles

triangles with a height of 10 cm from the apex to the middle of the base. Find the surface area of the pyramid in square centimetres.

S. Area = ( 1/2 x 10 x 8)4 + 82 (M2 triangle, square) = 160 + 64 = 224

(A1)

224 cm2 ……………. (Total 3 marks) (3)


Question 3 Find the total surface area of

this box, which is a prism with an L shaped face.

2 L faces = 2(24 + 9) = 66 (M1, A1 three or more faces correct) Back = 84 Base = 72 Steps down = 36+36+36+48 =156 Total = 378 (M1 finding total)

(A1)

………378 cm2…. (4) (Total 4 marks) Total /10


Trigonometry 2 Grade 5 Solutions

Objective: Know and use the trigonometric ratios for right-angled triangles

Question 1

ABC is a right angled triangle. AC = 11 cm and the angle ACB is 67o Calculate the length of AB. Give your answer to 1 decimal place.

sin 67 = AB / 11 (M1) AB = 11 sin 67 (M1) = 10.1 (A1)

10.1 cm………………. (3) (Total 3 marks) Question 2 ABC is a right angled triangle.

AB = 9 cm, BC = 12 cm Calculate the angle ACB. Give your answer correct to the nearest degree.

tan ACB = 9 / 12 (M1) = 0.75 (M1) BAC = 37 (A1)

37o……………. (Total 3 marks) (3)


Question 3 ABCD is a rectangle.

AD = 13 m and the diagonal BD makes an angle of 74o with BC. Work out the length of the diagonal BD. Give your answer correct to 3 significant figures

cos 74 = 13 / BD (M1) BD = 13 /cos 74 (M1) = 47.16 (A1) (A1)

………47.2 m…. (4) (Total 4 marks) Total /10


Volume 2 Grade 5 Solutions

Objective: Calculate the volume of spheres, pyramids, cones and composite solids.

Question 1

Find the volume of this cone. Give you answer to the nearest cubic centimetre.

Volume = 1/3Πr2h = 1/3Π x 4.12 x 8.3 (M2 correct height, subst. into correct formula) = 146.1 (A1)

146 cm3………………. (3) (Total 3 marks) Question 2 A pyramid has a square base of side 8 cm. The height of the pyramid (measured

perpendicular to the base) is 9.2 cm. Find the volume of the pyramid to the nearest cubic centimetre.

Volume = 1/3 Base x height = 1/3 x 82 x 9.2 (M1) = 196.3 (A1)

(A1 rounding)

196 cm3 ……………. (Total 3 marks) (3)


Question 3 Find the volume of this box,

which is a prism with an L shaped face.

Cross section = 24 + 9= 33 (M1, A1) Volume = 33 x 12 (M1)

(A1)

………396 cm3…. (4) (Total 4 marks) Total /10

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