MEP: Demonstration Project Teacher Support Y9B

© The Gatsby Charitable Foundation

UNIT 12 Constructions and Loci Revision Test 12.1(Standard)

1. (a) Construct a triangle with sides of length 5 cm, 6 cm and 8 cm.

(b) Measure the angles in the triangle.

(6 marks)

2. Calculate the sizes of the angles marked with letters in the following diagram:

40˚

70˚ a b

(4 marks)

3. Measure each of these angles:

(a)

(b)

(2 marks)

MEP: Demonstration Project Teacher Support Y9B

© The Gatsby Charitable Foundation

4. The diagram shows a triangle.

A

C B40˚ 45˚6 cm

(a) Construct an accurate drawing of the triangle.

(b) Measure the lengths of the sides AC and AB.

(c) Calculate the size of the third angle of the triangle.

(8 marks)

5. Calculate the size of each of the angles marked with a letter inthe following diagram:

a

d bc

60˚

(5 marks)

6. Construct an equilateral triangle with sides of length 7 cm.

(3 marks)

7. The line AB has length 6 cm.

Draw the line and its perpendicular bisector.(2 marks)

Revision Test 12.1 (Standard)

MEP: Demonstration Project Teacher Support Y9B

© The Gatsby Charitable Foundation

UNIT 12 Constructions and Loci Revision Test 12.2(Academic)

1.

Determine the size of each of the angles marked with a letter in the diagram.(6 marks)

2. A triangle has sides of length 6 cm, 7 cm and 9 cm.

(a) Construct the triangle and measure its three angles.

(b) Bisect the largest angle of the triangle and measure the distancealong this bisector from the angle to the opposite side.

(9 marks)

3. The points A and B are 8 cm apart. Draw the locus of the points thatare equidistant from A and B and within 7 cm of B.

(4 marks)

4. A line has length 5 cm. Draw the locus of the points that are 2 cmfrom the line.

(3 marks)

5. The diagram shows the triangle ABC.

70˚ 30˚

B

A C5 cm

(a) Draw the triangle.

(b) Measure the sides AB and BC.

(c) Draw the locus of points that are 2 cm from the triangle.(8 marks)

d bca

121˚

20˚

MEP: Demonstration Project Teacher Support Y9B

© The Gatsby Charitable Foundation

UNIT 12 Constructions and Loci Revision Test 12.3(Express)

1. Construct angles of size,

(a) 120 ° (b) 45 °

(5 marks)

2. The following diagram consists of two lines of length 6 cm andtwo semicircles of radius 3 cm.

3 cm

6 cm

Draw the locus of points that are 2 cm from the shape.

(4 marks)

3. (a) Construct a triangle ABC that has sides

AB = 6 cm, BC = 5 cm and AC = 8 cm.

(b) Draw the locus of the points that are equidistant from A and Band within 6 cm of C.

(6 marks)

4. The triangle ABC is such that AB = 8 cm, ∠BAC = 40 ° and BC = 6 cm.

Draw the triangles that satisfy this description.

(6 marks)

MEP: Demonstration Project Teacher Support Y9B

© The Gatsby Charitable Foundation

Revision Test 12.3 (Express)

5. The diagram shows the triangle ABC.

70˚ 30˚

B

A C5 cm

(a) Draw the triangle.

(b) Measure the sides AB and BC.

(c) Draw the locus of points that are 2 cm from the triangle.(6 marks)

6. State the size of the angles a, b and c in the following diagram:

42˚

66˚

a

b

c

(3 marks)

MEP: Demonstration Project Teacher Support Y9B

© The Gatsby Charitable Foundation

Revision Test 12.1 (Standard) Answers

1. (a)

B3

(b) 93 48 39° ° °, , B1 B1 B1 (6 marks)

2. (a) a = 180 70 40° − ° − ° M1

= 70 ° A1

b = 180 70° − ° M1

= 110 ° A1 (4 marks)

3. (a) 120 ° B1

(b) 20 ° B1 (2 marks)

4. (a)

B4

(b) AC = 4.3 cm B1

AB = 3.9 cm B1

(c) 180 40 45 95° − ° − ° = ° M1 A1 (8 marks)

5. a = 180 60 120° − ° = ° M1 A1

b = 60 ° B1

c = 120 ° B1

d = 120 ° B1 (5 marks)

6.

B3 (3 marks)

A

C B40˚ 45˚

For Questions 1, 3 and 4 allow answers within an appropriate range.

MEP: Demonstration Project Teacher Support Y9B

© The Gatsby Charitable Foundation

7.

B2 (2 marks)

(TOTAL MARKS 30)

Revision Test 12.1 (Standard) ANSWERS

BA

MEP: Demonstration Project Teacher Support Y9B

© The Gatsby Charitable Foundation

Revision Test 12.2 (Academic) Answers

1. a = 20 ° B1

b = 121 ° B1

c = 180 121 20° − ° − ° M1 A1

= 39 ° A1

d = 39 ° B1 (6 marks)

2. (a)

Construction B3

∠ BAC = 42 ° B1

∠ ABC = 87 ° B1

∠ ACB = 51 ° B1

(b) Bisector B2

BX = 4.7 cm B1 (9 marks)

3.

B4 (4 marks)

6 cm

7 cm

9 cm

A

B C

X

A BLocus

For Questions 2 and 5 allow answers within an appropriate range.

MEP: Demonstration Project Teacher Support Y9B

© The Gatsby Charitable Foundation

4.

B3 (3 marks)

5. (a), (c)

Triangle B3

Locus B3

(b) AB = 2.5 cm B1

BC = 4.8 cm B1 (8 marks)

(TOTAL MARKS 30)

Revision Test 12.2 (Academic) ANSWERS

locus

70˚ 30˚

B

A C5 cm

MEP: Demonstration Project Teacher Support Y9B

© The Gatsby Charitable Foundation

Revision Test 12.3 (Express) Answers

1. (a)

B2

(b)

B3

(5 marks)

2.

outer B2inner B2 (4 marks)

3. (a), (b)

120˚

45˚

locus

locus

MEP: Demonstration Project Teacher Support Y9B

© The Gatsby Charitable Foundation

Revision Test 12.3 (Express) ANSWERS

Triangle B2

Locus B4 (6 marks)

4.

B3

B3 (6 marks)

B

A C

locus

6 cm

8 cm

C

A B40˚

6 cm

8 cmB

C

A 40˚

MEP: Demonstration Project Teacher Support Y9B

© The Gatsby Charitable Foundation

5. (a), (c)

Triangle B2

Locus B3

(b) AB = 2.5 cm, BC = 4.8 cm (allow answers within an appropriate range) B1 (6 marks)

6. (a) a = 108 ° B1

b = 72 ° B1

c = 114 ° B1 (3 marks)

(TOTAL MARKS 30)

70˚ 30˚

B

A C5 cm

Revision Test 12.3 (Express) ANSWERS