7.1 Lines and Angles

7.1 Lines and angles

1a)rightb)obtusec)acuted)straighte)reflex

2a)arrowheadsb)AB (BA)c)CD (DC)

d)Noe)BC and DE (CB and ED)

3a)37° and 143°b)They sum to 180°, which equals a straight angle

4a)EF (FE)b)5.8 cm (DE)c)110°

d)EBF (FBE)e)90°f)BEF (EFB,FBE)

5a)BFE (EFB)b)55°–65°

c)140°–160°d)DBC and CDB (CBD and BDC)

e)The answer to c)

6W 240°, X 288°, Y 251° and Z 301°

7Pupil’s sketch and RPQ 53°

8a)a 46° (straight line), b 106° (angles in a triangle), c 74° (straight line), d 106° (opposite angles or straight line)

b)40°c)GH (HG)

d)No, there are no right angles indicated.

e)BAG (GAB)f)332°

7.2 Angle rules

1a) and b)i)I, 107°ii)E, 58°iii)E, 103°iv)E, 90°

2a)31°b)56°c)125°d)23°

3a)i)supplementaryii)complementaryiii)corresponding

iv)alternatev)vertically opposite

b)acefg 39°, bd 141°, h 51°

c)i)f and g, c and gii)e and f, c and e

iii)c and d, c and b, 141° and f, b and e, e and 141°, 141° and g, b and getc.

d)vertically opposite:ca, supplementary: c 180° b, corresponding: cg,
alternate: ce

4a)alternateb)equalc)180°, e, g, e, f, g, 180°

5a)180°b)180°.c)180°, 180°, 360°.

6a)180°b)180°c)efn

10.2 Describing the nth term

1a)i)£75ii)£150

b)i)money raised (M)  number of miles (n) × 15ii)Mn× 15

c)8 miles

2a)30b)term-to-term rule is: ‘add 5’

c)The position-to-term rule is: ‘multiply the position number by 5.

d)T 5 ×n

3a)i)add 7ii)multiply the position number by 7iii)T 7 ×n

b)i)add 0.5ii)multiply the position number by 0.5iii)T 0.5 ×n

4a)The term-to-term rule is : add 3

b)The position-to-term rule is: multiply the position number by 3 and add 1

c)n→3 ×n 1

5a)multiply the position number by 2 then add 1

b)multiply the position number by 3 then subtract 1

c)multiply the position number by 10 then subtract 2

d)multiply the position number by 5 then add 2

e)multiply the position number by 2 then add 1.5

f)multiply the position number by 6 then subtract 5

6a)T 2 ×n 1b)T 3 ×n 1c)T 10 ×n 2

d)T 5 ×n 2e)T 2 ×n1.5f)T 6 ×n 5

7a)14

b) / Number of tables (n) / 1 / 2 / 3 / 4 / 5
Number of people(p) / 6 / 10 / 14 / 18 / 22

c)32  2  34; four people can sit on the sides of each table with one person at each end on the lines of tables.

Additional answers1

d)number of people number of tables× 4  2

e)p 4n 2

f)4 people at each table makes the multiplier 4, one person sitting at each end means we have to add 2.

14.1 Translation and reflection

1

2a)3 left and 2 upb)4 left and 6 up

3

c)rhombus, 16 square units

4a)2 right, 1 upb)2 left, 1 down

c)they have the same numbers but opposite directions

d)

5a)yxb)trapezium

6

d)Square

e)e.g. reflect in yx to produce top-right square then reflect object and image in x 0 followed by y 0.

f)Reflect in yx, translate object and image 3 left and then translate object and image 3 down.

14.2 Rotation

1a)90° anticlockwise (or 270° clockwise) about (1, 0)

b)180° clockwise (or anticlockwise) about (1, 0)

c)90° clockwise (or 270° anticlockwise) about (1, 0)

d)180° clockwise (or anticlockwise) about (1, 0)

e)180° clockwise (or anticlockwise) about (1, 0)

f)They are the same

2a)(1, 0), (3, 0), (1, −1)b)(−1, 0), (−3, 0), (−1, 1)

c)(0, −1), (0, −3), (−1, −1)

3

b)square, 8 square unitsd)square, 32 square units

4a)90° rotation clockwise about (2, −1)b)90° rotation clockwise about (1.5, −1.5)

5a)90° rotation clockwise about (1, −1)b)90° rotation clockwise about (1, 1)

c)90° rotation anticlockwise about (1, 3)d)translation 2 left, 2 up

e)translation 4 left, 4 up

6a)60° rotation clockwise about the centre, O

b)180° rotation clockwise (or anticlockwise) about O

c)Reflection in the line BF

7a)45°b)rotation (360 n)° with centre the centre of the polygon

17.4 Graphs in all four quadrants

1a) and b) Axes drawn and points plotted correctly.c)Rectangle

d)i)y 5ii)x5

2a)(1, 2)b)(1, 0), (1, 1), (1, 3), (1, 4)

c)(1, 2) or (1, 3)

3a) / x / −3 / 0 / 1 / 4
y / 9 / 6 / 5 / 2

b)Correct graph plotted.

4a)5 values from

i) / x / −5 / −4 / −3 / −2 / −1 / 0 / 1 / 2 / 3 / 4 / 5
y / −24 / −19 / −14 / −9 / 4 / 1 / 6 / 11 / 16 / 21 / 26
ii) / x / −5 / −4 / −3 / −2 / −1 / 0 / 1 / 2 / 3 / 4 / 5
y / −11 / −8 / −5 / −2 / 1 / 4 / 7 / 10 / 13 / 16 / 19

b)Correct graphs plotted

5a)y-intercept

b)The value of y where the line crosses the y-axis equals the number part of the equation

6a)Cb)Bc)A

7a)y-interceptb)gradientc)y 7x 1

d)equation with m > 7

e)equations with same value of m but different values of c.

18.2 Drawing 3-D shapes

1a)tetrahedron; F  4, V  4, E  6b)triangular prism; F  5, V  6, E  9

c)pyramid; F  5, V  5, E  8

2a)F  5, V  6, E  9b)F  6, V  8, E  12

3

4

Additional answers1

5

616

7Accurate construction

18.4 More nets

11 cuboid, 6 rectangles; square-based pyramid, one square and four triangles; cylinder, two circles and one rectangle; tetrahedron, four triangles; triangular prism, two triangles and three rectangles.

2a)cube – E, cuboid – C, triangular prism – A, cylinder – D, square-based pyramid – B, triangular-based pyramid – G

b)F

3C, D and F

4

5

6a)Irregularb)

7

Additional answers1

18.5 Surface area

125.6 m2

2a)e.g. b) and c)e.g.

d)126 cm2

3a)112 cm2b)190 cm2c)26 m2d)4298 mm2

4a)600 cm2b)60 cm2c)2100 cm2d)6.5 m2

5a)1928 cm2

b)Extra paper needed to create flaps/paper will not be in the shape of a net

6a)1700 cm2b)1800 cm2

c)No as although the area of the net is less than 1800 cm2, the net has overall dimensions of 36 cm × 51 cm.

7a)520 cm2b)1206 m2

8a)154.2 m2b)£59.95

Additional answers1