# H Angles and Shapes

Document Sample

```					Q1.         In the diagram AB and CD are parallel.

Not drawn accurately

(a)    Write down the value of x.

(1)

(b)    Work out the value of y.

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

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

(2)
(Total 3 marks)

Q2.         The diagram shows a regular pentagon and a regular decagon joined at side XY.

Not drawn accurately

Page 1 of 25
Show that the points A, B and C lie on a straight line.

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

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

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

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

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

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

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

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

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

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

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

..................................................................................................................................
(Total 5 marks)

Q3.      XYZ is an isosceles triangle in which XZ = XY
M and N are points on XZ and XY such that angle MYZ = angle NZY.

Page 2 of 25
Prove that triangles YMZ and ZNY are congruent.

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

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

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

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

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

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

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

..................................................................................................................................
(Total 4 marks)

Page 3 of 25
Q4.         Three circles fit inside a rectangle as shown.
Two of the circles are identical and the third is larger.
The circles have radii 9 cm, 9 cm and 25 cm.

Not drawn accurately

Calculate the length, l, of the rectangle.

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

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

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

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

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

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

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

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

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

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

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

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

(Total 6 marks)

Page 4 of 25
Q5.         ABCDEF is a regular hexagon.
AFGH and AJKB are squares.

Not drawn accurately

Show that triangle AHJ is equilateral.

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

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

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

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

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

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

..................................................................................................................................
(Total 4 marks)

Page 5 of 25
Q6.      Airport runways have a two-digit number painted on them.
These numbers are used to work out the direction of the runway.
To work out the three-figure bearing, multiply the runway number by 10.
Here is a diagram of a runway on a three-figure bearing of 280° and a runway on a three-figure
bearing of 040°.

(a)   (i)     Write down the three-figure bearing for a runway pointing due South.

(1)

(ii)    Write down the runway number for a runway pointing due South.

(1)

(iii)   A runway has a three-figure bearing of 060°.

Write down the runway number.

(1)

Page 6 of 25
(b)   A runway is being painted.

By measuring the three-figure bearing, work out the runway number.

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

(2)

(c)   Runways are used in both directions.
This means that they have two different runway numbers, one at each end.
A runway has the number 30 at one end.

What runway number is at the other end?

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

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

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

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

(3)
(Total 8 marks)

Page 7 of 25
Q7.        A sign maker designs a letter L.
All arcs are quarter circles of radius 2 cm.

Not drawn accurately

Calculate the area of the L.

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

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

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

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

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

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

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

(Total 4 marks)

Page 8 of 25
Q8.         The diagrams show a trapezium and a parallelogram.

Not drawn accurately

(a)    Use the trapezium to explain why                              2x + y = 180

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

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

(b)    The parallelogram can be used to form another equation connecting x and y.

Tick a box to show the correct equation.

3x + y = 130                                                      3x + y = 230

3x = y – 50                                                       3x + y = 410

(1)

(c)    Hence, or otherwise, work out the values of x and y.

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

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

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

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

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

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

Answer x = ................ , y = …...............
(3)
(Total 5 marks)

Page 9 of 25
M1.         (a)     41
B1

(b)    180 – 67
71 + their 41 oe 360 – 41 – 67 – 139
M1

113
A1
[3]

Page 10 of 25
M2.      360 ÷ 10 or 360 ÷ 5
or 36 or 72 or 144 or 108
NB Angles may be marked on diagram
M1

144 and 108
or 36 and 72
A1

Page 11 of 25
∠BXC = 360 – (144 + 108)
or ∠BXD = 36 + 72 or 108
(X is point where decagon and pentagon meet between B and C)
M1

∠XBC = ∠XCB = (180 – 108) ÷ 2
or ∠XBC = 36
M1

Page 12 of 25
∠ABX + ∠XBC = 144 + 36 ( = 180)
oe
eg, ∠CBX calculated from ΔBXC equals exterior angle
of decagon
A1
[5]

Page 13 of 25
M3.       YZ = ZY
B1

Angle MZY = angle NYZ
base angles of (Isosceles) ∆ XYZ
Note Reason necessary
eg you might see
If XZ = XY then angle XZY = angle XYZ
B1

Angle MYZ = angle NZY
B1

Triangles congruent, ASA
Note Dependent on earning first 3 marks
Must give correct reason for congruence (ASA)
Only allow AAS if complete argument stating
‘third angles equal’
B1 dep
[4]

Page 14 of 25
M4.        Side of 34
B1

50 – 18 or 25 – 9
M1

Side of 32 or 16
A1

162 + x 2 = 342
M1

x = 30
2 × ‘8, 15, 17’ triangle get M1, A1
A1

64
A1
[6]

Page 15 of 25
Page 16 of 25
M5.         BAF = 120°
This can just be stated
or exterior angle of hexagon = 60°
or reflex     FAB = 240°
B1

360 – (120 + 90 + 90) = 60°
oe
HAJ must be shown to be 60° by calculation
B1

Page 17 of 25
AH = AJ
This can just be stated or shown on diagram
B1

AJH =   AHJ = (180 – 60) ÷ 2
Dep on first B2
B1dep
[4]

Page 18 of 25
M6.   (a)      (i)        180
B1

(ii)     18
Their (a)(i) ÷ 10
Not ft 280 or 040 or > 360
B1 ft

(iii)         06
Do not allow 6
B1

Page 19 of 25
(b)   210
Allow 208 – 212
B1

21
SC1 15
Not 21.0
B1 ft

Page 20 of 25
(c)   300 – 180
180 ÷ 10
M1

120
30 – 18
A1

12
A1 ft
[8]

Page 21 of 25
M7.   Breaks down into areas of rectangles and areas of (quarter) circles
Any combination of rectangles and circles
or 12.56... or       is enough evidence for area of circles
NB 12.56 from 2 × π × 2, if seen is M0
NB 3.14 on its own is not evidence of the area
of a quarter circle as it is π
M1

Page 22 of 25
Uses an ‘addition’ method (method 1) and finds

Area of one (or 5) ‘external’ quadrants

or

or
Uses a ‘subtraction’ method (methods 2 and 3) and finds

or
M1 dep

= 0.8584..., {0.9, 0.86, 0.858}

or = (× 5) 4.292... {4.3, 4.29}
15.71, 15.7
A1

52.3 or 52.29... 68 – 5π
Allow 52 if 52.3 or 52.29... or a full method seen
A1
[4]

Page 23 of 25
M8.         (a)   Valid explanation
eg allied angles (add up to 180)
inside parallel lines (add up to 180)
y + y + 2x + 2x = 360 so y + 2x = 180
2y + 4x = 360
In a C add up to 180
Condone interior angles (add up to 180)
B1

(b)    3x + y = 230
oe
B1

Page 24 of 25
(c)   Attempt to eliminate a variable
(with 2x + y = 180)
eg 6x + 2y = 460 and 6x + 3y = 540 and subtraction
Note: Full marks can be awarded for this part on
M1

x = 50
A1 ft

y = 80
A1 ft
3x + y = 130 → x = –50, y = 280
3x = y –50 → x = 26, y = 128
3x + y = 410 → x = 230, y = –280
[4]

Page 25 of 25

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 121 posted: 8/20/2010 language: English pages: 25