MAKE THE
GRADE
QUESTIONS
1-6
ANSWERS  = 1 mark
1. a) Reflect triangle ABC in the x axis. Label the new triangle A’B’C’
b) Translate triangle A’B’C’

(
-4
0
) . Label the image A’’B’’C’’
SHAPE,
SPACE &
MEASURES
(1)
(1)

c) Describe the single transformation that will map triangle ABC onto triangle
A’’B’’C’’
Rotation 180º clockwise ( or anticlockwise) about the origin (or (0,0))



(3)
S A LOMAX 2006
2. Trapezia A and B are similar.
NOT TO SCALE
yº
30º
15cm
10cm
x
3cm
Calculate the values of:
x 10

=
3 15
10 
30

x=
× 3=
= 2cm
15
15
a) x
30º 
b) y
(4)
3. Calculate the value of x in the diagram below:
NOT TO SCALE
5cm
5cm
2cm
 for diagrams
x
6cm
6cm
5cm
S A LOMAX 2006
x
2cm
x 5
=

6 2
5
x = x 6 = 15cm 
2
(3)
4. Find the value of a in the diagram below:
NOT TO SCALE
12cm
4cm
a
3cm
 for diagrams
4cm
12cm
3cm
a + 3 12

=
3
4
36
a +3 =
=9 
4
a = 6cm 
a + 3 cm
(4)
5. x, y and z represent lengths in the following formulae. By considering
dimensions, which of the formulae below could represent length (L), area (A)
or volume (V)?
x+y+z
xyz
3xy
x(y+z)
4 π x²
y²+2z
L
V
A
A
A
-





x+y
z
L

(6)
S A LOMAX 2006
6. Find the missing angles in the diagrams below, giving reasons for your
answers:
a)
90º
a
50º
O
a = 40º


because angles in a semi-circle is a right angle (and the sum of the
angles in a triangle is 180 º)
(2)
b)
50º
O
b
c
b = 100º


because angle at the centre is twice the angle at the circumference
(2)
c = 110º 
because opposite angles in a cyclic quadrilateral add up to 180 º 
(2)
S A LOMAX 2006
c)
e
d
20º
g
15º
f
d = 20º 
because angles in the same segment are equal 
(2)
e = 20º 
because angles in the same segment are equal 
(2)
f = 15º 
because angles in the same segment are equal 
(2)
g = 145º 
because the sum of the angles in a triangle add up to 180º 
(2)
S A LOMAX 2006
7. Find the missing side indicated in each the following triangles,
giving your answer to a sensible degree of accuracy:
a)
NOT TO SCALE
H
O
S H
12cm
O
a
CALCULATORS
ARE ALLOWED
FOR QUESTIONS
7 - 10
 for sine
O = SXH
a = sin30 x12 
30º
a = 6cm 
(3)
b)
A
C H
A
b
A = CXH
 for cosine
b = cos 40 x10 
40º
a = 7.7cm(1dp ) 
10cm
H
(3)
c)
O
O
T A
c
 for tangent
O = TXA
12m
40º30º
c = tan 40 x12 
A
a = 10 .07 m(2dp ) 
(3)
A
d)
H
8cm
8cm
C H
A = CXH
 for cosine
x = cos 50 x8 
50º
50º
d
S A LOMAX 2006
x
A
x = 5.1423 ...cm(1dp )
d = 2x5.1423 ... = 10 .3cm(1dp ) 
(3)
e)
O
50º
5m
H
S H
O
e
H =O÷S
 for sine
e = 5 ÷ sin 50 
e = 6.53m(2dp ) 
(3)
O
f)
4cm
f
70º
A
O
T A
A=O÷T
 for tangent
f = 4 ÷ tan 70 
(3)
e = 1.5cm(2dp ) 
8. Find the missing angle indicated in each the following triangles, giving your
answer to a sensible degree of accuracy:
NOT TO SCALE
a)
 for sine
0 8
sin a = =
H 12cm

H 12
8
a = sin-1 ( ) = 41.8  (1dp )
8cm O O = TXA
12

c = tan 40 x12
a
b)
A
9cm
b
S A LOMAX 2006
a = 10 .1cm(1dp )
 for tangent
O = TXA
(3)
c = tan 40 x12
O a = 10.1cm(1dp0 ) 5 
tan b = =
A 9
5cm
5
b = tan -1 ( ) = 29.1  (1dp )
9

(3)
 for tangent
c)
0 80
=

A 120
80
c = tan -1 (
) = 33.7  (1dp ) 
120
tan c =
80cm
O
c
30º
1.2m A
(3)
d)
 for cosine
A 2
=

H 8
2
d = cos -1 ( ) = 75.5  (1dp ) 
8
H
cos d =
8cm
d
4cm
A=2cm
(3)
9. A step ladder can only be safely climbed if the angle of elevation to the
ground is less than 75º.
How far away from a wall must the ladder be to safely reach 3m above the
ground?
 for tangent
3m O
O
TA
A=0÷T

x = 3 ÷ tan 75
x = 0.8m(1dp )
75º
x

A
The ladder must be

(4)
greater than 0.8m away
wallsails due South for a
10. A ship sails from Harbour due East forfrom
4km.the
It then
further 6km.
Calculate the bearing of the ship from the harbour.
N
4km A
O 6
tan x = = 
x
A 4
6
x = tan -1 ( ) = 56.3 (1dp ) 
6km
4
O
 for diagram
Bearing of the ship = 90 + 56.3 = 146º 
(4)
S A LOMAX 2006
Did you ‘Make the Grade’ ?
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Skill
can transform shapes using reflections
can transform shapes using translations
can describe transformations
can find missing sides in simple similar shapes
can find missing sides in more complex similar shapes
can find missing angles in similar shapes
can use dimensions to identify types of formulae
can solve circle problems using angle properties
can state the circle properties correctly
can find missing sides using trigonometry in simple cases
can find missing sides using trigonometry in harder cases
can find missing angles using trigonometry in simple cases
can find missing angles using trigonometry in harder cases
can solve problems using trigonometry
Qu
1a
1b
1c
2a
3,4
2b
5
6
6
7a - d
7e - f
8a,b
8c - d
9,10
 Yippee!! - I got all the questions correct.
 I made mistakes and need to practise this topic more.
Top 3 topics I need to revise are
☺
☺
☺
If your score is:
51 – 73
26 – 50
0 – 25
- Well done. You are working at grade B with your shape and
space skills.
- Promising work – make sure you ask for help and revise the
topics that you had difficulty with. You can still get that B !!!
- Serious revision and help is needed. Sort it out now.
Don’t wait any longer
S A LOMAX 2006
 