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4A - Angles
4
89
Geometrical reasoning
4A - Angles
LIN 2, 19, 27, 29, 31, 33 MOD 7, 18, 29, 34, 39, 41
o
Distinguish between alternate and
corresponding angles on parallel lines
o
Find angles in a triangle knowing that their
sum is 180o, exterior angles = sum of interior
opposites and base angles of an isosceles
triangle are equal
Use trigonometry to find the size of an
angle in a right–angled triangle, given the
length of two sides
o
o
o
Use trigonometry in complex problems
o
Find the exterior angle using the sum of the
exterior angles of a polygon is 360o
o
Make simple sketches of graphs of sine,
cosine and tangent
o
Find the size of interior and exterior angles
of a regular polygon
o
Use trigonometry graphs to solve simple
trigonometry equations
o
Solve geometric configurations using circle
theorems of chord and tangents
o
Compare corresponding sides in similar
triangles to calculate missing lengths
o
Solve geometric configurations using circle
theorems
o
Prove that two triangles are similar
triangles
o
Use trigonometry to find the length of a
side of a right–angled triangle, given the
length of one side and the size of an angle (not 90°)
o
Use ratio of length = a:b, ratio of area = a2:b2 and
ratio of volume = a3:b3
o
Find the conditions in order to prove that
two triangles are congruent
A03 - Shape, space and measures
Use sine, cosine and area of a triangle rules
to find unknowns in a scalene triangle
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
Topic Tutor GCSE Higher Maths St89 89
19/12/06 14:35:37
4A - Angles
90
1. 6.
Leave
blank
Diagram NOT
accurately drawn
BEG and CFG are straight lines.
ABC is parallel to DEF.
Angle ABE = 48°.
Angle BCF = 30°.
(a) (i) Write down the size of the angle marked x.
x = .............°
(ii) Give a reason for your answer.
................................................................................................................................
(2)
(b) (i) Write down the size of the angle marked y.
y = .............°
(ii) Give a reason for your answer.
................................................................................................................................
(2)
Q6
(Total 4 marks)
*N16915A0720*
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Topic Tutor GCSE Higher Maths St90 90
7
Turn over
19/12/06 14:35:39
4A - Angles
2. 5.
91
Leave
blank
D
C
x
Diagram NOT
accurately drawn
B
A
y
103°
F
E
ABCD and AFE are straight lines.
BF is parallel to CE.
Angle CBF = 103o.
AB = AF.
................................... o
(ii) Give a reason for your answer.
................................................................................................................................
................................................................................................................................
(2)
(b) Find the size of angle y.
................................... o
(2)
A03 - Shape, space and measures
(a) (i) Find the size of angle x.
Q5
(Total 4 marks)
*M22892A0508*
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
Topic Tutor GCSE Higher Maths St91 91
5
Turn over
19/12/06 14:35:40
y = ....................
(2)
4A - Angles
92
Q2
(Total 3 marks)
3. 3.
Diagram NOT
accurately drawn
a°
138°
65°
Leave Leave
blank blank
Work out the value of a.
SECTION
B B
SECTION
Answer
ALLALL
SEVEN
questions.
Answer
SEVEN
questions.
WriteWrite
youryour
answers
in theinspaces
provided.
answers
the spaces
provided.
4.
You must
NOTNOT
use ause
calculator
for this
You must
a calculator
for section.
this section. a = ....................
(3)
(Total 3 marks)
You must
writewrite
downdown
all stages
in your
working.
You must
all stages
in your
working.
1.
1.
Q3
N17482A
4
WorkWork
out the
angle
x. x.
outsize
the of
size
of angle
x = ...................°
x = ...................°
Give Give
reasons
for your
answer.
reasons
for your
answer.
..............................................................................................................................................
..............................................................................................................................................
..............................................................................................................................................
..............................................................................................................................................
Q1 Q1
..............................................................................................................................................
..............................................................................................................................................
(3)
(Total
3 marks)
(Total
3 marks)
2.
Given
that that
2. Given
36003600
× 5.8×=5.8
20 =880
20 880
WriteWrite
downdown
the value
of of
the value
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
(i) 36
0.58
(i) × 36
× 0.58
Topic Tutor GCSE Higher Maths St92 92
...........................
...........................19/12/06
14:35:45
4A - Angles
5. 2.
93
Leave
blank
The diagram shows the exterior angles of a quadrilateral.
88º
Diagram NOT
accurately drawn
bº
121º
57º
Work out the value of b.
3.
(a) Expand
3(4x – 5)
....................................
(1)
(b) Factorise
A03 - Shape, space and measures
b = .............................
(2)
(Total 2 marks)
Q2
5y + 40
....................................
(1)
(c) Simplify
3a + 7b + 9a – 4b
....................................
(2)
Q3
(Total 4 marks)
4
*M22891A0408*
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Topic Tutor GCSE Higher Maths St93 93
19/12/06 14:35:46
7.
94
Put a ring around each fraction which gave a recurring decimal.
4A - Angles
Q6
(Total 2 marks)
6. 7. x
7.
7.
Diagram NOT
accurately drawn
N
N
Diagram NOT
Diagram
accurately
drawn
Diagram NOT
NOT
accurately
accurately drawn
drawn
A
A
x
Leave
blank
Leave
blank
63°
63°
138°
138° P
P
B
B
Work out the bearing of
Work out the bearing of
The diagram shows a regular octagon.
(i) B from P,
(i) B from P,
Work out the size of the angle marked x.
°
............................°
............................
The diagram shows a regular octagon.
(ii)
P from
A. size of the angle marked x.
Work
out the
(ii) P from A.
Q7
°
............................°
Q7
............................°
x = .............................
Q7
(Total 3 marks)
(4)
(Total 3 marks)
(Total 4 marks)
8.
7. 8.
6
TOTAL FOR SECTION B: 19 MARKS
x = .............................
°
Diagram
NOT
Diagram
NOT
TOTAL FOR
PAPER:
38 MARKS
accurately
drawn
(Total
4 marks)
accurately
drawn
END
Q7
TOTAL FOR SECTION B: 19 MARKS
*M22884A008*
Calculate the size of an exterior angle of a regular hexagon.
TOTAL FOR PAPER: 38 MARKS
Calculate the size of an exterior angle of a regular hexagon.
END
Maths147303_M22884A.indd 6
6
05/09/2005 09:55:31
*M22884A008*
Maths147303_M22884A.indd 6
05/09/2005 09:55:31
°
Q8
............................°
Q8
............................
(Total 2 marks)(3)
(Total 2 marks)
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
N17481A
N17481A
Topic Tutor GCSE Higher Maths St94 94
8
8
19/12/06 14:35:52
4A - Angles
8.
6.
95
Leave
blank
C
Diagram NOT
accurately drawn
5.4 cm
A
2.3 cm
B
ABC is a right-angled triangle.
Angle A = 90º.
AB = 2.3 cm.
BC = 5.4 cm.
Work out the size of angle B.
Give your answer correct to 3 significant figures.
A03 - Shape, space and measures
º
..................................
(3)
(Total 3 marks)
Q6
TOTAL FOR SECTION B: 19 MARKS
TOTAL FOR PAPER: 38 MARKS
END
*M22898A0708*
7
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Topic Tutor GCSE Higher Maths St95 95
19/12/06 14:35:53
4A - Angles
96
9. 5.
B
Leave
blank
C
6m
Diagram NOT
accurately drawn
A
56º
10 m
E
F
D
6m
ABCDE is a pentagon.
BC = ED = 6 m.
Angle BCD = angle CDE = 90º.
Angle BAE = 56º.
The point F lies on CD so that AF is the line of symmetry of the pentagon and AF = 10 m.
Calculate the perimeter of the pentagon.
Give your answer correct to 3 significant figures.
........................... m
(6)
Q5
(Total 6 marks)
TOTAL FOR SECTION B: 19 MARKS
TOTAL FOR PAPER: 38 MARKS
END
6
*M22882A0608*
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
Topic Tutor GCSE Higher Maths St96 96
19/12/06 14:35:55
4A - Angles
10.
Leave
97
blank
15.
H
G
E
F
3cm
A
D
5 cm
Diagram NOT
accurately drawn
C
7 cm
B
The diagram represents a cuboid ABCDEFGH.
AB = 5 cm.
BC = 7 cm.
AE = 3 cm.
(a) Calculate the length of AG.
Give your answer correct to 3 significant figures.
(b) Calculate the size of the angle between AG and the face ABCD.
Give your answer correct to 1 decimal place.
°
..........................
(2)
A03 - Shape, space and measures
...................... cm
(2)
Q15
(Total 4 marks)
N17484A
18
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Topic Tutor GCSE Higher Maths St97 97
19/12/06 14:35:56
4A - Angles
98
LeaveLeave
blank blank
11. 19.
19.
The The
diagram
shows
somesome
of the
on aon
baseball
field.field.
diagram
shows
of markings
the markings
a baseball
29 m29 m
29 m29 m
18.418.4
m m
Diagram
NOTNOT
Diagram
accurately
drawn
accurately
drawn
ABCD
is a square.
ABCD
is a square.
AC isAC
a diagonal
of ABCD.
is a diagonal
of ABCD.
P is P
a point
on
AC.
is a point on AC.
ADEADE
and ABF
are straight
lines.lines.
and ABF
are straight
AP =AP
18.4
m. m.
= 18.4
Angle
PAE
= 45°.
Angle PAE
= 45°.
EF isEF
anisarc
centre
P and
29 m.
an of
arcthe
of circle,
the circle,
centre
P radius
and radius
29 m.
(a) (a)
By considering
triangle
PAE,PAE,
calculate
the size
of angle
AEP.AEP.
By considering
triangle
calculate
the size
of angle
GiveGive
youryour
answer
correct
to 3 to
significant
figures.
answer
correct
3 significant
figures.
…………………..°
…………………..°
(3) (3)
(3)
18
18
*N20905A01820*
*N20905A01820*
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
Topic Tutor GCSE Higher Maths St98 98
19/12/06 14:35:59
.............................................
4A - Angles
12. 17.
(Total 3 marks)
Q16
99
Diagram NOT
accurately drawn
The diagram shows a sketch of part of the curve y = sin x°.
(a) Write down the coordinates of point A.
( ............ , ..............)
(1)
*N20904A01320*
(2)
(Total 3 marks)
A03 - Shape, space and measures
(b) On the same diagram, sketch the graph of y = sin 2x°.
Q17
13
Turn over
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Topic Tutor GCSE Higher Maths St99 99
19/12/06 14:36:01
4A - Angles
100
Leave
blank
13. 20. Diagram 1 is a sketch of part of the graph of y = sin x°.
y
P
Q
Diagram 1
x
O
(a) Write down the coordinates of
(i) P,
( ......... , ......... )
(ii) Q.
( ......... , ......... )
(2)
Diagram 2 is a sketch of part of the graph of y = 3cos 2x°.
y
R
O
Diagram 2
x
S
(b) Write down the coordinates of
(i) R,
( ......... , ......... )
(ii) S.
( ......... , ......... )
(2)
(Total 4 marks)
16
Q20
*N20835A01620*
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
Topic Tutor GCSE Higher Maths St100 100
19/12/06 14:36:03
4A - Angles
101
Leave
blank
14. 20.
Diagram NOT
accurately drawn
The diagram shows part of two graphs.
The equation of one graph is
The equation of the other graph is
y = a sin x°
y = cos x° + b
(a) Use the graphs to find the value of a and the value of b.
b = ....................
(2)
(b) Use the graphs to find the values of x in the range 0° - x -720° when
a sin x° = cos x° + b
A03 - Shape, space and measures
a = ....................
x = ............................................
(2)
(c) Use the graphs to find the value of a sin x° – (cos x° + b) when x = 450°.
..........................
(2)
Q20
(Total 6 marks)
N17483RA
Topic Tutor GCSE Higher Maths St101 101
19
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Turn over
19/12/06 14:36:05
4A - Angles
102
15.
Leave
blank
6.
Diagram NOT
accurately drawn
AB is parallel to DE.
ACE and BCD are straight lines.
AB = 6 cm,
AC = 8 cm,
CD = 13.5 cm,
DE = 9 cm.
(i) Work out the length of CE.
………………… cm
(ii) Work out the length of BC.
………………… cm
(3)
(Total 3 marks)
*N20905A0720*
Q6
7
Turn over
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Topic Tutor GCSE Higher Maths St102 102
19/12/06 14:36:07
4A - Angles
16.
24.
103
Leave
blank
A
Diagram NOT
accurately drawn
X
B
C
D
ABC is an equilateral triangle.
AD is the perpendicular bisector of BC.
BX is the angle bisector of angle ABC.
(a) Show that triangle BXD is similar to triangle ACD.
In triangle ACD,
AC = 2 cm,
AD = √3 cm.
(b) Show that XD =
1
cm.
3
(3)
A03 - Shape, space and measures
(2)
Q24
(Total 5 marks)
END
20
TOTAL FOR PAPER: 100 MARKS
*N20904A02020*
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Topic Tutor GCSE Higher Maths St103 103
19/12/06 14:36:08
5 cm5 cm
4A - Angles
The The
diagram
shows
a model.
diagram
shows
a model.
The The
model
is a cuboid
withwith
a pyramid
on top.
model
is a cuboid
a pyramid
on top.
18.
The
base
of
the
model
is
a
square
with
sides
of length
5 cm.
The
base
of
the
model
is
a
square
with
sides
of length
5 cm.
17.
The The
height
of
the
cuboid
in
the
model
is
10
cm.
height of the cuboid in the model is 10 cm.
The The
height
the
in the
is 6 is
cm.
height
of pyramid
the pyramid
in model
the model
6 cm.
6ofcm
Diagram NOT
accurately drawn
(a) (a)
Calculate
the volume
of the
Calculate
the volume
of model.
the model.
104
Leave
blank
10 cm
5 cm
5 cm
................................
cm3 cm3
................................
The diagram shows a model.
(3) (3)
The model is a cuboid with a pyramid on top.
The base of the model is a square with sides of length 5 cm.
The The
model
represents
a concrete
post.
The
model
represents
a concrete
post. is 10 cm.
height
of
the cuboid
in the
model
The The
model
is
built
to
a
scale
of
1:30
The height
model of
is built
to a scale
the pyramid
in of
the1:30
model
is 6 cm.
The The
surface
area area
of the
is 290
cm2.cm2.
surface
of model
the model
is 290
(a) Calculate the volume of the model.
(b) (b)
Calculate
the surface
area area
of the
Calculate
the surface
of post.
the post.
GiveGive
youryour
answer
in
square
metres.
answer in square metres.
................................ cm3
(3)
The model represents a concrete post.
The model is built to a scale of 1:30
The surface area of the model is 290 cm2.
14
14
(b) Calculate the surface area of the post.
Give your answer in square metres.
.................................
m2 m2
.................................
(3) (3)Q18Q18
(Total
6 marks)
(Total
6 marks)
*N20904A01420*
*N20904A01420*
................................. m2
(3)
Q18
(Total 6 marks)
14
*N20904A01420*
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Topic Tutor GCSE Higher Maths St104 104
19/12/06 14:36:12
4A - Angles
105
Leave
blank
18. 18.
Diagram NOT
accurately drawn
Q
P
4 cm
Two cylinders, P and Q, are mathematically similar.
The total surface area of cylinder P is 90π cm2.
The total surface area of cylinder Q is 810π cm2.
The length of cylinder P is 4 cm.
(a) Work out the length of cylinder Q.
The volume of cylinder P is 100π cm3.
(b) Work out the volume of cylinder Q.
Give your answer as a multiple of π .
.................. cm3
(2)
A03 - Shape, space and measures
.................... cm
(3)
Q18
(Total 5 marks)
14
*N20835A01420*
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
Topic Tutor GCSE Higher Maths St105 105
19/12/06 14:36:13
4A - Angles
106
T = ....................
Q16
(Total 4 marks)
19. 17. X and Y are two geometrically similar solid shapes.
The total surface area of shape X is 450 cm2.
The total surface area of shape Y is 800 cm2.
The volume of shape X is 1350 cm3.
Calculate the volume of shape Y.
Leave
17. Two similar tins have heights 12 cm and 20 cm.
The volume of the smaller tin is 162 cm3.
3
.................... cm
(3)
(Total 3 marks)
20. 17. Calculate
thetins
volume,
in cm3, 12
of the
Two similar
have heights
cm larger
and 20tin.
cm.
3
N17484AThe volume of the smaller tin is 162 cm .
19
blank
Q17
Leave
blank
Turn over
Calculate the volume, in cm3, of the larger tin.
...................................... cm3
(3)
(Total 3 marks)
...................................... cm3
TOTAL FOR SECTION A: 60 MARKS
Q17
Q17
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
END
Topic Tutor GCSE Higher Maths St106 106
(Total 3 marks)
TOTAL FOR SECTION A: 60 MARKS
19/12/06 14:36:17
4A - Angles
Leave
107
blank
5.
21.
Diagram NOT
accurately drawn
B
A
O
C
D
A, B, C and D are four points on a circle, centre O.
AOC and BOD are straight lines.
A03 - Shape, space and measures
Prove that triangle AOD and triangle BOC are congruent.
You must give reasons for each stage of your proof.
Q5
(Total 3 marks)
(3)
*M22877A0508*
5
Turn over
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Topic Tutor GCSE Higher Maths St107 107
19/12/06 14:36:18
Q14Q14
....................
cm2 cm2
....................
(Total
3 marks)
(Total
3 marks)
4B - Properties of shapes
108
22. 15.
15.
PQRS
is a quadrilateral.
PQRS
is a quadrilateral.
P
Q
P
Q
Leave
blank
Leave
blank
Answer ALL SEVENTEEN questions.
Answer
SEVENTEEN
questions.
Write
yourALL
answers
in the spaces
provided.
instages
the spaces
provided.
YouWrite
mustyour
writeanswers
down all
in your
working.
S You
R Rin your working.
down some
all stages
S must write
1. Here is a list of ingredients
for making
Greek food for 6 people.
PQ is
parallel
to SR.
PQ
is parallel
to SR.
1. isSP
is aof
listgarlic
of
ingredients for making some Greek food for 6 people.
SP
parallel
to
RQ.
is parallel
to RQ.
2Here
cloves
4 ounces of chick peas
cloves
garlic
(a) (a)
Prove
thatofthat
triangle
PQSoil
is congruent
to triangle
RSQ.RSQ.
Prove
triangle
PQS
is congruent
to triangle
42 tablespoons
of
olive
4
ounces
of
chick
peas
5 fluid ounces of Tahina paste
4 tablespoons of olive oil
5 fluidout
ounces
of Tahina
paste
Work
the amount
of ingredients
to make the Greek food for 9 people.
Work out the amount of ingredients to make the Greek food for 9 people.
.......... cloves of garlic
(3) (3)
(3)
.......... ounces
cloves of
..........
of garlic
chick peas
(b) (b)
In quadrilateral
PQRS,
angleangle
SPQ is obtuse.
In quadrilateral
PQRS,
..........
ounces of chick
peasoil SPQ is obtuse.
..........
tablespoons
of olive
4B - Properties
shapes
Explain
whyof
PQRS
cannot
be a be
cyclic
quadrilateral.
Explain
why
PQRS
cannot
a cyclic
quadrilateral.
LIN 2 MOD 19
Q1
.......... fluid
tablespoons
oilpaste
..........
ounces of
of olive
Tahina
o
Q1
(Total 2 marks)
(2)Q15Q15
(Total 2 (2)
marks)
Find the number of sides of a polygon given
.......... fluid ounces of Tahina paste
exterior angles
2.
A regular polygon has an exterior angle of 20°
1. 2.
A regular polygon has an exterior angle of 20°
!
N17483RA
N17483RA
!
13
13
(Total
5 marks)
(Total
5 marks)
TurnTurn
overover
How many sides has this regular polygon?
How many sides has this regular polygon?
...........................
(2)
...........................
(Total 2 marks)
Q2
Q2
(Total 2 marks)
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
Topic Tutor GCSE Higher Maths St108 108
19/12/06 14:36:24
4C - 3-D Shapes and volumes
4C - 3-D shapes and volumes
1.
o
Draw and use plan and elevation of 3-D
shapes
o
Find the surface area of shapes by using area
of known 2-D shapes
o
o
109
LIN 22 MOD 31
Calculate volumes of prisms and cylinders
Find the volume and surface area of a
variety of complex shapes
Leave
blank
19. Here are the plan, front elevation and side elevation of a 3-D shape.
plan
front
elevation
side
elevation
A03 - Shape, space and measures
In the space below, draw a sketch of the 3-D shape.
Q19
(Total 2 marks)
637
20. Work out an estimate for the value of
3.2 × 9.8
(2)
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
Topic Tutor GCSE Higher Maths St109 109
19/12/06 14:36:26
4C - 3-D Shapes and volumes
110
Leave
blank
2. 10. Here are the plan and front elevation of a prism.
The front elevation shows the cross section of the prism.
Plan
Front Elevation
In the space below, draw a 3-D sketch of the prism.
Q10
(Total 2 marks)
(2)
268
GCSE Mathematics 2540/2544 Sample Assessment Material UG017663
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Topic Tutor GCSE Higher Maths St110 110
19/12/06 14:36:27
4C - 3-D Shapes and volumes
3.
111
Leave
blank
19.
Diagram NOT
accurately drawn
10 cm
8 cm
9 cm
6 cm
Work out the surface area of the triangular prism.
State the units with your answer.
A03 - Shape, space and measures
............................
(4)
(Total 4 marks)
Q19
20. The table shows some expressions.
a, b, c and d represent lengths.
π and 3 are numbers which have no dimensions.
3a
2
πab 3
3d
πbc
ac + bd
π (a + b)
3(c + d ) 3
3πbc 2
Q20
Tick () the boxes underneath the three expressions which could represent volumes.
(Total 3 marks)
*N20833A01520*
15
Turn over
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Topic Tutor GCSE Higher Maths St111 111
19/12/06 14:36:30
Leave
blank
4.
112
4C - 3-D Shapes
volumes
and
4. 4.
3.
(ii)
down
the greatest
possible
height
of the tower.
WorkWrite
out the
surface
area of the
triangular
prism.
3. A tower has a height of 124 m, correct to the nearest metre.
(i) Write down the least possible height of the tower.
Leave
blank
............................. m
Leave
blank
............................. m
Q3
(Total 2 marks)
............................. m
(ii) Write down the greatest possible height of the tower.
4.
5.
A tower has a height of 124 m, correct to the nearest metre. (i) Write down the least possible height of the tower.
Work out the surface area
ofthe triangular prism.
4.
Leave
blank
r cm
............................. m
Q3
(Total 2NOT
marks)
Diagram
................................. cm2
accurately drawn
(3)
(Total 3 marks)
Q4
................................. cm2
5.
The distance of the Earth from the Sun is 93 000 000 miles.
10 cm
(a) Write the number 93 000 000 in standard form.
5. The distance of the Earth from the Sun is 93 000 000 miles.
The diagram shows a cylinder.
The
radius the
of the
cylinder
is r 000
cm. in standard form.
(a) Write
number
000
r93cm
The length of the cylinder is 10 cm.
The volume of the cylinder is 140 cm3.
10 cm
–6
One Angstrom unit is 3.94 × 10 inches.
Work out the value of r.
The
showscorrect
a cylinder.
Givediagram
your answer
to 3 significant figures.
(b) Write this as an ordinary number.
–6
The
radius
of
the
cylinder
inches.
One Angstrom unit is 3.94 is× r10cm.
The length of the cylinder is 10 cm.
(b) Write this as an ordinary number.3
The volume of the cylinder is 140 cm .
Work out the value of r.
Give your answer correct to 3 significant figures.
Q4
(Total 3 marks)
Diagram NOT
accurately drawn
..............................................
(1)
..............................................
(1)
..............................................
(1)
Q5
..............................................
(Total 2 marks)
(1)
Q5
(Total 2 marks)
193
GCSE Mathematics 2540/2544 Sample Assessment Material UG017663
r = ............................. Q4
(3)
GCSE Mathematics 2540/2544 Sample Assessment
Material
UG017663
193
(Total
3 marks)
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
5
Topic Tutor GCSE Higher Maths St112 112
*M22878A0508*r = .............................TurnQ4over
19/12/06 14:36:35
15.
4C - 3-D Shapes and volumes
6. 15.
Diagram NOT
accurately drawn
113
Leave
blank
5 cm
4 cm
7 cm
Diagram NOT
accurately drawn
5 cm
3 cm
4 cm
Calculate the volume of the triangular prism.
7 cm
3 cm
Leave
Leave
blank
blank
Calculate the volume of the triangular prism.
5.
5.
Leave
blank
5.
..........................
(4)
(Total 4 marks)
Q15
..........................
(Total 4 marks)
Q15
7.
5.
(a)
(a) Calculate
Calculate the
the length
length of
of AC.
AC.
A03 - Shape, space and measures
(a) Calculate the length of AC.
Leave
blank
........................................
........................................ cm
cm
(2)
(2)
........................................ cm
(b)
(b) ABC
ABC isis the
the side
side of
of aa triangular
triangular prism
prism of
of length
length 10cm.
10cm.
(2)
(a) Calculate the length of AC.
Calculate
Calculate the
the volume
volume of
of the
the triangular
triangular prism.
prism.
(b) ABC is the side of a triangular prism of length 10cm.
Calculate the volume of the triangular prism.
........................................
........................................ cm
cm
(3)
(3) cm
Q5
Q5
........................................
N17481A
Turn
over
13
(2)3
........................................ cm
(Total
(Total 55 marks)
marks)
(3)
Q5
(b) ABC is the side of a triangular prism of length 10cm.
6.
3x
6. Simplify
Simplify
3x33yy22 ×× xx22yy33
(Total 5 marks)
N17481A
Turn over
13
Calculate the volume of the triangular prism.
6.
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
Simplify
Topic Tutor GCSE Higher Maths St113 113
3x3y2 × x2y3
19/12/06 14:36:44
LeaveLeave
blank blank
4C - 3-D Shapes and volumes
114
18. 18.
8.
6 cm6 cm
Diagram
NOTNOT
Diagram
accurately
drawn
accurately
drawn
10 cm
10 cm
5 cm5 cm
5 cm5 cm
The The
diagram
shows
a model.
diagram
shows
a model.
The The
model
is
a
cuboid
with
a pyramid
on top.
model is a cuboid with
a pyramid
on top.
The The
basebase
of the
is a square
withwith
sidessides
of length
5 cm.5 cm.
ofmodel
the model
is a square
of length
The The
height
of
the
cuboid
in
the
model
is
10
cm.
height of the cuboid in the model is 10 cm.
The The
height
of the
in theinmodel
is 6 cm.
height
ofpyramid
the pyramid
the model
is 6 cm.
(a) Calculate
the volume
of the
(a) Calculate
the volume
ofmodel.
the model.
................................
cm3 cm3
................................
(3) (3)
The The
model
represents
a concrete
post.post.
model
represents
a concrete
The The
model
is
built
to
a
scale
of
1:30
model is built to a scale of 1:30
2
The The
surface
area area
of the
is 290
surface
ofmodel
the model
is cm
290.cm2.
(b) Calculate
the surface
area area
of the
(b) Calculate
the surface
ofpost.
the post.
GiveGive
youryour
answer
in
square
metres.
answer in square metres.
.................................
m2 m2
.................................
(3) (3)Q18Q18
(Total
6 marks)
(Total
6 marks)
14
14
*N20904A01420*
*N20904A01420*
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Topic Tutor GCSE Higher Maths St114 114
19/12/06 14:36:47
Leave
115
blank
4C - 3-D Shapes and volumes
7.
9.
Diagram NOT
accurately drawn
10 cm
11 cm
3.5 cm
12 cm
A rectangular container is 12 cm long, 11 cm wide and 10 cm high.
The container is filled with water to a depth of 8 cm.
A metal sphere of radius 3.5 cm is placed in the water.
It sinks to the bottom.
Calculate the rise in the water level.
Give your answer correct to 3 significant figures.
A03 - Shape, space and measures
......................... cm
(4)
(Total 4 marks)
Q7
TOTAL FOR SECTION B: 19 MARKS
TOTAL FOR PAPER: 38 MARKS
END
*M22900A008*
7
Turn over
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Math147295_M22990A.indd 7
Topic Tutor GCSE Higher Maths St115 115
31/08/2005 14:0
19/12/06 14:36:48
116
Leave
blank
4C - 3-D Shapes and volumes
21.
10.
The radius of the base of a cone is x cm and its height is h cm.
The radius of a sphere is 2x cm.
The volume of the cone and the volume of the sphere are equal.
Express h in terms of x.
Give your answer in its simplest form.
h = ....................................
(3)
(Total 3 marks)
*N20835A01720*
Q21
17
Turn over
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Topic Tutor GCSE Higher Maths St116 116
19/12/06 14:36:49
4C - 3-D Shapes and volumes
117
Leave
blank
11. 23. The diagram shows a sector of a circle with a radius of x cm and centre O.
PQ is an arc of the circle.
Angle POQ = 120°.
Leave
blank
x cm
O
P
The sector is the net of the curved surface
of
this
cone.
120°
Arc PQ forms the circumference of the circle that makes the base of the cone.
Diagram NOT
accurately drawn
x cm
Q h cm
The sector is the net of the curved surface of this cone.
Arc PQ forms the circumference of the circle that makes the base of the cone.
The
sector
is
the
netexpression
of the curved
surface
this xcone.
π and
for
(a) Write down an
in terms
of of
Arc PQ forms the circumference of the circle that makes the base of the cone.
Leave
blank
(i) the area of this sector,
x cm
x cm
..........................
(ii) the arc length of this sector.
Given that V = 3A,
(b) find the value of h.
2
The curved surface area of the cone is A cm .
The volume of the cone is V cm3.
2
.
The curved surface
area ofofthe
The height
thecone
coneisisAhcm
cm.
3
The volume of the cone is V cm .
The height of the
conethat
is hVcm.
Given
= 3A,
..........................
(2)
A03 - Shape, space and measures
The curved surface area of the cone ishAcm
cm2.
3
The volume of the cone is V cm .
The height of the cone hiscm
h cm.
Given that V = (b)
3A, find the value of h.
(b) find the value of h.
..........................
(3)
Q23
(Total 5 marks)
N17483RA
22
TOTAL FOR PAPER: 100 MARKS
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END
Topic Tutor GCSE Higher Maths St117 117
19/12/06 14:36:55
4D - Pythagoras' theorem
118
4D - Pythagoras' theorem
o
1.
Use Pythagoras' theorem to find one side of
a right– angled triangle given the other two
sides
4.
LIN 19, 31 MOD 29, 39
o
Use Pythagoras' theorem in unstructured
situations
o
Use Pythagoras' theorem in 3-D configurations
Diagram NOT
accurately drawn
P
Leave
blank
5.7 cm
Q
9.3 cm
R
In triangle PQR,
QR = 9.3 cm.
PQ = 5.7 cm.
Angle PQR = 90º.
Calculate the length of PR.
Give your answer correct to 3 significant figures.
............................... cm
(3)
(Total 3 marks)
5.
Q4
(a) Write 0.032 in standard form.
....................................
(1)
(b) Write 1.58 × 104 as an ordinary number.
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
Topic Tutor GCSE Higher Maths St118 118
....................................
(1)
19/12/06
Q5
14:36:57
accurately
drawn
accurately
drawn
Leave
119
blank
4D - Pythagoras' theorem
O O
16 cm
16 cm
A
19.
2.
C
C
12 cm
12 cm
B
Diagram NOT
accurately drawn
B
O
The diagram
shows
triangle
ABC ABC
and a16
circle,
centre
O. O.
The diagram
shows
triangle
and
a
circle,
centre
cm
A, B A,
andBCand
areCpoints
on the
of theofcircle.
are points
oncircumference
the circumference
the circle.
AB isAB
a diameter
of theofcircle.
is a diameter
the circle.
12 cm
B
AC =AC
16 =cm
12 =cm.
16and
cmBC
and=BC
12 cm. C
(a) Angle
ACB ACB
= 90o=. 90o.
(a) Angle
The Give
diagram
shows
triangle ABC and a circle, centre O.
Give
a reason
why. why.
a reason
A, B and C are points on the circumference of the circle.
AB
is.......................................................................................................................................
a diameter of the circle.
.......................................................................................................................................
(1) (1)
AC = 16 cm and BC = 12 cm.
A03 - Shape, space and measures
(a)
ACB
90o. AB ofAB
(b) Work
out the
diameter
theofcircle.
(b) Angle
Work
out
the= diameter
the circle.
Give a reason why.
.......................................................................................................................................
(1)
(b) Work out the diameter AB of the circle.
............................
cm cm
............................
(3) (3)
(c) Work
out the
theofcircle.
(c) Work
outarea
the of
area
the circle.
Give Give
your your
answer
correct
to 3 significant
figures.
answer
correct
to 3 significant
figures.
............................ cm
(3)
(c) Work out the area of the circle.
Give your answer correct to 3 significant figures.
............................
cm2 cm2
............................
(3) (3)Q19 Q19
(Total
7 marks)
(Total
7 marks)
*M20834A01524*
*M20834A01524*
15
15
TurnTurn
over over
............................ cm2
Q19
(3)
(Total 7 marks)
*M20834A01524*
15
Turn over
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
Topic Tutor GCSE Higher Maths St119 119
19/12/06 14:37:02
120
Leave
blank
4D - Pythagoras' theorem
20.
A
3. 20.
A
10 cm
17 cm
10 cm
D
17 cm
B
Diagram NOT
accurately drawn
B
Diagram NOT
accurately drawn
Leave
blank
C
ABCD is a rectangle.D
AC = 17 cm.
AD = 10 cm.
ABCD is a rectangle.
AC = 17 cm.
Calculate the length of the side CD.
AD = 10 cm.
Give your answer correct to one decimal place.
C
Calculate the length of the side CD.
Give your answer correct to one decimal place.
5. 5.
5.
4.
.....................cm
Q20
Leave
Leave
(3)
Leave
blank
blank
blank
(Total 3 marks)
.....................cm
Q20
(Total 3 marks)
Calculate
the length
of AC.
(a) (a)
Calculate
the length
of AC.
(a) Calculate
the length
of AC.
N17482A
22
........................................
........................................
cm cm
........................................
cm
(2) (2)
(2)
(b) ABC is the side
a triangular
prism
of length
10cm.
of a of
triangular
prism
of length
10cm.
side
of a triangular
prism
of length
10cm.
22
(b) ABC
is theisside
(b) ABC
the
N17482A
This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited
Calculate
the volume
of triangular
the triangular
prism.
Calculate
the volume
of the
prism.
Calculate
the volume
of the triangular
prism.
Topic Tutor GCSE Higher Maths St120 120
19/12/06 14:37:09
LeaveLeave
blank121
blank
4D - Pythagoras' theorem
15. 15.
H
5.
E
E
F
A
5 cm5 cm
D
B
G
G
Diagram
NOTNOT
Diagram
accurately
drawn
accurately
drawn
C
C
F
3cm 3cm
A
H
D
7 cm7 cm
B
The diagram
represents
a cuboid
ABCDEFGH.
The diagram
represents
a cuboid
ABCDEFGH.
AB =AB
5 cm.
= 5 cm.
BC =BC
7 cm.
= 7 cm.
AE =AE
3 cm.
= 3 cm.
(a) Calculate
the length
of AG.
(a) Calculate
the length
of AG.
GiveGive
youryour
answer
correct
to 3 significant
figures.
answer correct
to 3 significant
figures.
(b) Calculate
the size
between
AG and
ABCD.
(b) Calculate
the of
sizetheofangle
the angle
between
AG the
andface
the face
ABCD.
GiveGive
youryour
answer
correct
to
1
decimal
place.
answer correct to 1 decimal place.
A03 - Shape, space and measures
......................
cm cm
......................
(2) (2)
° °
..........................
..........................
(2) (2)Q15 Q15
(Total
4 marks)
(Total
4 marks)
N17484A
N17484A
18
18
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Topic Tutor GCSE Higher Maths St121 121
19/12/06 14:37:12