Purpose: To apply the proficiencies of understanding and fluency and reasoning and problem solving across the topics of Geometric Reasoning, Pythagoras’ Theorem and Trigonometry. Students will apply
mathematical processes, solve problems and communicate their understanding. This exam contributes 50% to the final grade for the semester.
A B C D E
The folio of a student’s work has the following characteristics:
Un
de
s
ta
nd
in
g
an
d
flu
en
cy
Co
nc
ep
tu
al
un
de
s
ta
nd
in
g connection and description of
mathematical concepts and
elationships in unfamiliar situations
connection and description of
mathematical concepts and relationships
in complex familiar situations
ecognition and identification of
mathematical concepts and relationships
in simple familiar situations
some identification of simple
mathematical concepts
statements about obvious mathematical
concepts
P
oc
ed
u
al
flu
en
cy
recall and use of facts, definitions,
technologies and procedures to find
solutions in unfamiliar situations
ecall and use of facts, definitions,
technologies and procedures to find
solutions in complex familiar situations
ecall and use of facts, definitions,
technologies and procedures to find
solutions in simple familiar situations
some recall and use of facts, definitions,
technologies and simple procedures
partial recall of facts, definitions or simple
procedures
Ma
th
em
at
ica
l
lan
gu
ag
e a
nd
sy
m
o
ls effective and clear use of appropriate mathematical
terminology, diagrams, conventions
and symbols
consistent use of appropriate
mathematical terminology, diagrams,
conventions and symbols
use of appropriate mathematical
terminology, diagrams, conventions and
symbols
use of aspects of mathematical
terminology, diagrams and symbols
use of everyday language
P
o
lem
-s
ol
vin
g
an
d
e
as
on
in
g P
o
l
em
so
lvi
ng
ap
p
oa
ch
es
systematic application of relevant
problem-solving approaches to
investigate unfamiliar situations
application of relevant problem-solving
approaches to investigate complex
familiar situations
application of problem-solving
approaches to investigate simple familiar
situations
some selection and application of
problem-solving approaches in simple
familiar situations
partial selection of problem-solving
approaches
Ma
th
em
at
ica
l
m
od
ell
in
g
development of mathematical
models and representations in
unfamiliar situations
development of mathematical models
and representations in
complex familiar situations
development of mathematical models
and representations in simple familiar
situations
statements about simple mathematical
models and representations
isolated statements about given mathematical
models and representations
Re
as
on
in
g
an
d
ju
st
ifi
ca
tio
n clear explanation of mathematical
thinking and reasoning, including
logical justification of choices made,
evaluation of strategies used, proofs
formulated and conclusions reached
explanation of mathematical thinking and
easoning, including reasons for choices
made, strategies used, proofs formulated
and conclusions reached
description of mathematical thinking and
easoning, including discussion of
choices made, strategies used, proofs
formulated and conclusions reached
statements about choices made,
strategies used and conclusions reached
isolated statements about given strategies or
conclusions
Key shading emphasises the qualities that discriminate between the A–E descriptors
Formula sheet (10 Mathematics – Standard)
Mensuration
circumference of a
circle C = 2π r area of a circle A = π r²
area of a
parallelogram A = b h area of a trapezium A = ½(a + b)h
area of a triangle A = ½ b h volume of a prism V = A h
total surface area of
a cylinder S = 2π r h + 2π r² volume of a cylinder V = π r² h
Finance
simple interest ?? = ?????? compound interest ?? = ??(1 + ??)??
Trigonometry
trigonometric ratios ?????? ??= ????????????????â„Ž?????????????????? ?????? ??=
????????????????
â„Ž??????????????????
?????? ??= ????????????????
????????????????
Pythagoras’ theorem ??2 + ??2 = ??2
Statistics
mean ?? = ?????? ???? ?????? ???????? ????????????
???????????? ???? ???????? ????????????
?? = ∑????
??
median �??+1
2
�
??â„Ž
data value
Probability
probability of an
event occu
ing ??(??????????) =
???????????? ???? ???????????????????? ????????????????
?????????? ???????????? ???? ????????????????
probability of
independent events ??(?? ?????? ??) = ??(??) × ??(??)
conditional
probability ??(??|??) =
??(?? ∩ ??)
??(??)
WORKING is to be completed on this paper. If you need extra room or to redo a
question, note this on this paper and attach the extra pages used. Be sure to label
your work clearly.
Question 1 XXXXXXXXXXSF UF XXXXXXXXXXmark
State the bearing of the point P in each of the following diagrams:
a)
)
Question 2 XXXXXXXXXXSF PSR XXXXXXXXXXmarks
A helicopter hovers 152m directly above an ocean swimmer. A boat is 300m from the
swimmer.
Draw and label a diagram and determine the angle of depression from the helicopter to
the boat, co
ect to the nearest degree.
Question 3 XXXXXXXXXXSF UF XXXXXXXXXX½ marks
Use techniques of deduction to determine the following
a) If ?? = 12 and ?? = ?? then determine ??
) If ?? + ?? = 31 and ?? = ?? then determine ?? + ??
c) If ?? + ?? = 18 and ?? + ?? = 18 then what is the relationship between ?? and ??.
Question 4 XXXXXXXXXXSF PSR XXXXXXXXXXmarks
A square field has a diagonal of 18m. The owner would like to install a fence on all four sides of
the field. Determine the length of fencing required. (Give your answer co
ect to 2 decimal places)
Question 5 XXXXXXXXXXSF UF XXXXXXXXXXmarks
Calculate the value of t in the triangle below, co
ect to two decimal places.
Question 6 XXXXXXXXXXSF UF XXXXXXXXXX½ marks
In the diagram given, ???? = ???? and ???? ∥ ????
Prove ∆?????? is congruent to ∆?????? by completing the table.
Statement Reason
1
???? = ????
XXXXXXXXXXGiven
2
3
4
∆?????? ≅ ∆??????
Question 7 XXXXXXXXXXSF UF XXXXXXXXXX½ marks
The two triangles in the diagram are similar. Determine the width of the river, to the
nearest metre.
Question 8 XXXXXXXXXXSF PSR XXXXXXXXXX½ marks
An observer who is standing 32m from a building measures the angle of elevation of the top of the
uilding as 25°. If the observer’s eye is 170cm from the ground, determine the height of the
uilding, co
ect to 2 decimal places.
Question 9