Download Gr 10 Term 1 Investigation 2019

Basic Education
KwaZulu-Natal Department of Education
REPUBLIC OF SOUTH AFRICA
NAME:...........................................................................................................................
MATHEMATICS
COMMON TASK - INVESTIGATION
TERM 1 2019
S.B.A
TASK
GRADE 10
MARKS:
60
TIME:
1 hour
2
INSTRUCTIONS AND INFORMATION
Read the following instructions carefully before answering the questions.
1. This investigation consists of 3 questions.
2. Answer ALL the questions.
3. Number the answers correctly according to the numbering system used in this
question paper.
4. Clearly show ALL calculations, diagrams, graphs et cetera that you have used
in determining your answers.
5. Answers only will not necessarily be awarded full marks.
6. You may use an approved scientific calculator (non-programmable and nongraphical), unless stated otherwise.
7. If necessary, round off answers to TWO decimal places, unless stated
otherwise.
8. Write neatly and legibly.
3
QUESTION 1
1.1
Solve for x in the triangle below given that AB = 4cm , BC = 3cm and AC = x.
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(2)

1.2
In the diagram below, given that XY = 3cm , X Z Y  30 0 and YZ = x, is it
possible to solve for x using the theorem of Pythagoras? Motivate your
answer.
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(2)
[4]
4
QUESTION 2
In each of the similar triangles labelled 1 to 5 on your diagram sheet, the OPP
(opposite), ADJ (adjacent) and HYP (hypotenuse) sides are denoted by the letters o,
a and h respectively:
2.1
2.2
2.3
Measure the length of each side, and record your measurements in the
columns assigned for that, to the nearest mm, in the table below.
(5)
Measure each of the marked angles and record your measurement in the
column assigned for that, to the nearest degree, in the table below.
(5)
When you are done with your measurements, use them to complete the
remaining columns on ratios, as indicated.
(18)
Lengths in mm

Angle
OPP
(0)
ADJ
(a)
HYP
(h)
Ratios
Fraction
Decimal
(2dp)
Fraction
Decimal
(2dp)
Fraction
Decimal
(2dp)
1
2
3
4
5
2.4
Write down the mean values of your ratios below:
(use the decimal columns to work them out):
(6)
opposite
=
hypotenuse
2.5
=
=
Complete the statement below by writing down your observation on the values
of your respective ratios for each of the triangles 1 to 5:
2.5.1. Even though the triangles are all different sizes, the decimal values for each
ratio are____________________________.”
(2)
5
2.5.2. Although the sides of the triangles are of different measurements
2.5.2.1. all triangles are ……………………angled triangles .
(1)
2.5.2.2. the angle opposite the OPP side is ………..………..
(1)
2.5.2.3. the corresponding sides of all these triangles are in ………......
(1)
[39]
QUESTION 3
These ratios (from 2.4. above) are given special names .
=
sine
= cosine
= tangent
All 3 of the above ratios are written as sin Θ or cos Θ or tan Θ
Where Θ is the angle of reference .
For example sin 30̊ , so sin 30̊ =
3.1
Now use your calculator to evaluate the following values to 2 decimal places:
sin30o
cos30o
tan30o
(6)
3.2. Compare your values in question 3.1 with the mean values you calculated in
question 2.4 and draw a conclusion from your observation. Write down your
conclusion below.
___________________________________ ________________________________
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(3)
6
3.3. What would happen if the angle measured in table 2.3 was 42̊ ?
Explain your answer by calculating any one of the three trigonometric
ratios discussed above.
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(4)
3.4.
Using the knowledge, you have discovered in this investigation, solve for x in
question 1.2.
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(4)

3.5
In  PQR below, QR = 5,5 cm and Q R P =60o, calculate the length of PR.
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(3)
[20]
GRAND TOTAL: 60
Diaeram Sheet
1. ldentify sides
2. Measure the length of
each side (in mm). '
3.' Measure the marked angle
4. Record on table Provided