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Department of Education
MOPANI DISTRICT
MARKS: 100 DURATION: 2 hours
This investigation has 9 pages including the cover page and diagram sheet
CAPS
GRADE 10
MATHEMATICS TERM 1 INVESTIGATION
FEBRUARY 2024
MOPANI WEST TERM 1 INVESTIGATION 2024 GRADE 10
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INSTRUCTIONS AND INFORMATION
1. This investigation consists of 5 questions.
2. Answer ALL the questions.
3. Number the answers correctly according to the numbering system used in this
investigation.
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 non-graphical),
unless stated
otherwise.
7. If necessary, round off answers to TWO decimal places, unless stated otherwise.
MOPANI WEST TERM 1 INVESTIGATION 2024 GRADE 10
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QUESTION 1:
1.1 Solve for 𝑥 in the given triangle. It is given that 𝐴𝐵 = 4𝑐𝑚 , 𝐵𝐶 = 3𝑐𝑚
and 𝐴𝐶 = 𝑥. (2)
1.2 In the diagram below, given that = 3𝑐𝑚 , 𝑋�̂�𝑌 = 30° and 𝑌𝑍 = 𝑥. Is it possible
to solve for 𝑥 using the theorem of Pythagoras? Motivate your answer. (2)
[𝟒]
MOPANI WEST TERM 1 INVESTIGATION 2024 GRADE 10
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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. Copy the table below and answer the questions that follow:
2.1 Measure the length of each side, and record your measurements in the columns
assigned for that, to the nearest mm. (5)
2.2 Measure each of the marked angles and record your measurement in the column
assigned for that, to the nearest degree. (5)
2.3 When you are done with your measurements, use them to complete the remaining
columns on ratios, as indicated. (15)
2.4. Determine the mean values of your ratios: (use the decimal columns to work them
out)
2.4.1.
opposite
hypoteneus
= _____ (2)
2.4.2.
adjacent
hypoteneus
= ______ (2)
∆ Angle
Lengths in mm Ratios
OPP
(o)
ADJ
(a)
HYP
(h)
𝑂𝑃𝑃
𝐻𝑌𝑃
𝐴𝐷𝐽
𝐻𝑌𝑃
𝑂𝑃𝑃
𝐴𝐷𝐽
Fraction Decimal Fraction Decimal Fraction Decimal
1
2
3
4
5
MOPANI WEST TERM 1 INVESTIGATION 2024 GRADE 10
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2.4.3.
opposite
adjacent
= _____ (2)
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:
Even though the triangles are all different sizes, the decimal values of each ratio is
(2.5.1). Although the sides of the triangles are of different measurements, all the
triangles are (2.5.2) angled triangles. The angle opposite the OPP side is (2.5.3).
The corresponding sides of all these triangles are in (2.5.4) (4)
[36]
QUESTION 3
The ratios (from 2.4. above) are given special names:
opposite
hypoteneus
= sine
adjacent
hypoteneus
= cosine
opposite
hypoteneus
= tangent
All 3 of the above ratios are written as sin θ or cos θ or tan θ.
θ is the angle of reference.
For example: sin 30° , therefor sin 30° =
opposite
hypoteneus
3.1. Now use your calculator to evaluate the following values to 2 decimal places:
3.1.1 sin 30° (2)
3.1.2 cos 30° (2)
3.1.3 tan 30° (2)
MOPANI WEST TERM 1 INVESTIGATION 2024 GRADE 10
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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. (3)
3.3. What would happen if the angles measured in 2.2 was 42° ?
Explain your answer by calculating any one of the three trigonometric ratios discussed
above. (4)
3.4. Using the knowledge, you have gained in this investigation, solve for 𝑥 in question
1.2. (4)
3.5. In ∆𝑃𝑄𝑅 below, 𝑄𝑅 = 5,5 𝑐𝑚 and 𝑃�̂�𝑄 = 60°. Calculate the length of PR. (3)
[𝟐𝟎]
MOPANI WEST TERM 1 INVESTIGATION 2024 GRADE 10
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QUESTION 4:
The three circles have radii 2, 3 and 5 units.
4.1. Read, as accurately as possible, the co-ordinates of the points marked. Copy the table
below and complete the table below. (9)
𝑥 − co
ordinate
𝑦 − co
ordinate
𝑦
𝑟
𝑥
𝑟
𝑦
𝑥
𝐴1
𝐴2
𝐴3
𝐵1
𝐵2
𝐵3
𝐶1
𝐶2
𝐶3
MOPANI WEST TERM 1 INVESTIGATION 2024 GRADE 10
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4.2. Write any observations about what you have read and calculated using the co-
ordinates of the nine points. (6)
[𝟏𝟓]
QUESTION 5:
5.1. Use your calculator to investigate the properties of the following trigonometric ratios.
Record all your results in a table.
5.1.1. the maximum and minimum values (if they exist) of sin θ , cos θ and tan θ
for any values of θ (try multiples of 10°). (10)
5.1.2. the value(s) of sin 2θ + cos2θ for at least 5 values of θ (use θ = 0° , some
positive values and some negative values). (5)
5.1.3. the values of sinθ , cosθ ,
sinθ
cosθ
and tanθ for at least 5 values of θ. (5)
5.2. Write any observations about the results you obtained through your calculator work.
(5)
[𝟐𝟓]
MOPANI WEST TERM 1 INVESTIGATION 2024 GRADE 10
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DIAGRAM SHEET
𝑎
𝑜
ℎ
1
𝑎
𝑜
ℎ
3
𝑎
𝑜
ℎ
2
𝑎
𝑜
ℎ
4
𝑎
𝑜
ℎ
5
