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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