Grade 11 EoS1

Inductive/Deductive

100

Inductive or Deductive?

A teacher notices that in three different classes, students who practice math problems daily tend to score higher on tests. The teacher concludes that daily practice improves test performance.

Inductive - The teacher is making a general conclusion based on specific observations. 

200

School policy states: “All students who attend bi-weekly tutorials will receive extra support in higher-order thinking problems.”
Alex attends the bi-weekly tutorials. Therefore, Alex will receive extra support.

Deductive – The conclusion follows logically from a general rule applied to a specific case.

300

You observe the following pattern in a sequence:
2, 4, 8, 16, …
What conjecture can you make about the next term in the sequence?

The pattern shows each term is multiplied by 2. The next term is 32.

400

Inductive or deductive? Make a conjecture 

A rule states: If a number is divisible by 4, then it is also divisible by 2.
Given that 24 is divisible by 4, what can you conclude?

24 is divisible by 2.
This is deductive reasoning because the conclusion follows from a general rule applied to a specific case.

500

Make a conclusion

You observe that in several math tutorial sessions, students who attend regularly tend to perform better on higher-order thinking problems. Based on this pattern, what general conclusion can you draw about the impact of attending these tutorials?

Regular attendance at the tutorials is likely associated with improved performance on challenging math problems. This suggests that participation in these sessions may enhance problem-solving skills.

Properties of angles and triangles

100

Sum of the interior angles of a triangle is ______

180 degrees 

200

Sum of interior angles formula

Sn=(n-2)180

300

Find the size of an interior angle of a regular hexagon

120 degrees

400

Find the supplement angle of 50 degrees

130 degrees 

500

Find the size of an exterior angle of a regular pentagon

72 degrees 

Acute Triangle Trigonometry

100

What's the formula for the sine rule/law of sines?

a/SinA = b/SineB = c/SineC

OR

SinA/a = SinB/b = SinC/c

200

What is the formula for the cosine rule/Law of Cosines?

a^2=b^2+c^2-2bcCosA   OR

b^2=a^2+c^2-2acCosB   OR

c^2-a^2+b^2-2abCosC

300

In triangle ABCABCABC,

∠A=40∘, ∠B=75∘, and a=12 cm

Find the length of side b (to 1 decimal place)

18.0 cm

400

In triangle XYZ

x=8 cm, y=6 cm, ∠Z=120∘ 

Find the length of side z (round to the nearest whole number)

12cm

500

Triangle PQR has sides p=10 cm, q=7 cm, r=9 cm. Find ∠R. (round to the nearest angle)

61 degrees

Oblique Triangle Trigonometry

100

Determine the acute angle A so that sine A = 0.44 (round your answer to the nearest degree)

26 degrees

200

Determine the two angles between 0 degrees and 180 degrees that have the sine ratio of 0.125 (round to 2 decimal places)

angle 1 = 7.18 degrees

angle 2 = 180-7.18 = 172.82 degrees 

300

In triangle ABC, you are given:

∠A=40∘, side a=8 cm, and side b=10 cm (adjacent to ∠A).

Is this an SSA (Side-Side-Angle) situation? 

Yes

• You know one angle (∠A) and two sides (a and b).
• The known angle is not between the two given sides (it’s opposite one of them), which makes it SSA rather than SAS.

400

In triangle ABC

∠A=40∘, side a=12 cm, side b=15 cm.

Find possible sizes for ∠B (round to the nearest degree)

53 degrees and 127 degrees 

500

Which set of measurements can produce two possible triangles?

A. ∠A=62∘, a=3.2 cm, b=4.0
B. ∠A=90∘, a=5.0 cm, b=7.0 cm
C. ∠A=45∘, a=6.0 cm, b=6.0
D. None of the above

A