Quiz Answer Key and Fun Facts
1. We start with an infamous Pythagoras' Theorem question. The hardworking student Alicia takes one look at it and says: "this is a 3-4-5 triangle", a specific type of triangle that satisfies Pythagoras' Theorem, as 3^2 + 4^2 = 5^2.
However, the missing side length is not 5 cm long. What's the problem?
2. The corresponding angles rule is nicknamed "the F rule" (with friends "the C rule" and "the Z rule") because of the shape you need to look for in a diagram to find corresponding angles. The eager Alicia immediately writes down: "angle x° is 120° because corresponding angles are equal". However, here our "F rule" cannot be used to conclude this. Why not?
3. "Angles on a straight line add up to 180°" is what Alicia says when shown this image. We've been given one angle, 100°, so the other marked angle, x, must be 80°. What's the problem?
4. "This one is pi*4*4 = 16pi cm^2", Alicia says, when asked to find the area of the given circle. But it's not. What common mistake has she made?
5. What is the area of this triangle? Alicia recalls "half times the base times the height" as the rule, or "1/2bh" symbolically. So what's the problem with the proposed calculation of the area, 1/2*4*7 = 14 cm^2?
6. "Angles in a quadrilateral (four-sided polygon) add up to 360°. So the angles in this shape should sum to 360°: a°+b°+c°+d°+e° = 360°", Alicia thinks.
Her friend Benjamin says, "you can't do that!" What's the problem?
7. "Opposite angles in a cyclic quadrilateral add up to 180°", says Alicia. But Bob takes a look at the angle x° and knows that it can't be 80° - "it's clearly bigger than a right angle, which would be 90°". Which of them "can't do that!", and why not?
8. Bob takes a punt at the next question: "it's a triangle, so the angles add up to 180°, and we already have two marked angles of 90° and 30°, so that makes x° = 60°". Alicia says, "you can't do this... and something about this question isn't right". What isn't right?
9. Alicia is trying to find the gradient of this curve, and she recites the rule "the gradient is the change in y over the change in x". She plots two points on the curve, A(0,0) and B(2,4). According to Alicia, the change in y is 4-0 = 4, and the change in x is 2-0 = 2. Then, 4/2 = 2, so the gradient of the curve is 2.
What's the problem?
10. Lastly, let's help Alicia and Bob, who are confused about this question. Alicia is insisting that we can use "SOHCAHTOA" to find the missing side length, x.
SOHCAHTOA helps us select the right trig value, either "sine", "cosine" or "tangent" depending on which two sides out of "hypotenuse", "opposite" and "adjacent" we are looking at in the question.
"It must be 8*sin(30°) = 4 cm long", Alicia evaluates. Bob does not agree. What is the problem?
Source: Author
AdamM7
This quiz was reviewed by FunTrivia editor
rossian before going online.
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