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Two Truths and a Lie - Mathematics
For each question, you are given three math-related statements and... STOP IT! An evil demon has manipulated them so now there's a false statement in every question! Can you identify each false statement?
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Last updated: April 2, 2022
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| First submitted | March 24, 2022 |
| Times taken | 31 |
| Average score | 60.0% | Report this quiz | Report |
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1.
Which statement is false?
If y = kx for some constant k, then dy/dx = k
✓
The sum of a geometric series is given by the formula: S = a / (1 − r)
✓
If n is odd, then n2 must be odd
✓
The sum to infinity of a convergent geometric series is given by the formula S = a / (1 − r); the sum of the first n terms of a geometric series is given by S = a(1 − rn) / (1 − r) or S = a(rn − 1) / (r − 1)
2.
Which statement is false?
The following identity is always true: sin(A + B) = sin A + sin B
✓
The Pythagorean theorem states that: a2 + b2 = c2
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The distributive property of multiplication is: a(b + c) = ab + ac
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sin(A + B) = sin A cos B + cos A sin B
3.
Which statement is false?
The graph of y = 1 / x has asymptotes at the coordinate axes
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If y = sin x, then dy/dx = cos x
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If f'(x) = 0 for some value of x, then (x,f(x)) must be the maximum point of the curve
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It could be the local maximum point or the local minimum point, not necessarily the maximum point
4.
Which statement is false?
The slope of a line is given by the formula: m = (y2 − y1) / (x2 − x1)
✓
All angles in a quadrilateral must be smaller than 180°
✓
The graph of y = f(x + 3) is a translation of the graph of y = f(x) 3 units to the left
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Not necessarily; one of the angles could be reflex
5.
Which statement is false?
(a + b)2 = a2 + b2
✓
The following identity is always true: logab = 1 / logba (a≠1, b≠1)
✓
Any non-zero number raised to the power of zero is 1
✓
(a + b)2 = a2 + 2ab + b2
6.
Which statement is false?
The power of a power rule is: (am)n = am + n
✓
The modulus of vector x = 3i + 4j is 5
✓
The identity sin2x + cos2x = 1 is true for all values of x
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The power of a power rule should be: (am)n = amn
7.
Which statement is false?
The following sequence is arithmetic: 1, 3, 6, 10, ...
✓
Euler's identity states that: eiπ + 1 = 0
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The graph of y = 2x + 1 meets the x-axis at the point (−½,0)
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The difference between two consecutive terms in an arithmetic sequence must be equal
8.
Which statement is false?
The power of a product rule is: (ab)n = anbn
✓
The quadratic equation x2 − 2x − 3 = 0 has only one solution
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The binomial expansion of (x + 1)3 is: x3 + 3x2 + 3x + 1
✓
Calculating the discriminant of the equation: b2 − 4ac = (−2)2 − 4(1)(−3) = 4 + 12 = 16 > 0, so there are two solutions
9.
Which statement is false?
The only prime number that is also an even number is 2
✓
For all values of x, sin 2x = 2 sin x cos x
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For all values of x, tan x = sin x / cos x
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tan x is undefined when cos x = 0 (i.e. when x = 90°, 270°, ...)
10.
Which statement is false?
The Greek letter Σ (sigma) is used to signify a sum
✓
When converting degrees to radians, you divide by (360/π)
✓
The formula used to convert Celsius temperatures into Fahrenheit, F = 1.8C + 32, is a linear function
✓
You should divide by (180/π)
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Also if you say it's wrong because it's not specified that the series converges, then I would argue that e.g. the a, b and c in the Pythagorean theorem need to be specified before you could say it's correct.