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Math Mastery Quiz: Key Concepts

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Math Mastery Quiz: Key Concepts

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Challenge your calculus, algebra, and probability skills.

Created by

Dylan Reyes
Dylan Reyes
Ecuador

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Math Mastery Quiz: Key Concepts
 

Math Mastery Quiz: Key ConceptsOnline version

Challenge your calculus, algebra, and probability skills.

by Dylan Reyes
1

What does f'(a)=0 imply geometrically for a smooth curve?

2

What does f'(a) represent for a differentiable function?

3

In a geometric progression, what is constant between consecutive terms?

4

If two fair coins are tossed, what is the probability both show the same face?

5

In three fair coin tosses, what's the probability of exactly two heads and one tail?

6

For exponential functions, which statement is true about y = a^x with a>1?

7

If three consecutive terms sum to 45 in an arithmetic progression, what is the middle term?

8

A population of 5 bacteria doubles every hour. How many after 6 hours?

9

Compute the arithmetic mean of the data set: 8, 12, 15, 15, 13, 21, 24, 36.

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When the derivative at a is zero, the slope of the tangent line at x=a is zero, so the tangent is horizontal and the point is a potential extremum.

The derivative at a gives the instantaneous rate of change, i.e., the slope of the tangent to the graph at x=a.

A geometric progression has a common ratio r such that a(n+1)/a(n) = r for all n.

There are four equiprobable outcomes; two have matching faces (HH, TT), giving 2/4 = 1/2.

Count the combinations of positions for the two heads (3 ways) out of 8 total outcomes: 3/8.

As x→-∞, a^x→0+, so y=0 is a horizontal asymptote; the function grows without bound as x→∞.

In any arithmetic progression, the sum of three consecutive terms is 3 times the middle term, so middle = 45/3 = 15.

Doubling 6 times: 5 × 2^6 = 5 × 64 = 320.

Sum is 144; 144/8 = 18.

 
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