University Math Challenge

Froggy Jumps

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Advanced math questions

Created by

Vannisa Baal

Philippines

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Froggy Jumps University Math ChallengeOnline version Advanced math questions by Vannisa Baal 1 What is the derivative of f(x)=x^3+5x^2−2x at x=1? a 4 b 6 c 7 2 If A is a 2x2 matrix with det(A)=3, what is det(2A)? a 12 b 9 c 6 3 Evaluate the integral ∫ from 0 to ∞ e^(−x) dx. a 0 b 1 c ∞ 4 In a vector space R^3, what is the dimension of the span of {(1,0,0),(0,1,0)}? a 2 b 3 c 1 5 If a function is analytic on a domain D and has a zero of order 3 at z0, what is the smallest possible multiplicity of z0 as a zero of its derivative? a 3 b 2 c 1 6 Which of the following is a field? a Natural numbers b Even integers c Rational numbers 7 What is the eigenvalue equation for a matrix A? a trace(A)=0 b det(A+λI)=0 c det(A−λI)=0 8 In probability, what is P(A∪B) if A and B are independent events? a P(A)−P(B) b P(A)P(B) c P(A)+P(B) 9 If f is differentiable and f′(x)=2x, what is f(x) up to a constant, given f(0)=3? a x^2/2+3 b 2x+3 c x^2+3 10 Which structure satisfies all axioms of a ring with a multiplicative identity but not necessarily commutative? a Boolean algebra b Matrix ring M_n(R) c Field

Froggy Jumps

University Math ChallengeOnline version

Advanced math questions

by Vannisa Baal

What is the derivative of f(x)=x^3+5x^2−2x at x=1?

If A is a 2x2 matrix with det(A)=3, what is det(2A)?

Evaluate the integral ∫ from 0 to ∞ e^(−x) dx.

∞

In a vector space R^3, what is the dimension of the span of {(1,0,0),(0,1,0)}?

If a function is analytic on a domain D and has a zero of order 3 at z0, what is the smallest possible multiplicity of z0 as a zero of its derivative?

Which of the following is a field?

Natural numbers

Even integers

Rational numbers

What is the eigenvalue equation for a matrix A?

trace(A)=0

det(A+λI)=0

det(A−λI)=0

In probability, what is P(A∪B) if A and B are independent events?

P(A)−P(B)

P(A)P(B)

P(A)+P(B)

If f is differentiable and f′(x)=2x, what is f(x) up to a constant, given f(0)=3?

x^2/2+3

2x+3

x^2+3

Which structure satisfies all axioms of a ring with a multiplicative identity but not necessarily commutative?

Boolean algebra

Matrix ring M_n(R)

Field

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University Math Challenge

Froggy Jumps

About this activity

Created by

Download the paper version to play

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University Math ChallengeOnline version

by Vannisa Baal

What is the derivative of f(x)=x^3+5x^2−2x at x=1?

If A is a 2x2 matrix with det(A)=3, what is det(2A)?

Evaluate the integral ∫ from 0 to ∞ e^(−x) dx.

In a vector space R^3, what is the dimension of the span of {(1,0,0),(0,1,0)}?

If a function is analytic on a domain D and has a zero of order 3 at z0, what is the smallest possible multiplicity of z0 as a zero of its derivative?

Which of the following is a field?

What is the eigenvalue equation for a matrix A?

In probability, what is P(A∪B) if A and B are independent events?

If f is differentiable and f′(x)=2x, what is f(x) up to a constant, given f(0)=3?

Which structure satisfies all axioms of a ring with a multiplicative identity but not necessarily commutative?

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