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Algebra Question from Mathematics GRE

score 936 · Answer 1 · 2026-04-12 01:46:14

936

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Algebra Question from Mathematics GRE

Published on 12 Apr 2026 - 1:46

score 645 · Answer 2 · 2026-04-12 06:15:18

645

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Local Extrema of a 2D Surface in R^3 (Math GRE Question)

Published on 12 Apr 2026 - 6:15

score 31.2k · Answer 3 · 2026-02-25 20:32:47

31.2k

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Finding a number given its remainder when divided by other numbers

Published on 25 Feb 2026 - 20:32

score 141 · Answer 4 · 2026-02-25 20:37:23

141

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Is $\text{for}\ n\in \mathbb{N},\dfrac{u_{n+1}}{u_n}=q \iff \text{for}\ n\in \mathbb{N},u_{n+1}=q u_n$?

Published on 25 Feb 2026 - 20:37

score 292 · Answer 5 · 2026-02-25 20:37:02

292

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Let $P$ be a polynomial with integer coefficients satisfying $P(0)=1, P(1)=3, P'(0)=-1, P'(1)=10$. What is the minimum possible degree of $P$?

Published on 25 Feb 2026 - 20:37

score 47 · Answer 6 · 2026-04-12 18:41:41

47

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The order of $C=\sum_{k=0}^{90}(90-k)\cos(k ^{\circ}), S=\sum_{k=0}^{90}(90-k)\sin(k ^{\circ})$, and $T=\sum_{k=0}^{90}(90-k)\tan(k ^{\circ})$.

Published on 12 Apr 2026 - 18:41

score 229 · Answer 7 · 2026-04-12 17:34:25

229

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Possible dimensions of $V \cap W$ in $\mathbb{R}^n$

Published on 12 Apr 2026 - 17:34

score 759 · Answer 8 · 2026-04-13 13:38:41

759

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Let $h$ be the function defined by $h(x)=\int_{0}^{x^2}e^{x+t}dt$ for all real numbers $x$. Then $h'(1)=\dots$

Published on 13 Apr 2026 - 13:38

score 46 · Answer 9 · 2026-04-13 06:20:35

46

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$u=f(x,y)$ and the partial derivatives are themselves differentiable functions of $x$ and $y$ (Typo?)

Published on 13 Apr 2026 - 6:20

score 69 · Answer 10 · 2026-02-25 20:30:59

69

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Matrix in $M_2(\mathbf{R})$ of order $2$ has trace $0$

Published on 25 Feb 2026 - 20:30

score 215 · Answer 11 · 2026-04-13 01:00:13

215

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Showing that $AB$ is a subgroup.

Published on 13 Apr 2026 - 1:00

score 151 · Answer 12 · 2026-04-12 16:41:07

151

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If a $3\times 3$ matrix satisfies $A^3-A^2-A+I=0$, then it is not necessarily diagonalisable.

Published on 12 Apr 2026 - 16:41

score 39 · Answer 13 · 2026-04-09 21:23:18

39

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Finding relative extrema

Published on 09 Apr 2026 - 21:23

score 91 · Answer 14 · 2026-02-25 20:32:01

91

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If $f(x)=p \sin x + q x \cos x + x^2$ and $f(2)=3$, find $f(-2)$

Published on 25 Feb 2026 - 20:32

score 130 · Answer 15 · 2026-02-25 20:32:47

130

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How $5^{40} < 4^{60} < 27^{30}$, $8^{1/11} < 9^{1/10} < 10^{1/9}$, $e^{e} < \pi^{e} < e^{\pi}$, and $200^{100} < 200! < 100^{200}$?

Published on 25 Feb 2026 - 20:32

List Question

Algebra Question from Mathematics GRE

Local Extrema of a 2D Surface in R^3 (Math GRE Question)

Finding a number given its remainder when divided by other numbers

Is $\text{for}\ n\in \mathbb{N},\dfrac{u_{n+1}}{u_n}=q \iff \text{for}\ n\in \mathbb{N},u_{n+1}=q u_n$?

Let $P$ be a polynomial with integer coefficients satisfying $P(0)=1, P(1)=3, P'(0)=-1, P'(1)=10$. What is the minimum possible degree of $P$?

The order of $C=\sum_{k=0}^{90}(90-k)\cos(k ^{\circ}), S=\sum_{k=0}^{90}(90-k)\sin(k ^{\circ})$, and $T=\sum_{k=0}^{90}(90-k)\tan(k ^{\circ})$.

Possible dimensions of $V \cap W$ in $\mathbb{R}^n$

Let $h$ be the function defined by $h(x)=\int_{0}^{x^2}e^{x+t}dt$ for all real numbers $x$. Then $h'(1)=\dots$

$u=f(x,y)$ and the partial derivatives are themselves differentiable functions of $x$ and $y$ (Typo?)

Matrix in $M_2(\mathbf{R})$ of order $2$ has trace $0$

Showing that $AB$ is a subgroup.

If a $3\times 3$ matrix satisfies $A^3-A^2-A+I=0$, then it is not necessarily diagonalisable.

Finding relative extrema

If $f(x)=p \sin x + q x \cos x + x^2$ and $f(2)=3$, find $f(-2)$

How $5^{40} < 4^{60} < 27^{30}$, $8^{1/11} < 9^{1/10} < 10^{1/9}$, $e^{e} < \pi^{e} < e^{\pi}$, and $200^{100} < 200! < 100^{200}$?

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