Mathematics - 2013 E.C (2020/2021) Ethiopian University Entrance Exam (EUEE)

A Its foci are at $(-5, 0)$ and $(5, 0)$

B Its vertices are at $(-2, 0)$ and $(2, 0)$

C Its center is at $(2, 1)$

D An asymptote to the hyperbola is $y = 2x$

A $p\land \neg q$

B $p\vee \neg q$

C $-p\land q$

D $p\land q$

A If 4 is an odd number, then 21 is not a prime number

B If 4 is an odd number, then 21 is a prime number

C If 4 is not an odd number, then 21 is not a prime number

D If 21 is not a prime number, then 4 is an even number

A $$\int \frac{\sin\sqrt{x}}{\sqrt{x}}dx = -2\cos\sqrt{x}+c$$

B $$\int(3x+5)^6dx = \frac{(3x+5)^7}{7}+c$$

C $$\ln xdx = \frac{1}{x}+c$$

D $$\int xe^xdx = \frac{x^2}{2}e^x+c$$

A $v(t)=1+4t-t^2+t^3$

B $v(t)=5+4t-t^2+t^3$

C $v(t)=-2+6t$

D $v(t)=9-t^2+t^3$

A $p,\neg q \vdash p\implies q$

B $\neg p,q \vdash p\implies q$

C $p,\neg q \vdash p\implies q$

D $p,\neg q \vdash p\land q$

A Proof by counter example

B Proof by the principle of mathematical induction

C Proof by contradiction

D Proof by indirect proof

A 6

B 0

C 576

D 500

A Its period is $3\pi$

B Its amplitude is $-4$

C The graph completes one cycle on the interval $\left[0, \frac{3\pi}{2}\right]$

D The graph completes one cycle on the interval $\left[0, \frac{2\pi}{3}\right]$

A 5

B 4

C $\sqrt{21}$

D $\sqrt{20}$