Mock 6 (Week 5-8)

Course: Jan 2026 - Mathematics I

Mock 6 (Week 5-8)

Introduction

Question 1

• $a^{x+y+z}$
• $a^{x^2+y^2+z^2-xy-yz-zx}$
• 1
• $a$

Question 2

• The functions $f(x) = -\sqrt{ln(x)}$ and $g(x) = e^{x^2}$ are inverses to each other.
• The domain of the real-valued function $f(x) = \sqrt{e^{x^2-8x} - 1}$ is $(-\infty,0] \cup [8,\infty)$.
• The line $x=3$ is a vertical asymptote of the function $f(x) = ln(x^2+5x-24)$.
• $f$ may be continuous at the point $x=a$ even if $f$ is not differentiable at a point $x= a$.

Question 3

• The domain of the composite function $(f \circ g)(x)$ is $(-\infty,-\sqrt{10}) \cup (-\sqrt{10},-1] \cup [1,\sqrt{10}) \cup (\sqrt{10},\infty)$.
• The domain of the composite function $(f \circ g)(x)$ is $\mathbb{R} \setminus \{-\sqrt{10},\sqrt{10}\}$.
• $(f \circ g)(x) = \frac{\sqrt{x^2-1}+5}{\sqrt{x^2-1}-3}$.
• $(g \circ f)(x) = \frac{4\sqrt{x+1}}{|x-3|}$.

Question 4

• The sequence $\{a_n\}$ is not convergent.
• $\displaystyle \lim\limits_{n \to \infty} a_n = \frac{2}{3}$.
• $\displaystyle \sum_{i = 3}^{n} a_i = \frac{a_2 + a_{n-1}}{2} + \displaystyle \sum_{i = 3}^{n-2} a_i$.
• $\displaystyle \sum_{i = 3}^{n} a_i = \frac{a_{n-1}}{2} + \displaystyle \sum_{i = 2}^{n-2} a_i$.

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

• If $n$ is odd, then $\lfloor{\frac{n}{2}}\rfloor = \frac{n-1}{2}$.
• If $n$ is even, then $\lfloor{\frac{n}{2}}\rfloor = \frac{n}{2}+1$.
• If $n$ is odd, then $\lfloor{\frac{n}{2}}\rfloor= \frac{n+1}{2}$.
• If $n$ is even, then $\lfloor{\frac{n}{2}}\rfloor = \frac{n}{2}$.

Question 13

Question 14