Latihan Soal 1 Persiapan PAS Gasal Matematika Wajib Kelas X

$\begin{array}{ll}\\ 1.&\textrm{Nilai untuk}\: \: -\left | -2021 \right |=...\: .\\ &\begin{array}{llllll}\\ \textrm{a}. &-2021\quad &&&\textrm{d}.&-2021^{-1}\\ \textrm{b}.&2021&\textrm{c}.&2021^{-1}\quad &\textrm{e}.&2021^{2} \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{a}\\ &\color{red}\begin{aligned}-\left | -2021 \right |&=-\left ( 2021 \right )=-2021 \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 2.&\textrm{Nilai untuk}\: \: \left | -4 \right |-\left | -6^{2}\times 2 \right |=...\: .\\ &\begin{array}{llllll}\\ \textrm{a}. &-68\quad &&&\textrm{d}.&68\\ \textrm{b}.&-40&\textrm{c}.&40\quad &\textrm{e}.&76 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{a}\\ &\begin{aligned}\left | -4 \right |-\left | -6^{2}\times 2 \right |&=\left ( 4 \right )-\left | -36\times 2 \right |\\ &=4-\left | -72 \right |\\ &=4-\left ( 72 \right )\\ &=\color{red}-68 \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 3.&\textrm{Nilai untuk}\: \: (-2022)-\left | -(-2021) \right |-\left | -3^{2} \right |^{2}=...\: .\\ &\begin{array}{llllll}\\ \textrm{a}. &-3960\quad &&&\textrm{d}.&-4068\\ \textrm{b}.&-4038&\textrm{c}.&-4050\quad &\textrm{e}.&-4124 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{e}\\ &\begin{aligned}&(-2022)-\left | -(-2021) \right |-\left | -3^{2} \right |^{2}\\ &=-2022-2021-\left | -9 \right |^{2}\\ &=-4043-9^{2}\\ &=-4043-81\\ &=-4124 \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 4.&\textrm{Nilai untuk}\: \: \left | -4 \right |^{\left | -2 \right |}-\left | -2 \right |^{\left | -4 \right |}=...\: .\\ &\begin{array}{llllll}\\ \textrm{a}. &-32\quad &&&\textrm{d}.&16\\ \textrm{b}.&-16&\textrm{c}.&0\quad &\textrm{e}.&32 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{c}\\ &\begin{aligned}\left | -4 \right |^{\left | -2 \right |}-\left | -2 \right |^{\left | -4 \right |}&=4^{2}-2^{4}\\ &=16-16\\ &=\color{red}0 \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 5.&\textrm{Nilai untuk}\\ & \left | 1-2^{2} \right |+\left | 2^{2}-3^{2} \right |+\left | 3^{2}-4^{2} \right |+\cdots +\left | 2020^{2}-2021^{2} \right |...\: .\\ &\begin{array}{llllll}\\ \textrm{a}. &-2021^{2}\quad &&&\textrm{d}.&2021^{2}-1\\ \textrm{b}.&1-2021^{2}&\textrm{c}.&-2021\quad &\textrm{e}.&2021^{2} \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{d}\\ &\begin{aligned}&\left | 1-2^{2} \right |+\left | 2^{2}-3^{2} \right |+\left | 3^{2}-4^{2} \right |+\cdots +\left | 2020^{2}-2021^{2} \right |\\ &=\left ( 2^{2}-1 \right )+\left ( 3^{2}-2^{2} \right )+\left ( 4^{2}-3^{2} \right )+\cdots +\left ( 2021^{2}-2020^{2} \right )\\ &=-1+2021^{2}\\ &=\color{red}2021^{2}-1 \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 6.&\textrm{Nilai untuk}\\ & \left | \displaystyle \frac{1}{2}-1 \right |\times \left | \displaystyle \frac{1}{3}-1 \right |\times \left | \displaystyle \frac{1}{4}-1 \right |\times \left | \displaystyle \frac{1}{5}-1 \right |\times \cdots \times \left | \displaystyle \frac{1}{2021}-1 \right |=...\: .\\ &\begin{array}{llllll}\\ \textrm{a}. &-\displaystyle \frac{1}{2021}\quad &&&\textrm{d}.&\displaystyle \frac{2020}{2021}\\\\ \textrm{b}.&-\displaystyle \frac{2020}{2021}&\textrm{c}.&-2021\displaystyle \frac{1}{2}\quad &\textrm{e}.&\displaystyle \frac{1}{2021} \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{e}\\ &\begin{aligned}&\left | \displaystyle \frac{1}{2}-1 \right |\times \left | \frac{1}{3}-1 \right |\times \left | \frac{1}{4}-1 \right |\times \left | \frac{1}{5}-1 \right |\times \cdots \times \left | \frac{1}{2021}-1 \right |\\ &=\left | -\displaystyle \frac{1}{2} \right |\times \left | -\frac{2}{3} \right |\times \left | -\frac{3}{4} \right |\times \left | -\frac{4}{5} \right |\times \cdots \times \left | -\frac{2020}{2021} \right |\\ &=\displaystyle \frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times \frac{4}{5}\times \cdots \times \frac{2019}{2020}\times \frac{2020}{2021}\\ &=\color{red}\displaystyle \frac{1}{2021} \end{aligned} \end{array}$.

$\begin{array}{ll} 7.&\textrm{Bentuk sederhana dari}\: \: x-5y\: \: \textrm{dan}\\ &5y-x\: \: \textrm{adalah}\: ....\\ &\begin{array}{llllll} \textrm{a}.&\left | 5y-x \right |&\textrm{d}.&\left | y-x \right |\\ \textrm{b}.&\left | y-5x \right |&\textrm{e}.&\left |-5y-x \right |\\ \textrm{c}.&\left | x-5y \right | \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textbf{c}\\ &\left | x-5y \right |=m=\begin{cases} \bullet & =x-5y \\ \bullet & =-(x-5y) \end{cases} \end{array}$.

$\begin{array}{ll}\\ 8.&\textrm{Nilai}\: \: m\: \: \textrm{yang memenuhi}\: \: \left | 4m \right |=16\: \: \textrm{adalah... .}\\ &\begin{array}{llll}\\ \textrm{a}.&2\\ \textrm{b}.&4\\ \textrm{c}.&\pm 2\\ \textrm{d}.&\pm 4\\ \textrm{e}.&\pm 8 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{d}\\ &\begin{aligned}\left | 4m \right |&=16\\ (4m)&=\pm 16\\ m&=\pm \displaystyle \frac{16}{4}\\ &=\color{red}\pm 4 \end{aligned}\end{array}$.

$\begin{array}{ll}\\ 9.&\textrm{Nilai}\: \: x\: \: \textrm{yang memenuhi untuk}\: \: \left | 2x+5 \right |=9\\ & \textrm{adalah}... .\\ &\begin{array}{llllll}\\ \textrm{a}.&2&&\textrm{d}.&-7\: \: \textrm{dan}\: \: 2\\ \textrm{b}.&2\: \: \textrm{dan}\: \: 7&&\textrm{e}.&-2\: \: \textrm{dan}\: \: 7\\ \textrm{c}.&-7\: \: \textrm{dan}\: \: -2& \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{d}\\ &\begin{aligned}\left | 2x+5 \right |&=9\\ \left ( 2x+5 \right )&=\pm 9\\ 2x&=\pm 9-5\\ x&=\displaystyle \frac{\pm 9-5}{2}\\ x&=\color{red}\begin{cases} =\displaystyle \frac{+9-5}{2}=\frac{4}{2}=2 \\\\ =\displaystyle \frac{-9-5}{2}=\frac{-14}{2}=-7 \end{cases} \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 10.&\textrm{Nilai}\: \: x\: \: \textrm{yang memenuhi}\: \: 10-4\left | 4-5x \right |=26\\ & \textrm{adalah}\: ... .\\ &\begin{array}{lllllll}\\ \textrm{a}.&2\: \: \textrm{atau}\: \: 1\displaystyle \frac{2}{3}&&\textrm{d}.&1\: \: \textrm{atau}\: \: -\displaystyle \frac{3}{5}\\\\ \textrm{b}.&2\: \: \textrm{atau}\: \: 2\displaystyle \frac{3}{5}&&\textrm{e}.&-1\: \: \textrm{atau}\: \: 2\displaystyle \frac{3}{5}\\ \textrm{c}.&-2\displaystyle \frac{3}{4}\: \: \textrm{atau}\: \: 1\quad&\\ \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{e}\\ &\begin{aligned}10-4\left | 4-5x \right |&=-26\\ -4\left | 4-5x \right |&=-36\\ \left | 4-5x \right |&=9\\ (4-5x)&=\pm 9\\ -5x&=-4\pm 9\\ x&=\displaystyle \frac{-4\pm 9}{-5}\\ x&=\begin{cases} \displaystyle \frac{-4+9}{-5} & =\color{red}-1 \\ \textrm{atau} & \\ \displaystyle \frac{-4-9}{-5} & = \displaystyle \frac{13}{5}=\color{red}2\frac{3}{5} \end{cases} \end{aligned} \end{array}$