Latihan Soal 1 Persiapan PAS Gasal Matematika Wajib Kelas X

$\begin{array}{l}\\ 1.& \text{Nilai untuk}-|-2021|=....\\ & \begin{array}{l}\\ \text{a}.& -2021& & & \text{d}.& -{2021}^{-1}\\ \text{b}.& 2021& \text{c}.& {2021}^{-1}& \text{e}.& {2021}^2\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{a}}\\ & \begin{array}{rl}-|-2021|& =-\left(2021\right)=-2021\end{array}\end{array}$.

$\begin{array}{l}\\ 2.& \text{Nilai untuk}|-4|-|-6^2\times 2|=....\\ & \begin{array}{l}\\ \text{a}.& -68& & & \text{d}.& 68\\ \text{b}.& -40& \text{c}.& 40& \text{e}.& 76\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{a}}\\ & \begin{array}{rl}|-4|-|-6^2\times 2|& =\left(4\right)-|-36\times 2|\\ & =4-|-72|\\ & =4-\left(72\right)\\ & =-68\end{array}\end{array}$.

$\begin{array}{l}\\ 3.& \text{Nilai untuk}(-2022)-|-(-2021)|-{|-3^2|}^2=....\\ & \begin{array}{l}\\ \text{a}.& -3960& & & \text{d}.& -4068\\ \text{b}.& -4038& \text{c}.& -4050& \text{e}.& -4124\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{e}}\\ & \begin{array}{rl}& (-2022)-|-(-2021)|-{|-3^2|}^2\\ & =-2022-2021-{|-9|}^2\\ & =-4043-9^2\\ & =-4043-81\\ & =-4124\end{array}\end{array}$.

$\begin{array}{l}\\ 4.& \text{Nilai untuk}{|-4|}^{|-2|}-{|-2|}^{|-4|}=....\\ & \begin{array}{l}\\ \text{a}.& -32& & & \text{d}.& 16\\ \text{b}.& -16& \text{c}.& 0& \text{e}.& 32\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{c}}\\ & \begin{array}{rl}{|-4|}^{|-2|}-{|-2|}^{|-4|}& =4^2-2^4\\ & =16-16\\ & =0\end{array}\end{array}$.

$\begin{array}{l}\\ 5.& \text{Nilai untuk}\\ & |1-2^2|+|2^2-3^2|+|3^2-4^2|+\cdots +|{2020}^2-{2021}^2|....\\ & \begin{array}{l}\\ \text{a}.& -{2021}^2& & & \text{d}.& {2021}^2-1\\ \text{b}.& 1-{2021}^2& \text{c}.& -2021& \text{e}.& {2021}^2\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{d}}\\ & \begin{array}{rl}& |1-2^2|+|2^2-3^2|+|3^2-4^2|+\cdots +|{2020}^2-{2021}^2|\\ & =(2^2-1)+(3^2-2^2)+(4^2-3^2)+\cdots +({2021}^2-{2020}^2)\\ & =-1+{2021}^2\\ & ={2021}^2-1\end{array}\end{array}$.

$\begin{array}{l}\\ 6.& \text{Nilai untuk}\\ & \left|{\displaystyle \frac{1}{2}-1}\right|\times \left|{\displaystyle \frac{1}{3}-1}\right|\times \left|{\displaystyle \frac{1}{4}-1}\right|\times \left|{\displaystyle \frac{1}{5}-1}\right|\times \cdots \times \left|{\displaystyle \frac{1}{2021}-1}\right|=....\\ & \begin{array}{l}\\ \text{a}.& -{\displaystyle \frac{1}{2021}}& & & \text{d}.& {\displaystyle \frac{2020}{2021}}\\ \\ \text{b}.& -{\displaystyle \frac{2020}{2021}}& \text{c}.& -2021{\displaystyle \frac{1}{2}}& \text{e}.& {\displaystyle \frac{1}{2021}}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{e}}\\ & \begin{array}{rl}& \left|{\displaystyle \frac{1}{2}-1}\right|\times |\frac{1}{3}-1|\times |\frac{1}{4}-1|\times |\frac{1}{5}-1|\times \cdots \times |\frac{1}{2021}-1|\\ & =|-{\displaystyle \frac{1}{2}}|\times |-\frac{2}{3}|\times |-\frac{3}{4}|\times |-\frac{4}{5}|\times \cdots \times |-\frac{2020}{2021}|\\ & ={\displaystyle \frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times \frac{4}{5}\times \cdots \times \frac{2019}{2020}\times \frac{2020}{2021}}\\ & ={\displaystyle \frac{1}{2021}}\end{array}\end{array}$.

$\begin{array}{ll}7.& \text{Bentuk sederhana dari}x-5y\text{dan}\\ & 5y-x\text{adalah}....\\ & \begin{array}{llll}\text{a}.& |5y-x|& \text{d}.& |y-x|\\ \text{b}.& |y-5x|& \text{e}.& |-5y-x|\\ \text{c}.& |x-5y|\end{array}\\ \\ & \mathbf{\text{Jawab}}:\mathbf{\text{c}}\\ & |x-5y|=m=\{\begin{array}{ll}\bullet & =x-5y\\ \bullet & =-(x-5y)\end{array}\end{array}$.

$\begin{array}{l}\\ 8.& \text{Nilai}m\text{yang memenuhi}\left|4m\right|=16\text{adalah... .}\\ & \begin{array}{l}\\ \text{a}.& 2\\ \text{b}.& 4\\ \text{c}.& \pm 2\\ \text{d}.& \pm 4\\ \text{e}.& \pm 8\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{d}}\\ & \begin{array}{rl}\left|4m\right|& =16\\ (4m)& =\pm 16\\ m& =\pm {\displaystyle \frac{16}{4}}\\ & =\pm 4\end{array}\end{array}$.

$\begin{array}{l}\\ 9.& \text{Nilai}x\text{yang memenuhi untuk}|2x+5|=9\\ & \text{adalah}....\\ & \begin{array}{l}\\ \text{a}.& 2& & \text{d}.& -7\text{dan}2\\ \text{b}.& 2\text{dan}7& & \text{e}.& -2\text{dan}7\\ \text{c}.& -7\text{dan}-2& \end{array}\\ \\ & \text{Jawab}:\mathbf{\text{d}}\\ & \begin{array}{rl}|2x+5|& =9\\ (2x+5)& =\pm 9\\ 2x& =\pm 9-5\\ x& ={\displaystyle \frac{\pm 9-5}{2}}\\ x& =\{\begin{array}{l}={\displaystyle \frac{+9-5}{2}=\frac{4}{2}=2}\\ \\ ={\displaystyle \frac{-9-5}{2}=\frac{-14}{2}=-7}\end{array}\end{array}\end{array}$.

$\begin{array}{l}\\ 10.& \text{Nilai}x\text{yang memenuhi}10-4|4-5x|=26\\ & \text{adalah}....\\ & \begin{array}{l}\\ \text{a}.& 2\text{atau}1{\displaystyle \frac{2}{3}}& & \text{d}.& 1\text{atau}-{\displaystyle \frac{3}{5}}\\ \\ \text{b}.& 2\text{atau}2{\displaystyle \frac{3}{5}}& & \text{e}.& -1\text{atau}2{\displaystyle \frac{3}{5}}\\ \text{c}.& -2{\displaystyle \frac{3}{4}\text{atau}1}& \end{array}\\ \\ & \text{Jawab}:\mathbf{\text{e}}\\ & \begin{array}{rl}10-4|4-5x|& =-26\\ -4|4-5x|& =-36\\ |4-5x|& =9\\ (4-5x)& =\pm 9\\ -5x& =-4\pm 9\\ x& ={\displaystyle \frac{-4\pm 9}{-5}}\\ x& =\{\begin{array}{ll}{\displaystyle \frac{-4+9}{-5}}& =-1\\ \text{atau}& \\ {\displaystyle \frac{-4-9}{-5}}& ={\displaystyle \frac{13}{5}=2\frac{3}{5}}\end{array}\end{array}\end{array}$