数と式の問題演習

1. 次の計算をしなさい．

   • •	${\displaystyle \frac{11}{3-\frac{1}{4}}}$　⇒ 解答

   • •	${\displaystyle \frac{\frac{1}{2}-\frac{3}{10}}{\frac{5}{12}+\frac{1}{4}}}$　⇒ 解答

   • •	${\displaystyle \frac{0.45\times 0.25}{0.12\times 0.03}}$　⇒ 解答

   • •	${\displaystyle \frac{3.54÷2.95}{5.04÷1.05}}$　⇒ 解答
2. 次の平方根を含む式を簡単にせよ．
   • ${\displaystyle \sqrt{1200}-\sqrt{{\left(-3\right)}^2\times 3}}$${\displaystyle -\sqrt{18}\times \sqrt{6}}$${\displaystyle -\frac{15}{\sqrt{3}}}$　⇒ 解答
   • ${\displaystyle \frac{1}{\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}}}$　⇒ 解答
3. 次の式を展開しなさい．

   • •	${\displaystyle \left(x+2\right)\left(x-5\right)}$　⇒ 解答

   • •	${\displaystyle \left(2x-5\right)\left(3x-2\right)}$　⇒ 解答

   • •	${\displaystyle \left(2x+3\right)\left(2x-3\right)}$　⇒ 解答

   •	${\displaystyle \left(x+2y+1\right)\left(x+2y-1\right)\left(x-2y-1\right)\left(x-2y+1\right)}$　⇒ 解答

   • •	${\displaystyle (2x-1)(x^2-3x+1)}$　⇒ 解答

   • •	${\displaystyle (3x+5)(3x-5)y}$　⇒ 解答

   • •	${\displaystyle (4a-3)(16a^2+12a+9)}$　⇒ 解答

   • •	${\displaystyle {\displaystyle {\left(s+\frac{2}{3}t-\frac{5}{4}u\right)}^2}}$　⇒ 解答

   • •	${\displaystyle \left(4p+5q-6r\right)\left(4p-5q-6r\right)}$　⇒ 解答
4. 次の式を因数分解しなさい．

   • •	${\displaystyle x^2-6x-7}$　⇒ 解答

   • •	${\displaystyle x^2-9}$　⇒ 解答

   • •	${\displaystyle x^3+11x^2+32x+28}$　⇒ 解答

   • •	${\displaystyle x^2+3x-\frac{7}{4}}$　⇒ 解答

   • •	${\displaystyle 3x^2+10x+3}$　⇒ 解答

   • •	${\displaystyle 6x^2+x-1}$　⇒ 解答

   • •	${\displaystyle 2x^2-9x+4}$　⇒ 解答

   • •	${\displaystyle x^2-x-72}$　⇒ 解答

   • •	${\displaystyle 6x^2+8x+2}$　⇒ 解答

   • •	${\displaystyle 8x^2+6x-5}$　⇒ 解答

   • •	${\displaystyle 2xy-8y}$　⇒ 解答

   • •	${\displaystyle 3a^3{b}^2+27a^2{b}^4-9a^4{b}^4}$　⇒ 解答

   • •	${\displaystyle a^2-\frac{1}{25}{b}^2}$　⇒ 解答

   • •	${\displaystyle x^2+x+\frac{1}{4}}$　⇒ 解答

   • •	${\displaystyle 8p^3+12p^{2}q+6p{q}^2+q^3}$　⇒ 解答

   • •	${\displaystyle x^3+\frac{1}{27}{y}^3}$　⇒ 解答

   • •	${\displaystyle x{y}^2+9xy+14x}$　⇒ 解答

   • •	${\displaystyle a^4+81b^4+9a^2{b}^2}$　⇒ 解答

   • •	${\displaystyle 2x^3-3x^2-11x+6}$　⇒ 解答

   • •	${\displaystyle 3x^2+xy+15x-2y^2-5y+12}$　⇒ 解答
5. 次の整式 ${\displaystyle A}$ を${\displaystyle B}$ で割った商${\displaystyle Q}$ ，余り${\displaystyle R}$ を求め，${\displaystyle A=BQ+R}$ の形を求めよ．
   • ${\displaystyle A=3x^2-x-1}$，${\displaystyle B=x+2}$　⇒ 解答
   • ${\displaystyle A=2x^4-x^3-6x^2-8x+7}$ ， ${\displaystyle B=x^2-3x+1}$　⇒ 解答
6. 次の式を簡単にしなさい．

   • •	${\displaystyle \frac{{\left(a^3{b}^2\right)}^5}{{\left(3a^{2}b{c}^3\right)}^3}}$　⇒ 解答

   • •	${\displaystyle \frac{3x+2}{3x^2-13x-10}}$　⇒ 解答

   • •	${\displaystyle \frac{5x+4}{5x^2-22x-15}-\frac{1}{x-5}}$　⇒ 解答

   • •	${\displaystyle \frac{a^2+1}{a^2-1}+\frac{a+1}{a-1}}$　⇒ 解答

   • •	${\displaystyle \frac{a+3}{a-2}\times \frac{a^3}{a^2-9}}$　⇒ 解答

   • •	${\displaystyle \frac{x-3}{x^2-25}\times \frac{x-5}{x^3-27}}$　⇒ 解答

   • •	${\displaystyle \frac{a-4}{a^2+8a+12}÷\frac{a^2-16}{a+6}}$　⇒ 解答

   • •	${\displaystyle \frac{5a-20}{a^3-9a}}$${\displaystyle \times \frac{a^2+7x+12}{a-4}}$${\displaystyle ÷\frac{5a+20}{a^2-3a}}$　⇒ 解答

   • •	${\displaystyle \frac{x{y}^2+xyz}{x{y}^2-x{z}^2}}$　⇒ 解答

   • •	${\displaystyle \frac{x^2-y^2}{{\displaystyle \frac{1}{x}+\frac{1}{y}}}}$　⇒ 解答
7. 次の分数を部分分数に分解しなさい．

   • •	${\displaystyle \frac{6}{x^2+4x+3}}$　⇒ 解答

   • •	${\displaystyle \frac{7}{x^2+3x-10}}$　⇒ 解答

   • •	${\displaystyle \frac{2x+1}{x^2+x-2}}$　⇒ 解答

   • •	${\displaystyle \frac{5x+1}{x^2-x-12}}$　⇒ 解答

   • •	${\displaystyle \frac{6x-2}{x^2-3x-10}}$　⇒ 解答

   • •	${\displaystyle \frac{2x+4}{x^2+4x-12}}$　⇒ 解答

   • •	${\displaystyle \frac{x}{{\left(x+1\right)}^2}}$　⇒ 解答

   • •	${\displaystyle \frac{3x-9}{{\left(x+3\right)}^2}}$　⇒ 解答

   • •	${\displaystyle \frac{5x+2}{{\left(x-2\right)}^2}}$　⇒ 解答

   • •	${\displaystyle \frac{2x-15}{{\left(x+5\right)}^2}}$　⇒ 解答

 

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最終更新日： 2024年10月5日

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