高度な数学
導入済み| English | 意味 |
|---|---|
| root/ruːt/ | 根 |
| domain/dəˈmeɪn/ | 定義域 |
A decision before an answer
- A quadratic can describe a ball’s height, but only the times before it lands belong to the physical model.
- Your goal: Transform equivalent polynomial and rational expressions.
Read the relationship
- Factor a quadratic when possible. The zero-product rule applies to a product equal to zero.
- Solve nonlinear equations and systems.
The minimum of y=(x−4)²+2 is:
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
A square is nonnegative and is zero at x=4.
Use the defining rule
- Completing the square reveals a vertex: x²−6x+5=(x−3)²−4.
- Interpret quadratic and exponential functions.
A quantity 100 grows 10% twice. Final value?
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
100×1.1²=121; growth compounds.
Check the conditions
- For rational expressions, record excluded denominator values before cancelling factors.
- Interpret quadratic and exponential functions.
Solve x²−5x+6=0. Factor: (x−2)(x−3)=0. Thus x=2 or 3. If instead (x²−5x+6)/(x−2)=0, x=2 is excluded; only 3 remains.
The roots of x²−9=0 are 3 and ____.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
The factorisation is (x−3)(x+3)=0.
Apply the task format
- An exponential model multiplies by a fixed factor per interval. A 20% increase means multiply by 1.2, not add 0.2.
- Interpret quadratic and exponential functions.
Squaring an equation can add extraneous roots. Substitute into the original equation, not just the transformed one.
このケースに当てはまる答えはどれか？
等価な多項式および有理式の変形
Cancelling (x−2) makes x=2 allowed in the original rational expression.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
Its original denominator remains zero at 2.
Keep the distinctions
- root 根 — An input for which a function equals zero.
- domain 定义域 — The allowed input values.
- Transform equivalent polynomial and rational expressions.
- Solve nonlinear equations and systems.
- Interpret quadratic and exponential functions.
Match each term with its precise meaning in this lesson.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
Keep the distinctions stated in the teaching example.
Put this lesson’s reasoning or event sequence in order.
難易度 3/5 · 200 コイン + 今日初回完了時に小ボーナス付与
The order follows the stated process; check each stage before the next.