Question 1
1 mark\( a = \sqrt{3} + 1 \) のとき、\( a^2 - 2a \) の値を求めなさい。
Senior High School · Mathematics
Numbers and Expressions: Practice Questions
5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Numbers and Expressions.
10 questions25 marksFree, no account
Question 2
1 mark不等式 \(|2x - 5| \le 3\) を解きなさい。
Question 3
1 mark\(x, y\) が実数で、\(x^2 + y^2 - 4x + 6y + 13 = 0\) を満たすとき、\(x + y\) の値を求めなさい。
Question 4
1 mark次の連立方程式を解きなさい。
\(\begin{cases} x + y = 5 \\ 2x - y = 1 \end{cases}\)
Question 5
1 mark\( a = \sqrt{3} \) のとき、\( |a - 1| + |a - 2| \) の値を求めなさい。
Question 6
2 marks\( x = 2 \) のとき、次の式の値を求めなさい。
\( 3x^2 - 4x + 1 \)
Write your answer out first, then check it against the worked solution.
Question 7
3 marks次の式を因数分解しなさい。
\( ac + ad + bc + bd \)
Write your answer out first, then check it against the worked solution.
Question 8
6 marks\( ∑_{k=1}^{n} (k^2+k) \) の計算結果を \( n \) を用いて因数分解された形で表しなさい。
Write your answer out first, then check it against the worked solution.
Question 9
4 marks次の式の値を求めなさい。
(a) \( (x+y)^2 \) を展開しなさい。
(b) \( x + y = 7 \)、\( xy = 10 \) のとき、\( x^2 + y^2 \) の値を求めなさい。
Write your answer out first, then check it against the worked solution.
Question 10
5 marks実数 \( x \) が \( x^2 - 3x + 1 = 0 \) を満たすとき、次の式の値を求めなさい。
(a) \( x + \frac{1}{x} \)
(b) \( x^2 + \frac{1}{x^2} \)
(c) \( x^5 + \frac{1}{x^5} \)
Write your answer out first, then check it against the worked solution.
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