Practice — Number and Algebra

Easy

If \(a = 3 + 2i\) and \(b = 1 - 4i\), what is the value of \(a + b\)?

Easy

Find the value of \(x\) if \(2^{x} = 8^{3}\).

Medium

Simplify the expression \(\frac{3x^2 - 12}{6x}\) for \(x \neq 0\).

Easy

If \(x^2 - 5x + 6 = 0\), what is the sum of the roots?

Medium

Solve for \(x\): \(\log_2 (x^2 - 3x) = 3\).

Medium

If \(a\) and \(b\) are real numbers such that \(a + b = 7\) and \(ab = 10\), find \(a^3 + b^3\).

Hard

Find the remainder when \(x^{100}\) is divided by \(x^2 - 1\).

Medium

If \(\alpha\) and \(\beta\) are roots of \(x^2 - 4x + 5 = 0\), find \(\alpha^2 + \beta^2\).

Medium

Evaluate \(\sum_{k=1}^{n} k(k+1)\).

Medium

If \(x + \frac{1}{x} = 3\), find \(x^3 + \frac{1}{x^3}\).

Number and Algebra