Maths4U Original · Short practice

The roots of \(x^{3} - 42 x^{2} + 587 x - 2730=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3\). Use symmetric sums rather than numerical root finding.

Find the sum of the roots.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

The roots of \(x^{3} - 45 x^{2} + 674 x - 3360=0\) are denoted by \(\alpha_1,\alpha_2,\alpha_3\). Use symmetric sums rather than numerical root finding.

Find the sum of the roots.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

The line \(r=\left[\begin{matrix}15\\27\\3\end{matrix}\right]+t\left[\begin{matrix}1\\1\\1\end{matrix}\right]\) meets the plane \(x+2y+2z=16\).

Find the intersection x-coordinate.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

The line \(r=\left[\begin{matrix}16\\29\\3\end{matrix}\right]+t\left[\begin{matrix}1\\1\\1\end{matrix}\right]\) meets the plane \(x+2y+2z=17\).

Find the intersection x-coordinate.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

\(A=\left[\begin{matrix}15 & 16\\0 & 18\end{matrix}\right],\ B=\left[\begin{matrix}1 & 0\\1 & 1\end{matrix}\right]\). Use column vectors; AB means B acts first.

Find the (1,1) entry of AB.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

\(A=\left[\begin{matrix}16 & 17\\0 & 19\end{matrix}\right],\ B=\left[\begin{matrix}1 & 0\\1 & 1\end{matrix}\right]\). Use column vectors; AB means B acts first.

Find the (1,1) entry of AB.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

Define \(S_n=\sum_{r=1}^n(17r+16)\) for positive integers n.

Find \(\displaystyle S_{19}\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

Define \(S_n=\sum_{r=1}^n(18r+17)\) for positive integers n.

Find \(\displaystyle S_{20}\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.