Linear Equations, Inequalities and Systems: math test, Grade 11 – download the PDF

1 Lines and slope / 3 pts

Let \(A(-2, 5)\) and \(B(4, -1)\).

1. Find the slope of line \(AB\).
2. Write the equation of line \(AB\) in slope-intercept form.
3. Write the equation of the line parallel to \(AB\) through \((0, -4)\).

2 Absolute value / 3 pts

Solve: (a) \(|2x - 5| = 11\); (b) \(|x + 1| \ge 5\).

3 Compound inequalities / 3 pts

Solve and write each answer in interval notation: (a) \(-9 \le 2x + 3 < 7\); (b) \(4x - 1 < 3\) or \(2x + 5 \ge 15\).

4 Concert tickets / 3 pts

A school concert sold 220 tickets. Student tickets cost 9 dollars and adult tickets cost 14 dollars. The ticket sales totaled 2,380 dollars.

1. Write a system of equations for the number \(s\) of student tickets and the number \(a\) of adult tickets.
2. Solve the system and state how many tickets of each kind were sold.

5 A system of three equations / 3 pts

Solve \(x + y + z = 9\), \(x - y + 2z = 9\), \(2x + y - z = 4\).

6 Linear programming / 3 pts

Maximize \(P = 4x + 5y\) subject to \(x + y \le 10\), \(x + 3y \le 18\), \(x \ge 0\), \(y \ge 0\).

7 Matrices / 2 pts

Let \(A = \begin{bmatrix} 4 & 3 \\ 1 & 1 \end{bmatrix}\).

1. Find \(A^{-1}\).
2. Use it to solve \(4x + 3y = 17\) and \(x + y = 5\).