Solving Linear Equations: math test, Grade 9 – download the PDF

1 Expressions and order of operations / 3 pts

1. Calculate \(36\div 4+2\cdot 7\).
2. Calculate \(5+3(9-4)^2\).
3. Evaluate \(2a^2-3b\) for \(a=-3\) and \(b=4\).

2 One-step and two-step equations / 3 pts

Solve each equation.

1. \(x-13=8\)
2. \(-3y=27\)
3. \(5k+7=-18\)

3 Multi-step equations / 4 pts

Solve each equation.

1. \(4(2x-3)+5=33\)
2. \(7x-2(x-4)=23\)

4 Variables on both sides / 4 pts

Solve each equation.

1. \(6x-5=2x+11\)
2. \(3(x+4)=5x-2\)

5 Ride-share fare / 3 pts

A ride costs a $3 base fare plus $2 per mile. Dana paid $21. Write an equation and find the length of the ride.

6 Formulas and special cases / 3 pts

1. Solve \(A=\dfrac{1}{2}bh\) for \(h\).
2. Find \(h\) when \(A=30\) and \(b=12\).
3. How many solutions does \(4x-1=4x+3\) have?