Question 1: Solve for x: \( \frac{2x}{3} + \frac{5}{6} = 1 \).

Answer: x = \frac{1}{2}

Question 2: Rearrange the formula \( y = \frac{a}{b} + c \) to solve for \( a \).

Answer: a = (y - c) \times b

Question 3: Simplify: \( \frac{3}{4}x - \frac{1}{2} = \frac{1}{4} \) and then solve for \( x \).

Answer: x = 2

Question 4: A formula relates speed \( s \), distance \( d \), and time \( t \) as \( d = \frac{st}{2} \). Rearrange to find \( s \) in terms of \( d \) and \( t \).

Answer: s = \frac{2d}{t}

Question 5: Calculate the value of \( x \) if \( \frac{5x}{2} + 3 = 7 \).

Answer: x = \frac{8}{5}

Question 6: A rectangular tank has a volume formula \( V = \frac{1}{3} \times \text{length} \times \text{width} \times \text{height} \). Rearrange this to solve for \( \text{length} \).

Answer: length = \frac{3V}{\text{width} \times \text{height}}

Question 7: Plot the graph of \( y = \frac{1}{2}x + 1 \) on the grid.

Answer: Student draws the line with slope 1/2 crossing y-axis at 1.

Question 8: Construct a triangle on the grid with sides \( \frac{3}{4} \), \( 1 \), and \( \frac{5}{4} \).

Answer: Student draws triangle with specified side lengths.

Question 9: Solve for \( x \): \( \frac{3x - 2}{4} = \frac{5}{8} \).

Answer: x = \frac{9}{4}

Question 10: Identify and correct the mistake in the following solution: \( \frac{2x}{3} + \frac{5}{6} = 1 \) \rightarrow \( \frac{2x}{3} = 1 - \frac{5}{6} \rightarrow \frac{2x}{3} = \frac{1}{6} \rightarrow x = \frac{1}{4} \).

Answer: Incorrect. When subtracting \( \frac{5}{6} \) from 1 (which is \( \frac{6}{6} \)), the result is \( \frac{1}{6} \). Then, multiply both sides by 3/2: \( x = \frac{1}{6} \times \frac{3}{2} = \frac{1}{4} \). However, check the step where dividing both sides by \( \frac{2}{3} \) was done correctly.