Dependent and Independent Variables: Grade 6 Math Test Answer Key – PDF Download

Question 1: Identifying Variables (2 points)

1. Pounds of apples
2. Total cost

Scoring: 1 point for each correct variable.

Question 2: Variables in an Equation (2 points)

1. \(h\) (hours worked)
2. \(p\) (pay)

Scoring: 1 point for each correct variable.

Question 3: Writing an Equation (2 points)

1. Distance equals rate times time: \(d = 55t\)
2. \(d = 55\times 4 = \) 220 miles

Scoring: 1 point for the equation; 1 point for the correct distance.

Question 4: Completing a Table (2 points)

Add \(9\) to each \(x\): \(1 + 9 = 10\), \(4 + 9 = 13\), \(7 + 9 = 16\), \(10 + 9 = 19\).

Scoring: 1 point for the first two values; 1 point for the last two.

Question 5: Equation from a Table (3 points)

1. Each \(y\) is \(6\) times \(x\): \(y = 6x\)
2. \(x\) (number of snack packs)
3. \(y = 6\times 9 = \) \(54\)

Scoring: 1 point for each part.

Question 6: Reading a Graph (3 points)

1. At \(t = 3\), the graph is at \(18\): $18
2. At \(c = 24\), the graph is at \(t = 4\): 4 tickets
3. Each ticket costs $6: \(c = 6t\)

Scoring: 1 point for each part.

Question 7: Plotting Points (2 points)

Plot \((0, 0)\), \((1, 5)\), \((2, 10)\), and \((3, 15)\), with \(t\) on the horizontal axis and \(d\) on the vertical axis. The points lie on a straight line.

Scoring: 1 point for all four points plotted correctly; 1 point for correct axes labels (t horizontal, d vertical).

Question 8: Saving Money (2 points)

1. \(s = 5w\)
2. \(65 = 5w\), so \(w = 65: 5 = \) 13 weeks

Scoring: 1 point for the equation; 1 point for the correct number of weeks.

Question 9: Explaining Variables (2 points)

Liam is not correct. The distance \(d\) depends on the time \(t\), because time is the quantity that changes freely and distance is determined by it. So \(t\) is independent and \(d\) is dependent. Being alone on one side of the equation does not make a variable independent.

Scoring: 1 point for saying he is incorrect; 1 point for a correct explanation that d depends on t.

See every chapter on the Grade 6 math page.