This is an estimate based on your percent correct on our practice tests. The official GED score conversion is not public, so your real score may differ. Scores of 145+ pass; 165+ is College Ready.
Tip: Estimate first: $148.75 for 8.5 h is a bit over $17 per hour; $99 for 6 h is a bit over $16. So the weekly difference should be about $40 — a quick way to catch a slip.
Question 3 of 10 · Compare proportional relationships
Select all
A store manager wants every price rule to match $0.75 per item, with no extra fees. Which of these relationships are proportional and have a constant of proportionality k = 0.75? Select all that apply.
Select all that apply.
Hint
For each one, check two things: does it go through (0, 0), and is \frac{y}{x} always 0.75?
Step-by-step solution
y = \tfrac{3}{4}x: proportional, and \tfrac{3}{4} = 0.75 ✓.
Line through (0, 0) and (8, 6): passes through the origin; \tfrac{6}{8} = 0.75 ✓.
12 cans for $9 at the same price each:\tfrac{9}{12} = 0.75 dollar per can ✓.
y = \tfrac{4}{3}x: proportional, but \tfrac{4}{3} \approx 1.33, not 0.75 ✗.
y = 0.75x + 2: the +2 means (0, 2) is on the line, not (0, 0) — not proportional ✗.
Table (2, 1.5), (4, 2.5), (6, 3.5):\tfrac{1.5}{2} = 0.75 but \tfrac{2.5}{4} = 0.625 — the ratio changes ✗.
Answer: y = \tfrac{3}{4}x; the line through (0, 0) and (8, 6); 12 cans for $9
Check: Each correct choice gives y = 7.5 when x = 10: \tfrac{3}{4}(10) = 7.5; \tfrac{6}{8}(10) = 7.5; 0.75(10) = 7.5 ✓.
Tip: A fraction and a decimal can be the same rate. Convert everything to decimals before you compare.
Question 4 of 10 · Compare proportional relationships
No calculator
The graph shows the cost of ribbon at a craft store.
Which statement correctly describes the unit rate shown by the graph?
Hint
The unit rate is the cost of exactly 1 yard. Where is the line when x = 1?
Step-by-step solution
The line passes through (0, 0), so it is proportional.
Use the marked point (5, 6): 5 yards cost $6.
Unit rate = dollars ÷ yards = \tfrac{6}{5} = 1.20 dollars per yard.
The same rate comes from (10, 12): \tfrac{12}{10} = 1.20.
Answer: Ribbon costs $1.20 per yard.
Check: At x = 1 the line is a little above the $1 level — consistent with $1.20. Also 1.20 \times 10 = 12, matching the point (10, 12) ✓.
Tip: "Unit rate" always means "per 1" of the input on the horizontal axis. Read the axis labels to get the units right.
Question 5 of 10 · Identify functions
No calculatorSelect all
Select all graphs that represent y as a function of x.
Select all that apply.
Hint
Use the vertical line test on each graph. Be careful with lines: which direction fails?
Step-by-step solution
Graph A — a parabola opening to the right. The vertical line x = 0 crosses it twice (near y \approx 1.7 and y \approx -1.7) → not a function.
Graph B — a non-vertical straight line. Every vertical line crosses it exactly once → function.
Graph C — the vertical line x = 2. The input 2 has infinitely many outputs → not a function.
Graph D — an S-shaped curve that always rises. Every vertical line crosses it once → function.
Answer: Graphs B and D
Check: For B and D, pick any x — you can find exactly one point above or below it. For A and C, x = 0 and x = 2 (respectively) each have more than one point ✓
Tip: Sideways shapes and vertical lines fail; curves that keep moving left-to-right (even if they wiggle up and down) pass.
Question 6 of 10 · Evaluate linear and quadratic functions
No calculatorHot spot
Let k(x) = x^2 - 4.
Click the point on the coordinate plane that represents \big(-1,\ k(-1)\big).
Click on the figure to mark your answer (or focus it and use the arrow keys).
Hint
First find k(-1). Remember that (-1)^2 is positive. Then plot (input, output).
Step-by-step solution
Evaluate: k(-1) = (-1)^2 - 4.
Exponent first: (-1)^2 = (-1)(-1) = 1.
Subtract: 1 - 4 = -3. So k(-1) = -3.
The point is (\text{input}, \text{output}) = (-1, -3).
Plot it: from the origin move 1 left and 3 down.
Answer: the point (-1, -3)
Check:k(1) = 1 - 4 = -3 too, so (1, -3) is also on the graph. A parabola x^2 + c is symmetric about the y-axis, so the outputs at -1 and 1 must match ✓
Tip: Squaring a negative number gives a positive result. If you wrote (-1)^2 = -1 you would land on (-1, -5), two units too low.
Question 7 of 10 · Evaluate linear and quadratic functions
No calculatorFill in
For the function g(x) = -5x + 8, exactly one input produces an output of 33. Find that input.
x =
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Here 33 is the output. Set -5x + 8 equal to 33 and solve. Watch the sign when you divide.
Step-by-step solution
"g(x) = 33" gives the output; you need the input.
Write the equation: -5x + 8 = 33.
Subtract 8 from both sides: -5x = 25.
Divide both sides by -5: x = \dfrac{25}{-5} = -5.
Answer: x = -5
Check:g(-5) = -5(-5) + 8 = 25 + 8 = 33 ✓
Tip: The output 33 is larger than the starting value g(0) = 8, but the slope is negative (the function goes down as x goes right). So the input must be to the left of 0, a negative number. This quick sign check catches the common answer x = 5.
Question 8 of 10 · Identify functions
No calculator
A shuttle bus drives a loop and visits some stops twice. Its morning schedule is shown.
Relation II: input = arrival time, output = stop number.
Which statement is true?
Hint
Check each relation separately. Which column is the input in each one, and does any input repeat?
Step-by-step solution
Relation I (stop → time): the inputs are 1, 2, 3, 4, 3, 1. Stop 3 has two times (7:20 and 7:40), and stop 1 has two times (7:05 and 7:52) → not a function.
Relation II (time → stop): the inputs are the six times, which are all different. Each time has exactly one stop → function.
In Relation II, stops 1 and 3 appear twice as outputs, which is allowed.
Answer: Only Relation II is a function.
Check: Ask Relation I "When does the bus reach stop 3?" — two answers. Ask Relation II "Where is the bus at 7:40?" — one answer, stop 3 ✓.
Tip: Swapping input and output can change the answer. Repeated values in a column only matter when that column is the input.
Question 9 of 10 · Compare functions in different forms
No calculatorDrop-down
The function f is defined by f(x) = -x^2 + 10. The function g is a line with slope 2 that passes through the point (1, 3).
Complete the statements.
f(3) =
g(3) =
At x = 3, f is g.
Choose an answer from each menu.
Hint
For f, square first, then apply the negative sign. For g, start at (1, 3) and move 2 units right, rising 2 for each unit.
Step-by-step solution
f(3) = -(3)^2 + 10 = -9 + 10 = 1.
g: from (1, 3) to x = 3 is 2 units right; with slope 2 the output rises 2 \times 2 = 4. So g(3) = 3 + 4 = 7.
(Or find the equation: 3 = 2(1) + b, so b = 1 and g(x) = 2x + 1; g(3) = 7.)
Compare: 1 < 7, so f is less thang at x = 3.
Answer: f(3) = 1, g(3) = 7; f is less than g at x = 3.
Check:g(1) = 2 + 1 = 3 ✓ matches the given point.
Tip: In -x^2, the square is done first and the minus sign after: -(3)^2 = -9, never +9.
Question 10 of 10 · Identify functions
No calculator
A relation is shown in the table, where a is an unknown number.
x
a
3
6
9
y
10
4
10
2
Which value of a would make the relation NOT a function?
Hint
Try each choice. Does the new pair (a, 10) clash with another column that has the same input but a different output?
Step-by-step solution
The first column is the pair (a, 10). The relation fails only if a equals another input whose output is not 10.
a = 3: pairs (3, 10) and (3, 4) — input 3 has two outputs → not a function ✓.
a = 6: pairs (6, 10) and (6, 10) — the same pair twice; input 6 still has only the output 10 → function.
a = 10: 10 is a new input, so (10, 10) causes no clash → function.
a = 0: 0 is a new input → function.
Answer: a = 3
Check: With a = 3, asking "what is y when x = 3?" gets two answers, 10 and 4 ✓. (a = 9 would also fail, but it is not a choice.)
Tip: A repeated input only breaks a function when its outputs differ. The trap here is a = 6, which repeats the input but keeps the same output.