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.
Check: the diameter is 12 in, and C = \pi d = 3.14 \times 12 = 37.68 ✓. A circumference is always a bit more than 3 times the diameter: 3 \times 12 = 36 ✓.
Tip: Circumference = edge (ribbon, trim, fence). Area = surface (paint, fabric, grass). If you get a number with "square" units, you used the wrong formula.
Question 3 of 20 · Multiples and factors
No calculatorFill in
Find the largest whole number that divides both 42 and 70 with no remainder. (This number is called their greatest common factor.)
GCF =
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Write each number as a product of primes, or list the factors of the smaller number and test which ones divide the larger.
Step-by-step solution
Prime factorizations:
42 = 2 \times 3 \times 7
70 = 2 \times 5 \times 7
Primes they share: 2 and 7.
Multiply the shared primes (each appears once in both): 2 \times 7 = 14.
Listing method: factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. Which divide 70? 1, 2, 7, 14. The greatest is 14.
Answer: 14.
Check:42 \div 14 = 3 and 70 \div 14 = 5; since 3 and 5 share no factor except 1, no larger common factor exists. ✓
Tip: After dividing both numbers by your GCF, the results should have no common factor left. If they still share one, your GCF is too small.
Question 4 of 20 · Solve one-variable linear equations
Select all
Select all the equations that are true when x = -4.
Select all that apply.
Hint
Substitute -4 for x in each equation. Put the -4 in parentheses so you keep track of signs.
Step-by-step solution
Substitute x = -4 into each equation and compare both sides.
A:3(-4) + 20 = -12 + 20 = 8 ✓ true.
B:-2((-4) - 1) = -2(-5) = 10 ✓ true.
C:\dfrac{-4}{2} + 6 = -2 + 6 = 4, not 8 ✗ (this equation's solution is x = 4).
D:5 - (-4) = 5 + 4 = 9, not 1 ✗ (this equation's solution is x = 4).
E:0.5(-4) - 3 = -2 - 3 = -5 ✓ true.
The correct choices are A, B, and E.
Check: solve A directly: 3x = 8 - 20 = -12, so x = -4 ✓. Solve E: 0.5x = -2, so x = -4 ✓.
Tip: On "select all" questions, test every choice. Substituting is often faster than solving each equation, and parentheses around the negative value prevent sign mistakes.
Question 5 of 20 · Probability of simple and compound events
Fill in
A warehouse has 120 employees.
Full-time
Part-time
Total
Day shift
64
16
80
Night shift
24
16
40
Total
88
32
120
An employee on the night shift is chosen at random. What is the probability that this employee works part-time? Write your answer as a decimal.
Type your answer in the box. Fractions like 3/4 are fine.
Hint
You are choosing only from the night shift. How many people work nights?
Step-by-step solution
The employee is chosen from the night shift only, so the total is the night-shift row total: 40.
Check: The night row: 24 + 16 = 40 ✓, and \tfrac{24}{40} + \tfrac{16}{40} = 0.6 + 0.4 = 1 ✓
Tip: Watch the trap: 16 part-timers work days too, but they are not in the night-shift group. Dividing 16 by 32 (all part-timers) gives 0.5, which answers a different question.
Question 6 of 20 · Write linear equations from context
Fill in
Dana saves the same amount of money every week. The table shows her savings y, in dollars, after x weeks.
Week, x
2
5
8
11
Savings, y ($)
340
475
610
745
Write an equation for her savings in the form y = mx + b.
y =x\ +
Type your answer in the box. Fractions like 3/4 are fine.
Hint
The weeks go up by 3, not by 1. Find the change per one week, then work backwards from week 2 to week 0.
Step-by-step solution
Rate: from week 2 to week 5, savings rise 475 - 340 = 135 dollars in 5 - 2 = 3 weeks. Per week: \tfrac{135}{3} = 45. So m = 45.
Starting value: the table does not show week 0, so work backwards. From week 2 back to week 0 is 2 weeks, so subtract 2 \times 45 = 90: 340 - 90 = 250. So b = 250.
Tip: Two traps here. (1) The x-values jump by 3, so the change of 135 is not the weekly rate. (2) The first row is week 2, not week 0, so 340 is not the starting value. Always find b at x = 0.
Question 7 of 20 · Slope from a graph, equation or table
Fill in
A line passes through (2,\ 5) and (8,\ 9).
What is the slope of the line? Give your answer as a fraction or a decimal rounded to the nearest hundredth.
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Subtract the y-values, subtract the x-values in the same order, and simplify the fraction.
As a decimal: 2 \div 3 = 0.666\ldots \approx 0.67.
The slope is \tfrac{2}{3} (about 0.67).
Check: From (2, 5), go 3 right and 2 up twice: (5, 7), then (8, 9) — the second point ✓
Tip: A slope does not have to be a whole number. Leave it as a reduced fraction unless the question asks for a decimal — fractions are exact.
Question 8 of 20 · Graph solutions on a number line
No calculatorHot spot
Before shading a graph of \dfrac{x}{3} \le -1, Leo needs to draw the circle at the boundary. Click the number where that circle belongs.
Click on the figure to mark your answer (or focus it and use the arrow keys).
Hint
Solve the inequality first. The boundary is the value that makes both sides equal.
Step-by-step solution
x is divided by 3, so multiply both sides by 3. 3 is positive, so the sign does not change:
\frac{x}{3} \cdot 3 \le -1 \cdot 3 \quad\Rightarrow\quad x \le -3
The boundary is -3. (Because the symbol is \le, the circle will be closed and the shading will go left — but this question asks only where the circle goes.)
Answer: click -3 on the number line.
Check: At the boundary both sides are equal: \frac{-3}{3} = -1 ✓. Two common wrong clicks: 3 (sign error) gives \frac{3}{3} = 1 \ne -1; -4 (subtracting 3 instead of multiplying) gives \frac{-4}{3} \approx -1.33 \ne -1.
Tip: The boundary of any inequality is the solution of the matching equation. Solve \frac{x}{3} = -1, and the circle goes at that value.
Question 9 of 20 · Probability of simple and compound events
Fill in
A music app shuffles a playlist of 12 country songs, 20 pop songs, and 8 rock songs. It picks one song at random to play first.
What is the probability that the first song is rock? Write your answer as a percent.
%
Type your answer in the box. Fractions like 3/4 are fine.
Hint
First find how many songs are on the whole playlist.
Step-by-step solution
Total songs: 12 + 20 + 8 = 40.
Favorable (rock): 8.
P(\text{rock}) = \frac{8}{40} = \frac{1}{5}
As a decimal, 1 \div 5 = 0.2. As a percent, 0.2 \times 100\% = 20\%.
Tip: To change a fraction to a percent, divide and multiply by 100. The probabilities of all the categories must add up to 100%.
Question 10 of 20 · Composite 2-D figures
No calculatorDrag and drop
A U-shaped kitchen counter is drawn below. Dashed lines split it into rectangles A, B and C.
Drag the correct value into each box. Not every value is used.
Area of A (ft²)
Area of B (ft²)
Total area (ft²)
Tap a tile, then tap a box to place it.
Hint
Rectangle B sits under the notch. Its height is the full height minus the depth of the notch.
Step-by-step solution
Rectangle A (left arm): 4 ft wide and the full 8 ft tall: 4 \times 8 = 32\text{ ft}^2.
Rectangle B (bottom middle): its width is the notch width, 6 ft. Its height is 8 - 5 = 3 ft (the notch is 5 ft deep). Area 6 \times 3 = 18\text{ ft}^2.
Tip: After you split a figure, label each piece with its own width and height before multiplying. A piece under a notch is shorter than the whole figure.
Question 11 of 20 · Scatter plots and two-variable data
The scatter plot shows the years of experience and the hourly wage of 10 electricians. A trend line has been drawn through the data.
Based on the trend line, what is the predicted hourly wage for an electrician with 8 years of experience?
Hint
There is no data point at 8 years. Go up from 8 on the horizontal axis to the dashed line, then across.
Step-by-step solution
The question asks for a prediction from the trend line, not from a single data point. (No electrician in the data has exactly 8 years.)
Find where the line crosses gridlines. It starts at (0, 18) and ends at (12, 42). Over 12 years it rises 42 - 18 = 24 dollars, so it rises
\frac{24}{12} = 2 \text{ dollars per year}
Start at $18 and add $2 for each of 8 years:
18 + 2(8) = 18 + 16 = 34
On the graph: go up from 8 to the dashed line, then left to the axis. You land at $34.
The predicted wage is $34 per hour.
Check: On the line, 7 years gives 18 + 2(7) = 32 and 9 years gives 18 + 2(9) = 36. Halfway between $32 and $36 is $34 ✓
Tip: When a question says "based on the trend line," read the line, not the nearest dot. Finding the line's rate (rise over run between two clear gridline points) lets you predict any value exactly.
Question 12 of 20 · Scatter plots and two-variable data
A hot cocoa stand recorded the outdoor temperature and the number of cups sold on 10 winter days. A trend line has been drawn through the data.
The trend line has the equation y = -2x + 130. According to the trend line, at about what temperature would the stand sell 50 cups?
Hint
Is 50 a number of cups (y) or a temperature (x)? Put it in the right place in the equation and solve.
Step-by-step solution
The 50 is a number of cups, so it is a y-value. We need the matching x (temperature).
Set y = 50:
50 = -2x + 130
Subtract 130 from both sides:
-80 = -2x
Divide both sides by -2:
x = 40
The stand would sell about 50 cups at 40°F.
Check:-2(40) + 130 = -80 + 130 = 50 ✓ On the graph, the point (40, 52) is right next to the line near 50 cups.
Tip: Before plugging in, label the given number: is it an input (x) or an output (y)? Putting 50 in for x gives -2(50) + 130 = 30, which answers a different question: how many cups at 50°F.
The table shows the Nguyen family's electric bills for four months.
Month
Bill
January
$84
February
$105
March
$91
April
$70
What was the percent change in the bill from February to April?
Hint
Find the two values in the table first. Which month is the starting value?
Step-by-step solution
Read the table: February (the start) = \$105; April (the end) = \$70.
Find the change: 70 - 105 = -35 The bill went down by $35.
Divide by the starting value (February): \frac{-35}{105} = -\frac{1}{3} \approx -0.333
Change to a percent: -0.333 \times 100\% \approx -33.3\%
The bill decreased by about 33.3%.
Check:33.3\% of $105 is about \tfrac{1}{3} \times 105 = \$35, and 105 - 35 = \$70 ✓
Tip: With a table, circle the two values the question names (and ignore the others). The month that comes first in time is the original value, even if it is not the first row of the table.
Question 14 of 20 · Systems of two linear equations
A coffee shop mixes beans that cost $9 per pound with beans that cost $14 per pound. It wants 20 pounds of a blend worth $12 per pound. How many pounds of the $14 beans should it use?
Hint
Write one equation for the total weight and one for the total value. The blend is worth 20 \times 12 dollars.
Step-by-step solution
Let x = pounds of $9 beans and y = pounds of $14 beans.
The shop should use 12 pounds of the $14 beans (and 8 pounds of the $9 beans).
Check:9(8) + 14(12) = 72 + 168 = \$240, and \$240 \div 20 = \$12 per pound ✓
Tip: Estimate first. $12 is closer to $14 than to $9, so there must be more of the $14 beans — more than 10 pounds.
Question 15 of 20 · Systems of two linear equations
The graph shows the total cost of two car-share plans for different numbers of miles driven.
Plan A: $12 plus $0.50 per mile
Plan B: $4 plus $0.90 per mile
At how many miles do the two plans cost the same, and which plan costs less for a 30-mile trip?
Hint
The crossing point is where the costs are equal. Which axis shows miles? To the right of the crossing, which line is lower?
Step-by-step solution
Equal cost: the lines cross at the marked point (20, 22): at 20 miles, both plans cost $22. (The 22 is a cost in dollars, on the vertical axis.)
Confirm with algebra: 12 + 0.50m = 4 + 0.90m \Rightarrow 8 = 0.40m \Rightarrow m = 20, and 12 + 0.50(20) = 22.
30 miles: Plan A costs 12 + 0.50(30) = \$27. Plan B costs 4 + 0.90(30) = \$31. On the graph, the Plan A line is lower to the right of the crossing.
The plans cost the same at 20 miles, and Plan A is cheaper for a 30-mile trip.
Check: at 20 miles: Plan A 12 + 10 = 22, Plan B 4 + 18 = 22 ✓. At 30 miles: 27 < 31 ✓
Tip: A lower starting fee wins for short trips, but a lower per-mile rate wins for long trips. After the break-even point, the plan with the smaller rate (flatter line) is cheaper.
Question 16 of 20 · Write linear expressions from context
The table shows the total cost of online concert tickets, including a fixed service fee.
Number of tickets, t
1
2
3
4
Total cost ($)
13
21
29
37
Which expression gives the total cost, in dollars, for t tickets?
Hint
How much does the cost go up for each extra ticket? Then work out what the cost would be for 0 tickets.
Step-by-step solution
Find the rate: each extra ticket adds 21 - 13 = 8 dollars (also 29 - 21 = 8 and 37 - 29 = 8). So each ticket costs $8.
Find the fixed fee: go back one step from 1 ticket to 0 tickets: 13 - 8 = 5. The fee is $5.
Expression: 8t + 5.
The expression is 8t + 5.
Check:t = 3: 8(3) + 5 = 29 ✓ and t = 4: 8(4) + 5 = 37 ✓
Tip: the starting value is the output when the input is 0, which is often not in the table. Step back from the first row to find it.
Question 17 of 20 · Parallel and perpendicular lines
A second line crosses the graph of y = -3x + 4 at a right angle (it is perpendicular), and it goes through (6, 1). Find the equation of this second line.
Hint
Find the perpendicular slope first (flip and switch), then use the point to find b.
Step-by-step solution
The given slope is -3 = -\tfrac{3}{1}.
Perpendicular slope: flip to -\tfrac{1}{3}, switch the sign to +\tfrac{1}{3}.
Substitute (6, 1) into y = \tfrac{1}{3}x + b: 1 = \tfrac{1}{3}(6) + b = 2 + b.
Tip: A whole-number slope like -3 is the fraction -\tfrac{3}{1}. Writing the 1 makes the flip easy to see.
Question 18 of 20 · Linear expressions: combine, factor, expand
A teacher writes 14n - 35 on the board and asks the class to factor it completely. Which answer is correct?
Hint
List the factors of 14 and of 35. What is the biggest number on both lists?
Step-by-step solution
Factors of 14: 1, 2, 7, 14. Factors of 35: 1, 5, 7, 35.
The greatest common factor is 7.
Divide each term by 7: 14n \div 7 = 2n and 35 \div 7 = 5.
Write the GCF outside the parentheses: 14n - 35 = 7(2n - 5).
The answer is 7(2n - 5).
Check: expand: 7 \cdot 2n - 7 \cdot 5 = 14n - 35 ✓. Inside, 2n and 5 share no factor other than 1, so the factoring is complete.
Tip: after factoring, always look inside the parentheses. If the terms there still share a factor, you did not use the greatest one.
Question 19 of 20 · Pyramids and cones
Fill in
A children's play tent is shaped like a square pyramid with no floor. The base is 8 ft on each side, and the center pole is 3 ft tall.
How many square feet of fabric are needed to make the four triangular sides?
ft²
Type your answer in the box. Fractions like 3/4 are fine.
Hint
The fabric covers only the triangles, so you need the lateral area \tfrac{1}{2}ps. First find the slant height.
Step-by-step solution
Find the slant height. Half of a base edge is 8 \div 2 = 4 ft, and the height is 3 ft.
Pythagorean theorem: s^2 = 3^2 + 4^2 = 9 + 16 = 25, so s = 5 ft.
Perimeter of the base: p = 4 \times 8 = 32 ft.
Lateral area (no floor, so no B): \tfrac{1}{2}ps = \tfrac{1}{2}(32)(5) = 80.
Answer: 80 ft²
Check: Each triangle has base 8 and height 5, so its area is \tfrac{1}{2}(8)(5) = 20. Four triangles: 4 \times 20 = 80 ✓.
Tip: Read what the object covers. "No floor", "open top", or "just the sides" means you drop the base term B from the formula. The 3-4-5 triangle shows up a lot.
Question 20 of 20 · Unit rate as slope
Fill in
The table shows how much a part-time worker earns. Pay is proportional to hours worked.
Hours worked
2
5
9
Pay (dollars)
34.50
86.25
155.25
What is the worker's hourly pay rate?
$ per hour
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Divide the pay by the hours for one column. Check another column to be sure.
Step-by-step solution
The hourly rate is pay ÷ hours.
First column:
\frac{\$34.50}{2 \text{ h}} = \$17.25 \text{ per hour}
Second column: 86.25 \div 5 = 17.25 ✓
Third column: 155.25 \div 9 = 17.25 ✓
The ratio is the same every time, so the relationship is proportional with unit rate 17.25.
The worker earns $17.25 per hour.
Check:17.25 \times 9 = 155.25 — matches the last column ✓
Tip: In a proportional table, \frac{y}{x} is the same in every column. Checking two or three columns protects you from a typo or a non-proportional table.