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Question 1 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.
According to the trend line, about how much does an electrician's hourly wage increase for each additional year of experience?
Hint
Pick two points where the trend line crosses gridlines exactly. How much does the wage rise, and over how many years?
Step-by-step solution
The increase per year is the slope of the trend line: m = \frac{\text{change in wage}}{\text{change in years}} (The slope formula is on the GED formula sheet.)
Choose two clear points on the line: (0, 18) and (12, 42).
The units are dollars per hour per year of experience.
The wage increases by about $2 per hour for each year of experience.
Check: Use other points on the line: at 6 years the line is at $30, and \frac{30 - 18}{6 - 0} = 2 ✓
Tip: "Increase for each" or "per" signals the slope. The y-intercept ($18) is a starting value, and dividing one y-value by one x-value (42 \div 12) is not a slope unless the line goes through the origin.
Question 2 of 20 · Evaluate linear expressions
Jordan evaluated 10 - 4x when x = -2:
Step 1: 10 - 4(-2)
Step 2: 6(-2)
Step 3: -12
Which statement is true?
Hint
Look at Step 2. What should be done first in 10 - 4(-2): the subtraction or the multiplication?
Step-by-step solution
Step 1 is correct: the value -2 is substituted in parentheses.
Step 2 is wrong: Jordan did 10 - 4 = 6 first. Multiplication must come before subtraction.
The true statement is Step 2 is wrong; he should multiply first, and the correct value is 18.
Check: read -4x as (-4)(x): (-4)(-2) = +8, and 10 + 8 = 18 ✓
Tip: the number right in front of a variable is glued to it by multiplication. Never "borrow" it to subtract from the number before it.
Question 3 of 20 · Graph solutions on a number line
No calculatorSelect all
The number line shows the solution set of an inequality.
Select all values that are in the solution set.
Select all that apply.
Hint
Write the inequality from the graph first. Is -1 itself included?
Step-by-step solution
Circle: open → -1 is not included.
Direction: shaded right → greater than -1.
The graph shows x > -1.
Check each choice:
-3: -3 > -1? No (it is to the left).
-1: -1 > -1? No (open circle).
-0.5: -0.5 > -1? Yes — -0.5 is to the right of -1.
0: Yes.
4: Yes.
Answer: -0.5, 0, and 4
Check: On the number line, -0.5 sits halfway between -1 and 0, inside the shaded part ✓.
Tip: Negative numbers can be "greater": -0.5 > -1 because -0.5 is closer to zero, so it is farther right.
Question 4 of 20 · Write linear equations from context
Jamal bought 4 shirts that each cost the same amount and one belt for $12. He spent $96 in all. Which equation can be used to find p, the price of one shirt?
Hint
How much did the 4 shirts cost together, written with p? Then add what else he bought.
Step-by-step solution
One shirt costs p dollars, so 4 shirts cost 4p dollars.
The belt is bought once: $12.
Shirts + belt = total spent:
4p + 12 = 96
The equation is 4p + 12 = 96.
Check: solve it. 4p = 96 - 12 = 84, so p = 21. Four shirts at $21 cost $84, plus the $12 belt is $96 ✓
Tip: Only the item bought several times gets the multiplier. Something bought once (the belt) is added on its own, outside any parentheses.
Question 5 of 20 · Cubes and cube roots
No calculator
Which expression has a value of -8?
Hint
A cube root of a negative number is negative. Also check what a minus sign outside the root does.
Step-by-step solution
Evaluate each choice.
\sqrt[3]{-512}: 8^3 = 512, so (-8)^3 = -512 and \sqrt[3]{-512} = -8. ✓
-\sqrt[3]{-512} = -(-8) = 8. ✗ (the outside minus flips the sign)
\sqrt[3]{-24}: (-2)^3 = -8 and (-3)^3 = -27, so \sqrt[3]{-24} is between -2 and -3 (about -2.88). ✗
(-2)^3 \cdot (-1) = (-8)(-1) = 8. ✗
Answer: \sqrt[3]{-512}
Check:(-8)(-8)(-8) = 64 \cdot (-8) = -512 ✓.
Tip: Cube roots of negatives are allowed (unlike square roots): an odd number of negative factors stays negative. Count the minus signs carefully — one inside and one outside cancel out.
Question 6 of 20 · Points in the coordinate plane
No calculator
A point lies on the y-axis, 3 units below the origin. Which ordered pair names this point?
Hint
Every point on the y-axis has the same x-coordinate. What is it?
Step-by-step solution
A point on the y-axis has not moved left or right at all, so its x-coordinate is 0.
"3 units below the origin" means the y-coordinate is -3 (down is negative).
Put them in order (x,\ y).
The point is (0,\ -3).
Check: Plot it: start at the origin, move 0 left/right, then 3 down — you are on the vertical axis ✓
Tip: On the y-axis, x = 0. On the x-axis, y = 0. Points on an axis are not in any quadrant.
Question 7 of 20 · Pythagorean theorem
No calculator
In triangle PQR, angle Q is a right angle.
Which side of the triangle is the hypotenuse?
Hint
The hypotenuse is across from the right angle. Which side does not have Q as an endpoint?
Step-by-step solution
The right angle is at vertex Q.
The two sides that meet at Q are \overline{PQ} and \overline{QR}. These are the legs.
The hypotenuse is the side opposite the right angle — the only side that does not touch Q. That side connects the other two vertices: \overline{PR}.
The hypotenuse is \overline{PR}.
Check: a quick test — the hypotenuse's name never contains the letter of the right-angle vertex. PR has no Q ✓.
Tip: On the GED, triangles are often named by letters with no picture. Find the right-angle letter; the hypotenuse is named by the other two letters. In a^2 + b^2 = c^2, that side is c.
Question 8 of 20 · Write polynomial expressions from context
A bike rental shop rents 60 bikes a day at $25 each. For each $5 increase in the daily price, it expects to rent 4 fewer bikes. Let x be the number of $5 increases.
Which polynomial represents the shop's daily rental revenue, in dollars?
Hint
Price = 25 + 5x (each step is $5, not $1). Bikes rented = 60 - 4x. Multiply and combine like terms.
Tip: The size of each price step goes into the price factor: $5 steps give 25 + 5x. Using 25 + x would mean $1 steps.
Question 9 of 20 · Absolute value and distance on a number line
Fill in
Marcus's checking account was overdrawn, with a balance of −$45.50. After he deposited his paycheck, the balance was $120.25.
How much was the deposit, in dollars?
$
Type your answer in the box. Fractions like 3/4 are fine.
Hint
The deposit first had to cover the negative balance to bring it up to $0, and then add the rest.
Step-by-step solution
The deposit is the change in balance: new balance - old balance.
120.25 - (-45.50) = 120.25 + 45.50.
120.25 + 45.50 = 165.75.
The deposit was $165.75.
Check: start at -45.50 and add 165.75: -45.50 + 165.75 = 120.25. ✓
Tip: Of the deposit, $45.50 brought the balance up to zero and $120.25 is what is left. A common error is 120.25 - 45.50 = 74.75, which treats the overdraft as money he had.
Question 10 of 20 · Line from two points
The table shows several points on a line.
x
0
1
2
3
y
4
7
10
13
Which equation represents the line?
Hint
How much does y change each time x goes up by 1? What is y when x = 0?
Step-by-step solution
Each time x increases by 1, y increases by 3 (4 \to 7 \to 10 \to 13). So the slope is m = \dfrac{3}{1} = 3.
Using two points from the table, (0, 4) and (1, 7): m = \dfrac{7 - 4}{1 - 0} = 3 ✓.
The table contains x = 0 with y = 4, so the y-intercept is b = 4.
Tip: If a table includes x = 0, the y-value there is the y-intercept — no algebra needed. Always test one more row to be sure.
Question 11 of 20 · Compare functions in different forms
The graph of the function f is shown. The function g is defined by g(x) = x^2 - 4.
Which statement correctly compares the greatest x-intercept of each function?
Hint
Read where the graph of f crosses the x-axis. For g, solve x^2 - 4 = 0.
Step-by-step solution
x-intercepts are where the output is 0.
f (graph): the curve crosses the x-axis at x = -1 and x = 5. Greatest: 5.
g: solve x^2 - 4 = 0 → x^2 = 4 → x = 2 or x = -2. Greatest: 2.
Compare: 5 > 2.
Answer: f: 5 and g: 2, so f has the greater x-intercept.
Check:g(2) = 4 - 4 = 0 ✓. The graph of f fits f(x) = x^2 - 4x - 5 = (x + 1)(x - 5), and f(5) = 0 ✓
Tip: Don't confuse the three key points of a parabola: the x-intercepts (output 0), the y-intercept (input 0) and the vertex (turning point). The graph of f shows all three.
Question 12 of 20 · Write linear expressions from context
The sign below is shaped like an isosceles triangle. The base is b inches long, and each of the two equal sides is 2 inches longer than the base.
Which expression represents the perimeter of the sign, in inches?
Hint
The perimeter adds all three sides. Two of them are b + 2.
Step-by-step solution
List the sides: b, b + 2, b + 2.
Add them: b + (b + 2) + (b + 2), or b + 2(b + 2).
Simplify: b + 2b + 4 = 3b + 4.
The perimeter is 3b + 4 inches.
Check: if b = 10, the sides are 10, 12 and 12, and the perimeter is 34. The expression: 3(10) + 4 = 34 ✓
Tip: write each side separately before simplifying. That way you see that the +2 appears twice, giving +4.
Question 13 of 20 · Write rational expressions from context
No calculator
A delivery driver can take one of two routes.
Route A: 50 miles on the highway at r miles per hour.
Route B: 40 miles through town at 15 miles per hour slower than r.
Which expression represents how many hours longer Route B takes than Route A?
Hint
Write each route's time as distance ÷ speed. Subtract Route A's time from Route B's time over the common denominator r(r - 15).
Step-by-step solution
Route A time: \dfrac{50}{r}.
Route B speed: r - 15, so time: \dfrac{40}{r - 15}.
How much longer B takes: \dfrac{40}{r - 15} - \dfrac{50}{r}.
Tip: "Solutions," "roots," "zeros" and "x-intercepts" all point to the same places — where the graph touches the x-axis.
Question 15 of 20 · Multi-step real-world problems
Ana used a gift card to buy 2 movie tickets at $13.75 each and a popcorn combo for $18.40. She has $54.10 left on the card. How much was on the gift card at the start?
Hint
The money she spent plus the money left equals the starting amount. Undo the spending by adding.
Step-by-step solution
Cost of the tickets: 2 \times 13.75 = 27.50.
Total spent: 27.50 + 18.40 = 45.90.
Work backwards: spending is undone by adding. Start = 54.10 + 45.90 = 100.00.
Tip: When the problem gives the end amount and asks for the start, reverse each step with the opposite operation. Money spent → add it back. Don't forget to multiply by the quantity (2 tickets) before adding.
Question 16 of 20 · Cylinders
A paper label wraps exactly once around the curved side of a can, with no overlap. The label is 5\text{ in} tall and has an area of 94.2\text{ in}^2.
Using 3.14 for \pi, what is the radius of the can?
Hint
The label's area is the lateral area 2\pi rh. Solve for r.
Tip: Think of the label as a rectangle: its width is the can's circumference. Dividing the area by the height gives the circumference (18.84); dividing that by 2\pi gives the radius.
Question 17 of 20 · Right prisms
Fill in
A decorative candle is a prism whose base is a pentagon. The area of the pentagon is 35\text{ in}^2, and the candle is 12\text{ in} tall.
What is the volume of the candle?
\text{in}^3
Type your answer in the box. Fractions like 3/4 are fine.
Hint
You don't need a pentagon formula. The area of the base is already given; use V = Bh.
Step-by-step solution
For every prism, V = Bh, where B is the area of the base.
Here B = 35\text{ in}^2 (given) and h = 12\text{ in}.
V = 35 \times 12 = 420.
The candle's volume is 420\text{ in}^3.
Check:420 \div 12 = 35, the base area ✓.
Tip: When the problem hands you the base area, the shape of the base no longer matters. The formula V = Bh works for prisms with any polygon base, and it is on the GED formula sheet.
Question 18 of 20 · Real-world inequalities
A city water bill is a $18.50 monthly service charge plus $0.006 per gallon used. The Nguyen family wants their bill to be no more than $60 this month. What is the greatest number of whole gallons they can use?
Hint
Remove the service charge from the budget first. Dividing by a small decimal makes a big number — estimate to check.
Step-by-step solution
Let g = gallons used. Bill = 18.50 + 0.006g.
Bill must be no more than $60:
18.50 + 0.006g \le 60
Subtract 18.50: 0.006g \le 41.50.
Divide by 0.006:
g \le \frac{41.50}{0.006} = 6916.\overline{6}
Round down to stay within budget: 6,916 gallons.
Answer: 6,916 gallons
Check:18.50 + 0.006(6{,}916) = 18.50 + 41.496 = 59.996 \approx \$60.00 ✓. With 6,917 gallons: 18.50 + 41.502 = 60.002, which rounds to $60.00 but is over the limit ✗.
Tip: Estimate first: about $40 at less than a cent per gallon means several thousand gallons. If your answer is far off, recheck the decimal.
Question 19 of 20 · Scale factors and scale drawings
Fill in
A rectangular community garden is drawn on a plan as 5 inches by 3 inches. The actual garden has an area of 1,500 square feet. How many feet does 1 inch on the plan represent?
feet
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Compare the two areas first. Then remember that area grows by the square of the scale.
Step-by-step solution
Area on the plan: 5 \times 3 = 15\text{ in}^2
Each square inch on the plan stands for 1{,}500 \div 15 = 100\text{ ft}^2
A square inch is 1 inch by 1 inch, so it stands for a square of side s feet with s^2 = 100: s = \sqrt{100} = 10\text{ ft}
1 inch on the plan represents 10 feet.
Check: Real garden: 5 \times 10 = 50 ft by 3 \times 10 = 30 ft, and 50 \times 30 = 1{,}500 ft² ✓
Tip: The area ratio equals the square of the length scale. Divide the areas, then take the square root to get feet per inch. Stopping at 100 is the classic trap.
Question 20 of 20 · Polygons: area and perimeter
Select all
Select all of the figures that have an area of exactly 24 square units.
Select all that apply.
Hint
Compute each area with the right formula. Be careful about which number is the height and whether the formula has a \tfrac{1}{2}.
Step-by-step solution
Find each area.
Parallelogram, base 6, height 4: A = 6 \times 4 = 24 ✓
Trapezoid, bases 4 and 8, height 4: A = \tfrac{1}{2}(4)(4 + 8) = 2 \times 12 = 24 ✓
Parallelogram, base 8, slanted side 3, height 2: A = 8 \times 2 = 16 ✗ (using the slanted side gives 8 \times 3 = 24 — the trap)
Trapezoid, bases 4 and 8, height 2: A = \tfrac{1}{2}(2)(12) = 12 ✗ (forgetting the \tfrac{1}{2} gives 24)
Regular hexagon, side 4: its perimeter is 6 \times 4 = 24, but its area is not 24 (it is about 41.6) ✗
Correct: the parallelogram with base 6 and height 4, and the trapezoid with bases 4 and 8 and height 4.
Check: recompute the first trapezoid as average base × height: 6 \times 4 = 24 ✓.
Tip: In "select all" questions, the wrong choices are built from the classic slips — slanted side as height, a missing \tfrac{1}{2}, perimeter instead of area. Work each choice out fully rather than guessing from the numbers.