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.
The correct order is 0.6,\ \tfrac{5}{8},\ 0.65,\ \tfrac{2}{3}.
Check: Each number in the list is bigger than the one before it: 0.625 - 0.6 = 0.025 > 0, 0.65 - 0.625 = 0.025 > 0, and 0.667 - 0.65 > 0. ✓
Tip: Memorize the common fraction–decimal pairs for the no-calculator part: \tfrac{1}{8} = 0.125, \tfrac{5}{8} = 0.625, \tfrac{1}{3} \approx 0.333, \tfrac{2}{3} \approx 0.667. Adding zeros to the end of a decimal (0.6 = 0.600) makes the comparison easy.
Question 2 of 5 · Rules of exponents
No calculatorFill in
Simplify the expression. Write your answer as a whole number.
\dfrac{5^{6} \cdot 5^{-2}}{5^{3}}
Type your answer in the box. Fractions like 3/4 are fine.
Hint
When you multiply powers with the same base, add the exponents. When you divide, subtract them.
Step-by-step solution
Multiply in the numerator by adding exponents (same base 5): 5^{6} \cdot 5^{-2} = 5^{6 + (-2)} = 5^{4}.
Check: Work it out the long way: 5^{6} = 15{,}625 and 5^{-2} = \tfrac{1}{25}, so the top is 15{,}625 \div 25 = 625. Then 625 \div 5^{3} = 625 \div 125 = 5. ✓
Tip: A negative exponent does not make the number negative — it means "one over": 5^{-2} = \tfrac{1}{25}. A common slip is to multiply the exponents (6 \times -2 = -12); that rule is only for a power raised to a power, like (5^{6})^{2}.
Question 3 of 5 · Absolute value and distance on a number line
No calculator
What is the value of the expression below?
\lvert -8 + 3 \rvert - \lvert -4 \rvert
Hint
Treat absolute-value bars like parentheses: finish the work inside them first, then take the distance from zero.
Step-by-step solution
Work inside the first bars: -8 + 3 = -5.
Take the absolute value: \lvert -5 \rvert = 5.
The second absolute value: \lvert -4 \rvert = 4.
Subtract: 5 - 4 = 1.
The value is 1.
Check: Absolute value is always 0 or positive, so both pieces are positive (5 and 4). Subtracting the smaller from the larger must give a small positive number: 1. ✓
Tip: Never "make everything positive" before you combine what is inside the bars. \lvert -8 + 3 \rvert is 5, not 8 + 3 = 11. And the minus sign outside\lvert -4 \rvert stays: -\lvert -4 \rvert = -4.
Question 4 of 5 · Add, subtract, multiply and divide rational numbers
No calculator
A fitness trail is 6\tfrac{3}{4} miles long. The park places a water station at the end of every \tfrac{3}{4}-mile section. Into how many \tfrac{3}{4}-mile sections is the trail divided?
Hint
"How many \tfrac{3}{4}s fit into 6\tfrac{3}{4}?" is a division question. Change the mixed number to an improper fraction first.
Step-by-step solution
Change the mixed number to an improper fraction: 6\tfrac{3}{4} = \dfrac{6 \times 4 + 3}{4} = \dfrac{27}{4}.
Divide by \tfrac{3}{4} — multiply by its reciprocal \tfrac{4}{3}:
\dfrac{27}{4} \div \dfrac{3}{4} = \dfrac{27}{4} \times \dfrac{4}{3} = \dfrac{108}{12} = 9
Tip: "Keep – change – flip": keep the first fraction, change \div to \times, flip the second fraction. A quick estimate also helps: dividing by a number less than 1 gives an answer larger than the number you started with, so 6\tfrac{3}{4} \div \tfrac{3}{4} must be more than 6\tfrac{3}{4}. Answers like \tfrac{1}{9} or 5\tfrac{1}{16} cannot be right.
Question 5 of 5 · Cubes and cube roots
No calculatorFill in
Evaluate the expression.
4 + 3(5 - 2)^{2} - \sqrt[3]{27}
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Follow the order of operations: parentheses, then exponents and roots, then multiplication, then addition and subtraction from left to right.
Step-by-step solution
Parentheses:5 - 2 = 3, so the expression is 4 + 3(3)^{2} - \sqrt[3]{27}.
Add/subtract left to right:4 + 27 = 31, then 31 - 3 = 28.
The value is 28.
Check: Common wrong paths give different numbers: adding 4 + 3 first gives 7 \times 9 - 3 = 60; squaring 3 \times 3 gives 4 + 81 - 3 = 82. Only the correct order gives 28. ✓
Tip: The number touching the parentheses (3(\ldots)^2) multiplies after the exponent is applied. Know the small cubes by heart for Part 1: 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125.
Question 1 of 41 · Evaluate linear expressions
A taxi company charges a flat fee of $3.50 plus $2.25 per mile. The fare, in dollars, for a ride of m miles is
3.50 + 2.25m
What is the fare for an 8-mile ride?
Hint
Replace m with 8. Multiply before you add.
Step-by-step solution
Substitute m = 8 into the expression: 3.50 + 2.25(8).
Multiply first (order of operations): 2.25 \times 8 = 18.00.
Then add the flat fee: 3.50 + 18.00 = 21.50.
The fare is $21.50.
Check: Estimate: about $2 per mile for 8 miles is about $16–$18, plus a few dollars for the flat fee — around $20. $21.50 fits; $46.00 is far too high. ✓
Tip: In an expression like 3.50 + 2.25m, the number alone (3.50) is the one-time charge and the number next to the variable (2.25) is the charge per mile. Only the per-mile charge gets multiplied by the miles.
Question 2 of 41 · Unit rates
On a road trip, Marcus drove 270 miles and used 12 gallons of gasoline. What was his car's fuel economy, in miles per gallon?
Hint
"Miles per gallon" means miles \div gallons.
Step-by-step solution
The unit you want is miles per gallon, so miles go on top and gallons on the bottom:
\text{fuel economy} = \dfrac{270 \text{ miles}}{12 \text{ gallons}}
Divide: 270 \div 12 = 22.5.
The car got 22.5 miles per gallon.
Check:22.5 \text{ miles per gallon} \times 12 \text{ gallons} = 270 miles. ✓ Also, a typical car gets 20–35 mpg, so 22.5 is reasonable.
Tip: Let the units tell you what to divide. The word after "per" is always the denominator. If you divide the other way (12 \div 270) you get gallons per mile — a correct rate, but not the one asked for.
Question 3 of 41 · Solve one-variable linear equations
Fill in
Solve for x.
4(x - 3) + 2 = 18
x =
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Distribute the 4 first, combine the constant terms, then undo the operations one at a time.
Tip: When the 4 multiplies a parenthesis, it multiplies both terms inside: 4 \cdot xand4 \cdot (-3). Writing 4x - 3 (distributing to only the first term) is the most common mistake on this kind of question and would give x = 4.75.
Question 4 of 41 · Bar graphs and circle graphs
The bar graph shows the number of overtime hours Dana worked during each of five weeks.
How many more overtime hours did Dana work in Week 4 than in Week 3?
Hint
Read the height of each bar against the gridlines, then subtract the smaller from the larger.
Step-by-step solution
Find the Week 4 bar: it reaches halfway between the 10 and 12 gridlines, so Week 4 = 11 hours.
Find the Week 3 bar: it stops exactly on the 4 gridline, so Week 3 = 4 hours.
"How many more" means subtract: 11 - 4 = 7.
Dana worked 7 more overtime hours in Week 4.
Check: Count up from 4 to 11: 5, 6, 7, 8, 9, 10, 11 — that is 7 steps. ✓
Tip: Before you read any bar, check the scale of the vertical axis. Here each gridline is 2 hours, so a bar between two gridlines is an odd number. Also, point to the exact two bars named in the question — picking a neighboring bar is a very common slip.
Question 5 of 41 · Write linear expressions from context
A gym charges a one-time sign-up fee of $45 plus $29 per month. Which expression gives the total cost, in dollars, of a membership for m months?
Hint
Which amount is paid only once, and which amount is paid every month?
Step-by-step solution
The one-time fee is paid once, no matter how many months: 45.
The monthly charge is paid m times: 29 \times m = 29m.
Check: Test a value. For 2 months you pay $45 once plus $29 twice: 45 + 29 + 29 = 103. The expression gives 45 + 29(2) = 45 + 58 = 103. ✓
Tip: In a "flat fee plus a rate" situation, the rate is attached to the variable and the flat fee stands alone. Plugging in a small number like m = 1 or m = 2 is a fast way to test each answer choice.
Question 6 of 41 · Pythagorean theorem
A delivery truck leaves the depot, drives 16 miles east, then turns and drives 12 miles north to a customer, as shown.
What is the straight-line distance, in miles, from the depot to the customer?
Hint
East and north meet at a right angle. The straight-line distance is the hypotenuse.
Step-by-step solution
The east leg and the north leg form a right angle, so use the Pythagorean theorem (on the formula sheet): a^{2} + b^{2} = c^{2}.
Substitute the legs a = 16 and b = 12:
c^{2} = 16^{2} + 12^{2} = 256 + 144 = 400
Take the square root: c = \sqrt{400} = 20.
The straight-line distance is 20 miles.
Check: The hypotenuse must be longer than each leg (20 > 16 ✓) but shorter than their sum (20 < 28 ✓). Also, 12-16-20 is the 3-4-5 triangle multiplied by 4. ✓
Tip: Learn the common right-triangle "triples": 3-4-5, 5-12-13, 8-15-17 and their multiples (6-8-10, 9-12-15, 12-16-20). On the TI-30XS, press 2ndx² (√), then type 16x²+12x² under the root and press enter → 20.
Question 7 of 41 · Real-world inequalities
Luis drives for a delivery company. He earns $18 per hour plus a flat $40 weekly fuel allowance. What is the least whole number of hours Luis must work this week to earn at least $500?
Hint
Write an inequality: hourly pay plus the allowance must be greater than or equal to 500. After solving, think about which whole number actually reaches $500.
Step-by-step solution
Let h = hours worked. "At least $500" means \ge 500:
18h + 40 \ge 500
Subtract 40 from both sides: 18h \ge 460.
Divide both sides by 18: h \ge 25.\overline{5} (about 25.56).
Luis needs a whole number of hours that is at least 25.56. 25 is too small, so the least whole number is 26.
Luis must work 26 hours.
Check: 26 hours: 18(26) + 40 = 468 + 40 = 508 \ge 500 ✓. 25 hours: 18(25) + 40 = 450 + 40 = 490 < 500 ✗. So 26 is the smallest that works.
Tip: With "at least" questions, round up to the next whole number, even if the decimal is small — rounding down always leaves you short. Always test your answer and the number just below it.
A pair of running shoes is regularly priced at $120. The store is taking 25% off, and then a 7% sales tax is added to the sale price. What is the total cost of the shoes?
Hint
Do the two percents one at a time: first find the sale price, then add tax on the sale price.
Check: The total must be less than $120 (big discount) but more than $90 (tax added). $96.30 is between them. ✓
Tip: You cannot combine "25% off" and "7% tax" into one "18% off," because the two percents are taken of different amounts ($120 and $90). Multiply by 0.75, then by 1.07 — a fast, reliable method on the calculator.
Question 9 of 41 · Systems of two linear equations
Hot spot
Click the point on the coordinate plane that is the solution of this system of equations.
\begin{cases} y = x + 1 \\ y = -2x + 4 \end{cases}
Click on the figure to mark your answer (or focus it and use the arrow keys).
Hint
Both equations are already solved for y, so set the right sides equal to each other and solve for x first.
Step-by-step solution
Both expressions equal y, so set them equal: x + 1 = -2x + 4.
Add 2x to both sides: 3x + 1 = 4.
Subtract 1: 3x = 3, so x = 1.
Find y with either equation: y = 1 + 1 = 2.
The solution is the point (1,\ 2): from the origin move 1 right and 2 up, and click there.
The solution is (1,\ 2).
Check: Second equation: -2(1) + 4 = -2 + 4 = 2 ✓. The point works in both equations, so it is where the two lines cross.
Tip: The solution of a system is the one point that makes every equation true. Don't click a y-intercept like (0,\ 1) or (0,\ 4) — each works in only one equation. Also remember the order: (x,\ y) means across first, then up or down.
Question 10 of 41 · Slope from a graph, equation or table
The table shows the amount of fuel left in a delivery van's tank after it has been driven a certain number of miles.
Miles driven, x
0
60
120
180
Fuel left (gallons), y
16
13.6
11.2
8.8
What is the slope of the line through these points, in gallons per mile?
Hint
Slope = \dfrac{\text{change in } y}{\text{change in } x}. Pick any two columns. Is the fuel going up or down?
Step-by-step solution
Use the slope formula (on the formula sheet) with two points, for example (0,\ 16) and (60,\ 13.6):
m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{13.6 - 16}{60 - 0} = \dfrac{-2.4}{60}
Divide: -2.4 \div 60 = -0.04.
The slope is -0.04 gallon per mile — the van uses 0.04 gallon for every mile.
Check: Use two other columns: \dfrac{8.8 - 11.2}{180 - 120} = \dfrac{-2.4}{60} = -0.04 ✓. Over the whole table: \dfrac{8.8 - 16}{180 - 0} = \dfrac{-7.2}{180} = -0.04 ✓.
Tip: When y goes down as x goes up, the slope must be negative — use this to cross out positive choices right away. Keep the order the same on top and bottom (second point minus first point in both).
Question 11 of 41 · Mean, median, mode, range, weighted average
Fill in
Keisha is training for a race. Her goal is to average 5 miles per run over 5 runs this week. Her first four runs were 4.5, 6.2, 3.8, and 5.0 miles.
How many miles must she run on her fifth run to meet her goal exactly?
miles
Type your answer in the box. Fractions like 3/4 are fine.
Hint
An average of 5 over 5 runs means the five distances must add up to a certain total. What is that total?
Step-by-step solution
Mean = \dfrac{\text{sum}}{\text{count}}, so the required sum is \text{mean} \times \text{count} = 5 \times 5 = 25 miles.
Add the first four runs: 4.5 + 6.2 + 3.8 + 5.0 = 19.5 miles.
Subtract to find what is still needed: 25 - 19.5 = 5.5 miles.
Tip: For any "what score/amount do I need for an average of ___" question, multiply the target average by the total number of items (including the missing one), then subtract what you already have. Don't average the four runs and stop — that answers a different question.
Question 12 of 41 · Solve quadratic equations
What are the solutions of the equation below?
x^{2} - 2x - 15 = 0
Hint
Look for two numbers that multiply to -15 and add to -2.
Step-by-step solution
Find two numbers whose product is -15 and whose sum is -2. Try factor pairs of -15: (1,-15) adds to -14; (3,-5) adds to -2 ✓.
Factor: x^{2} - 2x - 15 = (x + 3)(x - 5).
Set each factor equal to zero: x + 3 = 0 \Rightarrow x = -3; x - 5 = 0 \Rightarrow x = 5.
Tip: The solutions have the opposite signs of the numbers in the factors: (x + 3) gives x = -3. If factoring is hard, the quadratic formula on the formula sheet always works: x = \dfrac{2 \pm \sqrt{4 + 60}}{2} = \dfrac{2 \pm 8}{2}, giving 5 and -3.
Question 13 of 41 · Cylinders
A truck stop stores diesel fuel in the cylindrical tank shown.
What is the volume of the tank, to the nearest cubic foot? Use \pi \approx 3.14.
Hint
Volume of a cylinder = \pi r^{2} h (on the formula sheet). Is the 3 ft a radius or a diameter?
Step-by-step solution
The figure labels the radiusr = 3 ft (center to edge) and the height h = 8 ft.
Use V = \pi r^{2} h:
V = 3.14 \times 3^{2} \times 8 = 3.14 \times 9 \times 8 = 3.14 \times 72 = 226.08
Round to the nearest cubic foot: 226.
The volume is about 226 cubic feet.
Check: Estimate with \pi \approx 3: 3 \times 9 \times 8 = 216 — close to 226 ✓. Using the calculator's π key gives 72\pi; press toggle to see 226.19, which also rounds to 226.
Tip: Square the radius before multiplying (3^{2} = 9, not 3 \times 2). If a problem gives the diameter, halve it first. Volume is in cubic units, area in square units — the units can help you pick the right formula.
Question 14 of 41 · Evaluate linear and quadratic functions
The function f is defined as f(x) = 2x^{2} - 3x + 1. What is the value of f(-2)?
Hint
Replace every x with (-2) — keep the parentheses. Square first, then multiply.
Check: On the TI-30XS type 2((−)2)x²−3((−)2)+1enter → 15 ✓.
Tip: A negative number squared is positive: (-2)^{2} = 4, but -2^{2} without parentheses means -(2^{2}) = -4. Always wrap a negative input in parentheses, both on paper and on the calculator (use the (−) key, not the minus key).
Question 15 of 41 · Probability of simple and compound events
A basketball player makes 80% of her free throws. Each shot is independent of the others. What is the probability that she makes both of her next two free throws?
Hint
For two independent events that both happen, multiply their probabilities.
Step-by-step solution
Write 80% as a decimal: P(\text{make}) = 0.80.
The shots are independent, so P(\text{make and make}) = P(\text{make}) \times P(\text{make}).
Multiply: 0.80 \times 0.80 = 0.64.
The probability is 0.64 (64%).
Check: Both shots succeeding should be less likely than one shot succeeding, so the answer must be below 0.80 ✓. Also, the four outcomes add to 1: make–make 0.64, make–miss 0.16, miss–make 0.16, miss–miss 0.04; 0.64 + 0.16 + 0.16 + 0.04 = 1 ✓.
Tip: "And" (both happen) → multiply. "Or" (either one) for events that can't happen together → add. A probability can never be greater than 1, so any answer above 1 is wrong immediately.
Question 16 of 41 · Line from two points
A bike-rental shop charges a fixed fee plus an hourly rate. A 2-hour rental costs $23, and a 6-hour rental costs $47. Which equation gives the total cost y, in dollars, of renting a bike for x hours?
Hint
Write the two rentals as points (x,\ y). Find the slope first, then use one point to find the y-intercept.
Step-by-step solution
The rentals give two points: (2,\ 23) and (6,\ 47).
Use y = mx + b with the point (2,\ 23): 23 = 6(2) + b \Rightarrow 23 = 12 + b \Rightarrow b = 11.
Equation: y = 6x + 11 (a $11 fixed fee plus $6 per hour).
The equation is y = 6x + 11.
Check: Test both rentals. x = 2: 6(2) + 11 = 23 ✓. x = 6: 6(6) + 11 = 47 ✓.
Tip: The y-value of a point is not the y-intercept unless x = 0. Always solve for b. Then test the equation with both given points — a wrong choice usually fails one of them.
Question 17 of 41 · Multi-step real-world problems
Renée earns $18.00 per hour for the first 40 hours she works in a week. For every hour over 40, she earns time-and-a-half (1.5 times her regular rate). Last week she worked 46 hours. What were her total earnings for the week, before taxes?
Hint
Split the week into regular hours and overtime hours. Find the overtime rate first.
Overtime rate: 1.5 \times 18 = 27 dollars per hour.
Overtime pay: 6 \times 27 = 162.
Total: 720 + 162 = 882.
Renée earned $882.00.
Check: If every hour were paid at $18, she would earn 46 \times 18 = 828. Overtime adds an extra half of $18 ($9) for each of the 6 overtime hours: 828 + 6 \times 9 = 828 + 54 = 882 ✓.
Tip: "Time-and-a-half" multiplies the rate, not the hours, and it applies only to the hours over 40. Organize wage problems as regular pay + overtime pay, each as hours × rate.
Question 18 of 41 · Solve linear inequalities
Drop-down
Complete the solution of the inequality.
-3x + 7 > 19
The solution is x .
Choose an answer from each menu.
Hint
Solve it like an equation. Watch what happens to the inequality sign when you divide by a negative number.
Step-by-step solution
Subtract 7 from both sides: -3x > 12.
Divide both sides by -3. Dividing by a negative number reverses the inequality sign: x < \dfrac{12}{-3}.
Simplify: x < -4.
The solution is x < -4. Choose < and -4.
Check: Test a number in the solution, x = -5: -3(-5) + 7 = 15 + 7 = 22 > 19 ✓. Test a number not in it, x = 0: 0 + 7 = 7, and 7 > 19 is false ✓. The boundary x = -4 gives exactly 19, and 19 > 19 is false, so the sign stays strict (<, not \le).
Tip: Multiplying or dividing both sides by a negative flips the sign; adding or subtracting never does. Always test one value from your answer in the original inequality.
Question 19 of 41 · Scatter plots and two-variable data
A running coach recorded the weekly training hours and the 5K race time (in minutes) for 12 runners. The results are shown in the scatter plot.
Which statement best describes the relationship shown?
Hint
Look at the overall direction of the points from left to right. Remember: a lower race time is a faster runner.
Step-by-step solution
Move from left to right (more training hours). The points move down (lower times).
When one variable increases while the other decreases, the association is negative.
The points lie close to a straight, downward-sloping band, so the association is strong and linear.
In context: runners who train more hours tend to finish the 5K in less time.
The best description is a strong negative association: more training hours tend to go with faster (lower) 5K times.
Check: Compare the ends of the graph: about 1 hour → 36.5 min, about 9 hours → 24 min. Times drop as hours rise ✓.
Tip: Up to the right = positive; down to the right = negative; a shapeless cloud = no association. A scatter plot shows a trend, not proof of cause, and it does not promise an exact change for every individual.
Question 20 of 41 · Polynomial operations
A company is paving a rectangular parking lot. The lot is (2x + 3) yards long and (x - 4) yards wide. Which expression represents the area of the lot, in square yards?
Hint
Area = length × width. Multiply every term in the first binomial by every term in the second (FOIL).
Step-by-step solution
Area of a rectangle = \text{length} \times \text{width} = (2x + 3)(x - 4).
Check: Let x = 10. Then the lot is 23 by 6, area 138. The expression gives 2(100) - 5(10) - 12 = 200 - 50 - 12 = 138 ✓.
Tip: Two binomials always give four products before you combine. Picking a value like x = 10 and testing each choice is a quick way to catch a dropped term or a sign error.
Question 21 of 41 · Circles: area and circumference
Fill in
A bicycle wheel has a diameter of 26 inches. How many feet does the bicycle travel when the wheel turns 50 complete times? Round your answer to the nearest foot.
feet
Type your answer in the box. Fractions like 3/4 are fine.
Hint
One full turn of the wheel moves the bike a distance equal to the wheel's circumference. Then change inches to feet (12 inches = 1 foot).
Step-by-step solution
Distance for one turn = circumference. With the diameter, C = \pi d (on the formula sheet): C = \pi \times 26 \approx 81.68 inches.
Distance for 50 turns: 81.68 \times 50 \approx 4{,}084.1 inches.
Convert to feet (divide by 12): 4{,}084.1 \div 12 \approx 340.3 feet.
Round to the nearest foot: 340.
The bicycle travels about 340 feet.
Check: Estimate with \pi \approx 3: one turn \approx 78 in \approx 6.5 ft, and 50 \times 6.5 = 325 ft — close to 340 ✓. Using 3.14 gives 26 \times 3.14 \times 50 \div 12 = 340.2, which also rounds to 340.
Tip: Use C = \pi d when you know the diameter and C = 2\pi r when you know the radius — don't double the diameter. Watch for a units change hidden at the end of the question ("how many feet").
Question 22 of 41 · Unit rate as slope
The graph shows the distance a cyclist has traveled over time while riding at a constant speed.
What is the cyclist's speed, in miles per hour?
Hint
Speed is the slope of a distance–time graph: change in distance divided by change in time.
Step-by-step solution
Speed = unit rate = slope = \dfrac{\text{change in distance}}{\text{change in time}}.
Use the labeled points (2,\ 30) and (4,\ 60):
m = \dfrac{60 - 30}{4 - 2} = \dfrac{30}{2} = 15
The units are miles per hour.
The cyclist rides at 15 miles per hour.
Check: The line starts at the origin, so you can also use one point: 30 \text{ mi} \div 2 \text{ h} = 15 mph ✓, and 60 \div 4 = 15 ✓. The formula d = rt (on the formula sheet) gives 60 = 15 \times 4 ✓.
Tip: On a graph of a proportional relationship (a straight line through the origin), the unit rate is the y-value when x = 1, which equals the slope. Reading a single y-value (like 30 or 60) gives a total distance, not a rate.
Question 23 of 41 · Write linear equations from context
Drop-down
An electrician charges a $65 service fee plus $48 per hour of work. A customer's total bill was $305.
Select the equation that can be used to find h, the number of hours the electrician worked.
Choose an answer from each menu.
Hint
The fee is charged once; the hourly rate is charged for each hour. Their total is the bill.
Step-by-step solution
Hourly charges: $48 for each of h hours = 48h.
Add the one-time service fee: 65 + 48h.
That total equals the bill: 65 + 48h = 305.
The equation is 65 + 48h = 305.
Check: Solve it: 48h = 305 - 65 = 240, so h = 240 \div 48 = 5 hours. Then 65 + 48(5) = 65 + 240 = 305 ✓ — a sensible whole number of hours.
Tip: Translate one piece at a time: "$48 per hour" → 48h; "plus a $65 fee" → +\,65; "total was $305" → = 305. The number that goes with the variable is always the one that repeats (per hour, per mile, per month).
Question 24 of 41 · Proportions and unit conversion
Fill in
A car is traveling on the highway at 65 miles per hour. What is the car's speed in feet per second? Round your answer to the nearest tenth.
(1 mile = 5,280 feet; 1 hour = 3,600 seconds)
feet per second
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Convert the miles to feet (multiply) and the hours to seconds (divide), keeping track of the units so they cancel.
Step-by-step solution
Set up the conversion so unwanted units cancel:
\dfrac{65 \text{ mi}}{1 \text{ h}} \times \dfrac{5{,}280 \text{ ft}}{1 \text{ mi}} \times \dfrac{1 \text{ h}}{3{,}600 \text{ s}}
Multiply the tops: 65 \times 5{,}280 = 343{,}200 feet.
Divide by the seconds in an hour: 343{,}200 \div 3{,}600 = 95.333\ldots
Round to the nearest tenth: 95.3.
The car travels about 95.3 feet per second.
Check: Work backwards: 95.3 \text{ ft/s} \times 3{,}600 \text{ s} \approx 343{,}080 ft, and 343{,}080 \div 5{,}280 \approx 65 miles ✓. Also, 1 ft/s is much slower than 1 mph, so the number of feet per second should be bigger than 65 ✓.
Tip: Write every conversion factor as a fraction and check that each unit you don't want appears once on top and once on the bottom. A handy fact: 60 mph is exactly 88 ft/s.
Question 25 of 41 · Write quadratic equations from context
A rectangular practice field is 20 yards longer than it is wide. The area of the field is 4,800 square yards. What is the width of the field, in yards?
Hint
Let w be the width. Write the length in terms of w, set length × width equal to 4,800, and solve the quadratic.
Step-by-step solution
Let w = width. Then length = w + 20.
Area = length × width: w(w + 20) = 4{,}800.
Expand and set equal to zero: w^{2} + 20w - 4{,}800 = 0.
Factor: find two numbers that multiply to -4{,}800 and add to 20: 80 and -60. So (w + 80)(w - 60) = 0.
Solutions: w = -80 or w = 60. A width cannot be negative, so w = 60.
The width is 60 yards (and the length is 60 + 20 = 80 yards).
Check:60 \times 80 = 4{,}800 square yards ✓, and 80 is 20 more than 60 ✓.
Tip: If factoring big numbers is hard, use the quadratic formula from the formula sheet: w = \dfrac{-20 \pm \sqrt{20^{2} + 4(4{,}800)}}{2} = \dfrac{-20 \pm 140}{2}. In real-world problems, throw out a negative length. And re-read what is asked: width, not length.
Question 26 of 41 · Counting, combinations and permutations
A soccer coach will choose a captain and a co-captain from the 12 players on her team. One player cannot hold both jobs. In how many different ways can the coach fill the two positions?
Hint
Does the order matter here? Being captain is different from being co-captain. Count the choices for each job.
Step-by-step solution
Captain: any of the 12 players can be chosen.
Co-captain: one player is already captain, so 11 players remain.
Use the counting principle — multiply the number of choices: 12 \times 11 = 132.
There are 132 ways.
Check: The two jobs are different, so "Ana captain, Ben co-captain" and "Ben captain, Ana co-captain" are two different outcomes. If order did not matter we would divide by 2 and get 66; because it does, 132 is right ✓.
Tip: Different roles (1st/2nd, president/vice-president, captain/co-captain) → order matters → multiply 12 \times 11. Identical roles (choose 2 players to carry the bags) → order doesn't matter → divide that product by 2.
Question 27 of 41 · Linear expressions: combine, factor, expand
Drag and drop
Drag the simplified form of each expression into its box. Not every tile is used.
3(x + 4) - x
5x - 2(x - 3)
4(2x - 1) + x
Tap a tile, then tap a box to place it.
Hint
Distribute first (multiply the number outside the parentheses by every term inside, including its sign), then combine like terms.
Step-by-step solution
3(x + 4) - x = 3x + 12 - x = 2x + 12.
5x - 2(x - 3): distribute -2 to both terms: -2 \cdot x = -2x and -2 \cdot (-3) = +6. So 5x - 2x + 6 = 3x + 6.
4(2x - 1) + x = 8x - 4 + x = 9x - 4.
Answers: 2x + 12, 3x + 6, 9x - 4. The tiles 3x - 6 and 2x + 4 are not used.
Tip: A minus sign in front of parentheses changes the sign of every term inside: -2(x - 3) = -2x + 6. Testing x = 1 (or any easy number) in the original and the simplified form is a quick way to catch errors.
Question 28 of 41 · Pyramids and cones
A road crew uses traffic cones shaped like right circular cones. Each cone has a base diameter of 12 inches and a height of 18 inches. What is the volume of one cone, to the nearest cubic inch? Use \pi \approx 3.14.
Hint
Volume of a cone = \tfrac{1}{3}\pi r^{2} h (on the formula sheet). The formula uses the radius.
Step-by-step solution
Find the radius: r = \dfrac{12}{2} = 6 inches. Height h = 18 inches.
Use V = \tfrac{1}{3}\pi r^{2} h:
V = \tfrac{1}{3} \times 3.14 \times 6^{2} \times 18 = \tfrac{1}{3} \times 3.14 \times 36 \times 18
Check: A cone holds exactly one-third of the cylinder with the same base and height. That cylinder: 3.14 \times 36 \times 18 \approx 2{,}035; one-third of 2{,}035 \approx 678 ✓.
Tip: Two traps live in every cone question: the \tfrac{1}{3} and the radius-vs-diameter. Circle the word "diameter" when you see it and halve it before doing anything else.
Question 29 of 41 · Parallel and perpendicular lines
On a city planning map, Main Street lies along the line y = 2x - 3. A new bike lane will be perpendicular to Main Street and will pass through the bus stop at the point (4,\ 1). Which equation describes the bike lane?
Hint
Perpendicular slopes are negative reciprocals (flip the fraction and change the sign). Then use the point to find b.
Step-by-step solution
The slope of Main Street is 2 (the number in front of x).
A perpendicular line has the negative reciprocal slope: flip \tfrac{2}{1} to \tfrac{1}{2} and change the sign: m = -\tfrac{1}{2}.
Use y = mx + b with the point (4,\ 1): 1 = -\tfrac{1}{2}(4) + b \Rightarrow 1 = -2 + b \Rightarrow b = 3.
Equation: y = -\tfrac{1}{2}x + 3.
The bike lane is y = -\tfrac{1}{2}x + 3.
Check: The point works: -\tfrac{1}{2}(4) + 3 = -2 + 3 = 1 ✓. The slopes multiply to -1: 2 \times \left(-\tfrac{1}{2}\right) = -1 ✓ — the test for perpendicular lines.
Tip: Parallel lines have the same slope; perpendicular lines have slopes that multiply to -1. You need both steps — flip and change sign. When solving for b, undo -2 by adding 2.
Question 30 of 41 · Mean, median, mode, range, weighted average
The table shows the price of one gallon of regular gasoline at seven gas stations along a highway.
Station
1
2
3
4
5
6
7
Price per gallon
$3.45
$3.29
$3.62
$3.38
$3.51
$3.29
$3.47
What is the median price per gallon?
Hint
Put the prices in order from least to greatest first. The median is the middle value.
Step-by-step solution
Order the seven prices from least to greatest:
3.29,\ 3.29,\ 3.38,\ \mathbf{3.45},\ 3.47,\ 3.51,\ 3.62
With 7 values, the median is the 4th value (3 values on each side).
The 4th value is $3.45.
The median price is $3.45.
Check: Count: three prices are below $3.45 (3.29, 3.29, 3.38) and three are above it (3.47, 3.51, 3.62) ✓.
Tip: Never take the middle of the list as it is printed — sort it first. Don't confuse the median (middle) with the mode (most frequent, $3.29 here) or the mean (sum ÷ count, about $3.43 here).
Question 31 of 41 · Write inequalities from context
A pickup truck can safely carry at most 2,000 pounds of passengers and cargo. The driver weighs 180 pounds, and each box of tiles weighs 45 pounds. Which inequality can be used to find b, the number of boxes the driver can safely carry?
Hint
What does the total weight include? Does "at most" mean less than, or less than or equal to?
Step-by-step solution
Total weight = driver + boxes = 180 + 45b.
"At most 2,000" means the total can be equal to 2,000 or less: \le 2{,}000.
Inequality: 180 + 45b \le 2{,}000.
The inequality is 180 + 45b \le 2{,}000.
Check: Solving it: 45b \le 1{,}820, so b \le 40.4 — the driver can carry up to 40 boxes. With 40 boxes the load is 180 + 1{,}800 = 1{,}980 \le 2{,}000 ✓; with 41 boxes it is 2{,}025, too heavy ✓.
Tip: Translate the phrases: "at most" / "no more than" → \le; "at least" / "no less than" → \ge; "more than" → >; "less than" → <. The per-item amount (45 per box) always multiplies the variable.
Question 32 of 41 · Scale factors and scale drawings
On a road map, 1 inch represents 15 miles. Two towns are 3.5 inches apart on the map. What is the actual distance between the towns?
Hint
Each inch on the map stands for 15 real miles. How many miles do 3.5 inches stand for?
Step-by-step solution
Write the scale as a ratio: \dfrac{1 \text{ in}}{15 \text{ mi}}.
Set up a proportion: \dfrac{1 \text{ in}}{15 \text{ mi}} = \dfrac{3.5 \text{ in}}{x \text{ mi}}.
Cross-multiply: x = 3.5 \times 15 = 52.5.
The towns are 52.5 miles apart.
Check: 3 inches is 3 \times 15 = 45 miles and half an inch is 7.5 miles; 45 + 7.5 = 52.5 ✓.
Tip: Map distance × scale = real distance. A real distance should be much larger than the map distance, so an answer like 4.3 miles is a red flag. Keep the units in the same positions on both sides of a proportion.
Question 33 of 41 · Key features of graphs and tables
Select all
A football is kicked into the air. Its height h, in feet, after t seconds is modeled by h(t) = -16t^{2} + 48t + 4 and shown in the graph.
Select all statements that are true.
Select all that apply.
Hint
Find the highest point, the starting point (t = 0), and where the height reaches 0. Check any claim about a specific time by plugging it into h(t).
Step-by-step solution
Maximum height: the highest point on the graph is (1.5,\ 40). Check: h(1.5) = -16(2.25) + 48(1.5) + 4 = -36 + 72 + 4 = 40. So the maximum height is 40 feet ✓, reached at 1.5 seconds ✓.
Starting height (y-intercept):h(0) = 0 + 0 + 4 = 4. The ball was kicked from 4 feet above the ground ✓.
Hits the ground at 3 seconds?h(3) = -16(9) + 48(3) + 4 = -144 + 144 + 4 = 4. At 3 seconds the ball is still 4 feet up, so this is false (it lands a little after 3 seconds, at about 3.08 s).
Increasing the whole time? The height increases from 0 to 1.5 seconds and then decreases, so this is false.
The true statements are: maximum height 40 ft, maximum at 1.5 s, and starting height 4 ft.
Check: The vertex formula t = -\dfrac{b}{2a} = -\dfrac{48}{2(-16)} = 1.5 agrees with the graph ✓.
Tip: Key features to read from any graph: y-intercept (starting value), maximum/minimum (vertex), x-intercepts (where the value is 0), and intervals where it increases or decreases. Verify close-looking readings by substituting into the equation.
Question 34 of 41 · Real-world linear equations
Fill in
A motorcycle starts a trip with 14 gallons of fuel in its tank and uses 0.05 gallon per mile. After how many miles will the tank have 3.5 gallons left?
miles
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Fuel left = starting fuel − (fuel used per mile × miles). Set that equal to 3.5 and solve.
Step-by-step solution
Let m = miles driven. Fuel used = 0.05m, so fuel left = 14 - 0.05m.
Set fuel left equal to 3.5: 14 - 0.05m = 3.5.
Subtract 14 from both sides: -0.05m = -10.5.
Divide by -0.05: m = \dfrac{-10.5}{-0.05} = 210.
The tank will have 3.5 gallons left after 210 miles.
Check:14 - 0.05(210) = 14 - 10.5 = 3.5 ✓.
Tip: Think in two steps: how much fuel is used (14 - 3.5 = 10.5 gallons), then how far that goes (10.5 \div 0.05 = 210 miles). Dividing 3.5 by 0.05 (= 70) would find how far the remaining fuel can go — a different question.
Question 35 of 41 · Factor polynomials
Drop-down
The area, in square feet, of a rectangular exercise mat is given by the expression x^{2} + 5x - 24.
Select the factored form of the expression.
x^{2} + 5x - 24 =
Choose an answer from each menu.
Hint
Find two numbers that multiply to -24 and add to +5.
Step-by-step solution
Look for two numbers with product -24 and sum +5. Because the product is negative, one number is negative and one is positive.
Try pairs: (6,\ -4) sums to 2; (12,\ -2) sums to 10; (8,\ -3) sums to 5 ✓.
Tip: When the constant is negative, the two numbers have opposite signs, and the larger one takes the sign of the middle term (+5 → the 8 is positive). Always check by multiplying back out — it takes 10 seconds.
Question 36 of 41 · Composite 2-D figures
The infield of a running track is shaped like a rectangle with a semicircle on each end, as shown.
What is the area of the infield, to the nearest square meter? Use \pi \approx 3.14.
Hint
Split the shape into a rectangle and two semicircles. Two semicircles of the same size make one full circle. What is the radius?
Step-by-step solution
Rectangle:A = l \times w = 100 \times 60 = 6{,}000 m².
Semicircles: each has diameter 60 m, so radius r = 30 m. Two semicircles = one full circle:
A = \pi r^{2} = 3.14 \times 30^{2} = 3.14 \times 900 = 2{,}826 \text{ m}^2
Total:6{,}000 + 2{,}826 = 8{,}826 m².
The infield area is about 8,826 square meters.
Check: The shape fits inside a 160 \times 60 rectangle (100 m plus 30 m on each end), whose area is 9{,}600 m², and it contains the 6{,}000 m² rectangle. 8{,}826 is between them ✓.
Tip: For composite figures, break the shape into pieces whose formulas are on the formula sheet, find each area, then add. Halve a diameter before using \pi r^{2}, and don't confuse area (square meters, inside) with perimeter (meters, around the edge).
Question 37 of 41 · Compare proportional relationships
Worker A's pay is shown in the graph. Worker B earns pay according to the equation y = 19.5x, where y is pay in dollars and x is hours worked.
How much more per hour does Worker B earn than Worker A?
Hint
Find each worker's hourly rate (unit rate). For the graph, divide pay by hours at a labeled point.
Step-by-step solution
Worker A (graph): the line passes through (0,\ 0) and (5,\ 90), so the hourly rate is the slope: \dfrac{90}{5} = 18 dollars per hour.
Worker B (equation): in y = 19.5x, the coefficient of x is the unit rate: $19.50 per hour.
Difference: 19.50 - 18.00 = 1.50.
Worker B earns $1.50 more per hour.
Check: In 5 hours, A earns $90 and B earns 19.5 \times 5 = \$97.50. The difference is \$7.50 for 5 hours, which is 7.50 \div 5 = \$1.50 per hour ✓.
Tip: To compare proportional relationships in different forms, turn each into a unit rate (the k in y = kx). On a graph through the origin, k = \dfrac{y}{x} at any labeled point. Re-read whether the question wants a rate, a total, or a difference.
Question 38 of 41 · Dot plots, histograms and box plots
The box plot summarizes the one-way commute times, in minutes, for the employees of a warehouse.
What is the interquartile range (IQR) of the commute times?
Hint
The IQR is the length of the box: third quartile minus first quartile.
Step-by-step solution
Read the five-number summary from the box plot: minimum 12, first quartile Q_1 = 20 (left edge of the box), median 28 (line inside the box), third quartile Q_3 = 35 (right edge of the box), maximum 50.
\text{IQR} = Q_3 - Q_1 = 35 - 20 = 15.
The interquartile range is 15 minutes.
Check: The IQR measures the spread of the middle half of the data, which is exactly the width of the box: from 20 to 35 is 15 units on the number line ✓.
Tip: Range uses the whiskers' ends (max − min = 38 here); IQR uses the box's edges (Q3 − Q1). The median is the line inside the box and is a measure of center, not spread.
Question 39 of 41 · Compare functions in different forms
Drag and drop
Three gyms describe their membership costs in different ways. In each case, C is the total cost in dollars after m months.
Gym A:C = 35m + 50
Gym B:
Months, m
1
2
3
Total cost, C ($)
70
110
150
Gym C: a $120 joining fee plus $30 for each month.
Drag each gym into the box that describes its monthly rate (the rate of change of C).
Lowest monthly rate
Middle monthly rate
Highest monthly rate
Tap a tile, then tap a box to place it.
Hint
Find the rate of change for each gym. In the table, look at how much the cost goes up from one month to the next — not the first cost listed.
Step-by-step solution
Gym A: in C = 35m + 50, the rate of change is the coefficient of m: $35 per month (the 50 is a one-time fee).
Gym B: from the table, each extra month adds 110 - 70 = 40 and 150 - 110 = 40: $40 per month. (The $70 for month 1 includes a $30 starting fee, since 70 - 40 = 30.)
Gym C: the words say $30 per month (the $120 is a one-time fee).
Order the rates: 30 < 35 < 40.
Lowest: Gym C; middle: Gym A; highest: Gym B.
Check: Write all three as equations: A: C = 35m + 50; B: C = 40m + 30 (test: 40(2) + 30 = 110 ✓); C: C = 30m + 120. The slopes are 35, 40 and 30 ✓.
Tip: When functions come in different forms (equation, table, words, graph), convert each to its rate of change before comparing. Don't let a large starting fee (like Gym C's $120) or the first table value (Gym B's $70) fool you — those are not monthly rates.
Question 40 of 41 · Line from slope and a point
A rideshare company charges a fixed booking fee plus $1.80 per mile. A 5-mile ride costs $14.50. Which equation gives the cost y, in dollars, of a ride of x miles?
Hint
The slope is the per-mile charge. Use the point (5,\ 14.50) to find the fixed fee, b.
Step-by-step solution
The rate per mile is the slope: m = 1.80.
The 5-mile ride gives the point (5,\ 14.50).
Substitute into y = mx + b: 14.50 = 1.80(5) + b \Rightarrow 14.50 = 9.00 + b.
Subtract 9: b = 5.50 (the booking fee).
Equation: y = 1.8x + 5.5.
The equation is y = 1.8x + 5.5.
Check:1.8(5) + 5.5 = 9 + 5.5 = 14.5 ✓. Point-slope form (on the formula sheet) gives the same line: y - 14.5 = 1.8(x - 5) \Rightarrow y = 1.8x - 9 + 14.5 = 1.8x + 5.5 ✓.
Tip: In y = mx + b, m is the "per" amount and b is the cost when x = 0. The cost of one particular ride ($14.50) is a point on the line, not the starting fee.
Question 41 of 41 · Graph linear equations
Hot spot
Click the point where the graph of the equation below crosses the x-axis.
2x - 3y = 6
Click on the figure to mark your answer (or focus it and use the arrow keys).
Hint
Every point on the x-axis has a y-coordinate of 0.
Step-by-step solution
On the x-axis, y = 0. Substitute: 2x - 3(0) = 6.
Simplify: 2x = 6, so x = 3.
The x-intercept is the point (3,\ 0): from the origin move 3 right and stay on the axis. Click there.
The graph crosses the x-axis at (3,\ 0).
Check:2(3) - 3(0) = 6 - 0 = 6 ✓. For comparison, the y-intercept is found with x = 0: -3y = 6, so y = -2, the point (0,\ -2) — that one is on the y-axis, not the x-axis.
Tip: To find intercepts from standard form Ax + By = C, cover up one term: covering the y-term gives the x-intercept \tfrac{C}{A} = \tfrac{6}{2} = 3; covering the x-term gives the y-intercept \tfrac{C}{B} = \tfrac{6}{-3} = -2.