AFQT Core Practice 10: Circles, Ratios and Author's Purpose

Answer: D

Correct answer: $51.36. Multiply the price by 1 plus the tax rate:

• A: This is only the tax; it must be added to the $48 price.
• B: This subtracts the tax as if it were a discount.
• C: This adds $7 instead of 7% of the price.
• D (correct): Tax is 0.07 × 48 = $3.36, so the total is 48 + 3.36 = $51.36 (or 1.07 × 48).

Answer: B

Correct answer: 22. A unit rate divides the first quantity by the second:

applications per day.

• A: This multiplies 132 by 6 instead of dividing.
• B (correct): Divide applications by days: 132 divided by 6 is 22.
• C: The decimal point is misplaced; 6 times 2.2 is only 13.2.
• D: This divides days by applications, which gives days per application.

Answer: A

Correct answer: 3x - 6. Build "three times a number" first as $3x$. "6 fewer than" that amount means take 6 away from it, giving $3x-6$.

• A (correct): Start with three times the number, 3x, and take 6 away from it.
• B: This reverses the order; "6 fewer than" means 6 is subtracted from the other quantity.
• C: This subtracts 6 before multiplying, but the words build three times the number first.
• D: "Fewer than" means subtract, not add.

Answer: A

Correct answer: 86 grams. Multiplying by 100 shifts the decimal point two places to the right:

The total is 86 grams, which is larger than one washer, as it should be.

• A (correct): Multiplying by 100 moves the decimal point two places right, so 0.86 becomes 86.
• B: This moves the decimal point only one place, which is multiplying by 10 instead of 100.
• C: This moves the decimal point three places, which is multiplying by 1,000.
• D: This moves the decimal point left, which divides by 100 instead of multiplying.

Answer: B

Correct answer: 11:00 a.m. Driving time is

which is 3 hours 30 minutes. Adding 3 hours 30 minutes to 7:30 a.m. gives 11:00 a.m.

• A: This reads 3.5 hours as 3 hours 50 minutes.
• B (correct): The trip lasts 3.5 hours, or 3 hours 30 minutes, and 7:30 a.m. plus that time is 11:00 a.m.
• C: This reads 3.5 hours as 3 hours 5 minutes.
• D: This drops the half hour and adds only 3 hours.

Answer: D

Correct answer: 18 mph. Convert the time: 10 minutes is

so the time is

Speed is distance divided by time:

per hour.

• A: This treats 2 hours 10 minutes as 2.10 hours, reading minutes as a decimal.
• B: This ignores the 10 minutes and divides by 2 hours only.
• C: This multiplies distance by time instead of dividing distance by time.
• D (correct): 2 hours 10 minutes is 2 1/6 hours, and 39 / (13/6) = 18 miles per hour.

Answer: A

Correct answer: 2 hours 24 minutes. Moving the same way, the gap grows by the difference of the speeds:

Time =

Since

that is 2 hours 24 minutes.

• A (correct): The gap grows 15 miles each hour, and 36 ÷ 15 = 2.4 hours, or 2 hours 24 minutes.
• B: This reads 2.4 hours as 2 hours 40 minutes instead of converting 0.4 hour to 24 minutes.
• C: This adds the speeds, which applies only when the riders head in opposite directions.
• D: This divides 36 miles by the faster rider's speed alone, as if the other rider stood still.

Answer: A

Correct answer: 16. Multiply along the diagonals:

so 15x = 240.

Divide both sides by 15: x = 16. Check:

• A (correct): Cross products give 15x = 6 × 40 = 240, so x = 16.
• B: This multiplies 6 by 15/40 instead of cross-multiplying, which solves a different equation.
• C: This sets 6x = 15 × 40, pairing the wrong terms across the diagonal.
• D: This adds the difference 40 - 15 = 25 to 6, but proportions work by multiplying, not adding.

Answer: C

Correct answer: $0.05. Find each unit rate:

per battery and

per battery.

The savings per battery is

• A: This is the price of one battery in the 12-pack, not the savings per battery.
• B: This is the difference in pack prices, which ignores that the packs hold different numbers of batteries.
• C (correct): The 8-pack is $0.75 each and the 12-pack is $0.70 each, a difference of $0.05.
• D: This divides the $2.40 price difference by the 4 extra batteries, which does not compare unit prices.

Answer: B

Correct answer: 10 miles per hour. Rate equals distance divided by time.

• A: This uses only 1 divided by 1/12 and leaves out the 5/6 mile distance.
• B (correct): Speed is distance divided by time: 5/6 times 12/1 = 10 miles per hour.
• C: This multiplies distance by time instead of dividing distance by time.
• D: This divides time by distance, which gives hours per mile, not miles per hour.

Answer: B

Correct answer: $288. Unit rate:

per gallon.

Gallons needed:

Cost:

• A: This is the cost of the 5 gallons in the coverage example, not the paint needed for 2,800 square feet.
• B (correct): Each gallon covers 350 square feet, so 2,800 ÷ 350 = 8 gallons, and 8 × $36 = $288.
• C: This adds the 5 gallons from the example to the 8 gallons needed, buying 13 gallons.
• D: This is the coverage per gallon in square feet, not a cost in dollars.

Answer: A

Correct answer: 48 miles per hour. Distances:

for 240 miles.

Total time including the stop:

Average speed:

per hour.

• A (correct): The convoy covers 180 + 60 = 240 miles in 3 + 0.5 + 1.5 = 5 hours, and 240 divided by 5 is 48.
• B: 50 averages the two driving speeds, ignoring both the different times and the stop.
• C: This divides 240 miles by only the 4.5 driving hours, leaving out the 30-minute stop the question says to count.
• D: This averages 60, 0, and 40 as if the stop and both legs lasted the same amount of time.

Answer: A

Correct answer: 2,534 bottles. Bottles issued:

Bottles received:

Start with 2,750, subtract what left, and add what arrived:

• A (correct): Issued 18 × 24 = 432 and received 9 × 24 = 216, so 2,750 − 432 + 216 = 2,534.
• B: This adds the issued bottles instead of subtracting them.
• C: This subtracts the received bottles instead of adding them.
• D: This adds 9 bottles instead of 9 cases of 24 bottles after the issue.

Answer: A

Correct answer: 6 hours 40 minutes. The combined rate is the inlet rate minus the drain rate, so the drain rate is the difference:

Invert: $\frac{20}{3}$ hours = 6 hours 40 minutes.

• A (correct): The drain's rate is 1/4 - 1/10 = 3/20 trough per hour, so it empties the trough in 20/3 hours, or 6 hours 40 minutes.
• B: This subtracts the times (10 - 4) instead of subtracting the rates.
• C: This adds the inlet and combined rates instead of subtracting to find what the drain removes.
• D: This adds the two times, which does not give any rate in the problem.

Answer: D

Correct answer: 25%. Reduced wage:

The raise needed is 18.00 minus 14.40, or $3.60.

The raise is figured on the reduced wage:

so a 25 percent raise is needed.

• A: This assumes the same percent undoes the cut, but 20 percent of the smaller $14.40 wage is only $2.88.
• B: This is the reduced wage as a percent of the original, not the raise needed.
• C: This is the factor 1.25 written as a percent; the raise itself is 25 percent.
• D (correct): The reduced wage is $14.40, and the $3.60 needed is 25 percent of 14.40.

Answer: A

Correct answer: loses. SHEDS is a verb with the object "fur," and the daily vacuuming shows fur falling out. Sheds here means loses.

• A (correct): Dogs drop old fur in spring, so "loses so much fur" matches the need to vacuum daily.
• B: Shed as a noun is a storage hut, but here the word is a verb with the object "fur."
• C: Growing fur would not leave hair on the floor; the daily vacuuming shows fur coming off.
• D: Brushing is something an owner does to a dog, not what the dog does to its own fur.

Answer: C

Correct answer: blocked. "Because" gives the cause: rock buried the road. A buried road cannot be traveled, so IMPASSABLE means blocked or impossible to get through.

• A: Heavy traffic is not mentioned; the cause given is a landslide.
• B: The shape of the road has nothing to do with being buried by rock.
• C (correct): Ten feet of rock across a road would stop all travel, so the road was blocked.
• D: A road buried under rock is the opposite of a fresh, open surface.

Answer: C

Correct answer: water down. Dilute means to make a liquid weaker or thinner by adding more liquid, as when you dilute bleach with water. Water down matches; pollute is a sound-alike and dissolve is a different process.

• A: Dissolving means mixing a solid into a liquid until it disappears; dilute means making a mixture weaker.
• B: Thickening is the opposite of thinning a mixture down.
• C (correct): To dilute is to thin or weaken something, usually by adding water or another liquid.
• D: Pollute rhymes with dilute but means to make dirty or contaminated.

Answer: B

Correct answer: Sink. Sub- means under. To submerge is to put or go under water, which means to sink.

• A: Float means to stay on the surface, the opposite of going under.
• B (correct): Sub- means under, and merge comes from a word for dip, so to submerge is to sink below the surface.
• C: Combine matches the look-alike word merge, but submerge is about going under water.
• D: Surface is the reverse movement, coming up from under the water.

Answer: A

Correct answer: tiresome. Tedious describes work that is dull and tiring because it drags on. Tiresome keeps that meaning; difficult adds a different condition, careful is only associated, and brief is opposite in spirit.

• A (correct): Tedious means dull and wearying because it is long or repetitive, which tiresome expresses.
• B: A tedious job can be easy; it is boring and repetitive rather than hard to do.
• C: Counting by hand might require care, but careful describes the worker, not the dull nature of the job.
• D: This contradicts the idea of a long, drawn-out task.

Answer: B

Correct answer: violent rush of water. Follow the comparison of degree: drip, then steady stream, then torrent. Each step is stronger, so a torrent is a violent rush of water.

• A: A trickle is the weakest stage, like the drip at the start, not the end of the build-up.
• B (correct): The sentence builds in degree from drip to stream to torrent, so a torrent is the strongest, a rushing flood.
• C: A puddle sits still; pouring across the floor shows forceful movement.
• D: The pipe may be the source, but torrent names the water flowing, not the plumbing.

Answer: A

Correct answer: keep. Retain means to keep possession of something. Keep fits 'until the trip expenses are approved'; return is the opposite, and collect and copy are related but different actions.

• A (correct): Retain means to continue to have or hold on to something, so keep is the closest match.
• B: Handing the receipts back is the opposite of holding on to them.
• C: Collecting means gathering things up, not continuing to hold what one already has.
• D: Making copies is a related office task, but it does not mean holding on to the originals.

Answer: B

Correct answer: strengthened. The -ed ending is inflectional: it marks past tense without changing the meaning of reinforce, to make stronger. A synonym must also be in the past tense, so strengthened fits and strengthen does not.

• A: Weakened is in the right tense but means the opposite of adding steel support.
• B (correct): Reinforce means to make stronger, and the -ed ending keeps it in the past tense, so strengthened fits.
• C: Adding beams to make a wall stronger is not painting or decoration.
• D: Forced shares letters with the target but means compelled, which does not fit adding beams.

Answer: A

Correct answer: Unable to move. Im- is the spelling of in- (not) before m, and mobile means able to move. A hiker in a full cast waiting on a stretcher is unable to move.

• A (correct): Im- is the form of in- (not) used before m, so immobile means not mobile, or unable to move.
• B: Easy to carry confuses the base mobile with portable and drops the negative prefix.
• C: Moving slowly is the wrong degree; immobile means not moving at all.
• D: Moved away reads im- as motion, but here it is the negative prefix.

Answer: B

Correct answer: rushed and careless. The clues ten minutes and no sealant point to speed and carelessness. Hasty means done too fast, often carelessly, so rushed and careless matches.

• A: This describes deliberate, the opposite of a ten-minute job done without sealant.
• B (correct): Hasty means done too quickly, often without enough care, which matches a ten-minute job with no sealant that soon failed.
• C: Price is never mentioned; the clues are speed and poor quality.
• D: Temporary means meant to last a short time; the patch failed because it was rushed, and a temporary repair can still be done well.

Answer: D

Correct answer: dangerously low body temperature. Therm means heat, and hypo means under, so hypothermia is body heat that has dropped too low. Wrapping the climber in blankets to warm her confirms the meaning.

• A: This is hyperthermia; mixing up hypo and hyper turns the meaning into its opposite.
• B: That describes dehydration; it uses a water root, not therm, heat.
• C: A climbing injury fits the scene, but the word contains therm, heat, not anything about bones.
• D (correct): Hypo means under or low and therm means heat, and blankets are used to warm someone who is too cold.

Answer: B

Correct answer: fluent and persuasive. Loqu is a variant of locut, speak. An eloquent speaker uses words fluently and persuasively, which is how he holds an audience for an hour.

• A: Volume is an intensity trap; eloquence is about skill with words, not loudness.
• B (correct): E- means out and loqu means speak, so an eloquent person speaks out well and moves listeners.
• C: This sound-alike trap mixes up eloquent with elegant.
• D: Fame is not built into the word; loqu, speak, points to speaking skill.

Answer: A

Correct answer: extreme tiredness. Exhaustion is the -ion noun from exhaust, to tire out or use up. The clues "thirty hours" and "had to rest" point to fatigue. Thoroughness belongs to exhaustive, a family member with a shifted meaning.

• A (correct): Exhaustion is the state of being tired out, which explains why a team that searched for thirty hours had to rest.
• B: Thoroughness matches exhaustive, which means covering everything; the team's need to rest shows the word is about fatigue.
• C: Exhaust as a noun means waste gases from an engine, but exhaustion here describes the condition of people.
• D: Mild boredom is far too weak and has the wrong cause; thirty hours of hard work produces fatigue, not boredom.

Answer: B

Correct answer: unfortunate. Regrettable (regret plus -able, with the t doubled) describes something that deserves regret, while regretful describes a person who feels it. The word modifies mistake, not a person, so unfortunate is the match.

• A: Carelessness may have caused the mistake, but regrettable describes the mistake as unfortunate, not its cause.
• B (correct): Regret plus -able means deserving regret, so a regrettable mistake is an unfortunate one.
• C: Forgettable shares the -able ending but means easily forgotten, a different base.
• D: Unavoidable means it could not be prevented, which the sentence never says.

Answer: B

Correct answer: tightfisted. Stingy and thrifty share a denotation, spending little, but differ in connotation. The sentence criticizes refusing a cheap and necessary repair, so the disapproving word tightfisted matches, while thrifty fails the tone filter.

• A: Thrifty shares the meaning of spending little but approves of avoiding waste; refusing a small, necessary repair is not praised here.
• B (correct): Stingy describes an unreasonable unwillingness to spend, which fits refusing a cheap, necessary repair in winter.
• C: Being too poor to pay means lacking money; the repair was cheap, so the refusal shows unwillingness, not inability.
• D: Careless means not paying attention; the landlord made a choice not to spend, which is not the same as overlooking the problem.

Answer: A

Correct answer: helped with the work. The sentence after the idiom lists what neighbors did: baked pies, peeled potatoes and delivered turkeys. Those examples show people joining in to share the work, so pitched in means helped with the work.

• A (correct): The baker, the students and the store owner each took on a task so the meals could be served.
• B: This decodes the words literally; the examples describe people doing jobs, not tossing objects.
• C: Pitching a tent is a different use of pitch; no tents appear in the passage.
• D: The passage shows people volunteering willingly and the kitchen having its biggest day, with no sign of complaints.

Answer: B

Correct answer: A steel toe. Sort each detail into a column for its boot. The Ridgeline column holds a steel toe and a weight of about 4 pounds; the other listed features belong to the Trailhead or to both.

• A: The waterproof lining is listed for the Trailhead boot, not the Ridgeline.
• B (correct): The passage states that the Ridgeline boot has a steel toe.
• C: The composite toe made of hard plastic belongs to the Trailhead boot.
• D: About 3 pounds is the Trailhead's weight; the Ridgeline weighs about 4 pounds.

Answer: C

Correct answer: The steel ferry made its last run of the season. The passage opens with the latest event and then flashes back: 1962 purchase, steel boat about twenty years later, county takeover in 2005, and the October 30 final run. The electric ferry is only scheduled for next spring, so it has not happened. The most recent real event is the season's final run.

• A: This happened in 2005, well before the October 30 run described at the start of the passage.
• B: The passage says this is scheduled for next spring, so it is a plan, not an event that has happened.
• C (correct): The passage opens with this event, but it is the latest event that has actually taken place; everything else is a flashback or a future plan.
• D: This happened twenty years after 1962, in the early 1980s, long before the final run of the season.

Answer: D

Correct answer: By describing everything about one setup before turning to the other. In block organization, the writer covers all the features of item A and then all the features of item B. Here the first paragraph gives the laundry rooms' cost, supplies, crowding and hours, and the second gives the same features for the paid service. A point-by-point passage would instead switch between the two setups on each feature.

• A: That would be point-by-point order; here the writer finishes one setup entirely before discussing the other.
• B: Wash, dry and fold are mentioned only to describe the service, not to teach a process.
• C: The passage never says the base created the service to solve crowding; it simply presents two existing setups.
• D (correct): The first paragraph covers only the laundry rooms and the second covers only the service, which is block organization.

Answer: B

Correct answer: Several easy habits can help households throw away less food. The passage opens and closes with the same idea, and the middle sentences give three examples: meal planning, proper storage, and freezing leftovers. The main idea is the umbrella statement about simple habits, not any single example.

• A: This is one of three example habits, so it is too narrow to serve as a title for the whole passage.
• B (correct): The opening and closing sentences both make this point, and each middle sentence is one supporting habit.
• C: The passage makes no comparison with restaurants or stores; this depends on information the paragraph never gives.
• D: Meal planning is one habit among several, and the word only overstates what the passage claims.

Answer: C

Correct answer: fairly hopeful but not yet sure. Authorial certainty is graded by word choice. Seems marks a belief that is not confirmed, and the note that the truck has only seen mild weather plus the plan to keep logging readings show caution. The writer is hopeful but waiting for proof, neither certain nor doubtful.

• A: This turns seems into certainty and ignores the writer's plan to keep testing before signing off.
• B: The gauge has stayed normal since the flush, and the writer leans toward the coolant working, so this reverses the writer's view.
• C (correct): The writer says the coolant seems to have solved the problem, notes that testing so far was only in mild weather, and plans more checks, which shows tentative confidence.
• D: The writer does form a view, that the fix seems to work; it is cautious, not absent.

Answer: A

Correct answer: The gauge never read above 70 percent that day. The rule is one-way: a reading above 70 percent requires the dehumidifier. The only safe reversal uses negation. The dehumidifier was not switched on and the rule was followed, so the reading did not go above 70 percent.

• A (correct): If the gauge had gone above 70 percent, the rule would have required the dehumidifier; since the rule was followed and it stayed off, the reading never passed 70 percent.
• B: The rule only tells you the reading did not exceed 70 percent; the figure of 50 percent is an invented number.
• C: The passage says staff followed the rule, so nothing points to a broken machine; this invents a cause.
• D: No damage is mentioned anywhere, and a low reading makes moisture damage even less likely; this adds an event.

Answer: B

Correct answer: The county's testing lab. Do a backward check on the pronoun "It." It is singular and refers to a thing, so it cannot mean Dr. Reyes, the assistant, or the plural samples. The nearest fitting noun before it is the county laboratory, so the lab promised the results within a week.

• A: Dr. Reyes is a person referred to as "her" and "she," not "it"; she plans to compare the results, but she made no promise about timing.
• B (correct): "It" points back to the nearest sensible singular noun, the county laboratory, which tests the water and promised the results.
• C: The assistant packed and delivered the samples; "it" would not be used for a person, and the assistant is not the one making the promise.
• D: The samples are plural and are referred to as "they," so the singular "it" cannot refer to them.

Answer: B

Correct answer: It suits the dry upland fields but not the wet clay fields of the river bottom. Separate the farmers' view (their stated reasons for no-till) from the author's own unattributed judgments. The author says the reasoning "holds up well" on dry upland fields, then turns with however to report cold, wet soil and lower yields on clay, so the author's view is qualified: helpful in one setting, not in the other.

• A: This credits the farmers' explained view to the author and ignores the however sentence, where the author points to lower yields on clay.
• B (correct): The author accepts the farmers' reasoning for the uplands, then uses however and the trial results to limit it on clay soil, which is a qualified view tied to field type.
• C: The author reports lower yields only on the river-bottom clay and says the reasoning holds up well on the uplands, so this answer is too broad and too strong.
• D: The passage gives fuel, labor and erosion as the farmers' reasons; assigning a hidden motive like laziness goes beyond the text.

Answer: A

Check both scope and certainty. The evidence comes from 60 turtles on one beach, and the researchers used might while listing limits of the study. Only the conclusion that stays with the tracked turtles and keeps the tentative wording matches; the others upgrade to cause, widen to the whole world, or add an unsupported explanation.

• A (correct): This keeps both the limited sample of tracked turtles and the researchers' tentative word might, so it matches the evidence.
• B: The researchers said temperature might influence swimming and did not separate it from other factors such as moonlight, so this turns a possibility into a certainty.
• C: The study covered 60 turtles from one Florida beach, so worldwide widens the scope far beyond the sample.
• D: The passage mentions moonlight only as an untested factor; it never says moonlight is the explanation.

Answer: A

Correct answer: 5. The largest multiple of 8 not above 125 is

The remainder is

Check:

• A (correct): 8 × 15 = 120 and 125 − 120 = 5, which is less than 8.
• B: 15 is the quotient, not the remainder.
• C: This rounds the quotient up to 16 and finds 128 − 125 = 3; the multiple of 8 must not exceed 125.
• D: This is the decimal part of 125 ÷ 8 = 15.625, not the whole-number amount left over.

Answer: A

Correct answer:

The fixed fee is the starting value and the hourly charge is the rate, so

For example, 2 hours costs

• A (correct): The rate 48 multiplies the hours, and the one-time fee 65 is added once.
• B: This swaps the roles, charging the service fee every hour and the hourly rate only once.
• C: This adds the fee to the rate, so the $65 fee would be charged again for every hour.
• D: This multiplies the fee by the hourly rate, making the fixed fee cost 48 × 65.

Answer: B

Correct answer: Undefined. The equation

is a vertical line. Between any two of its points the run is 0, so rise over run cannot be computed and the slope is undefined.

• A: A slope of 0 belongs to a horizontal line; x = -3 is vertical.
• B (correct): Every point has x = -3, so the run is 0, and division by zero is impossible.
• C: This reads the constant as the slope; -3 only tells where the vertical line crosses the x-axis.
• D: The line does not rise one unit for each unit of run; it does not run at all.

Answer: D

Correct answer: x = 4. Distribute:

Subtract 15: 3x = 12. Divide by 3: x = 4. You can also divide both sides by 3 first:

so x = 4.

• A: This comes from writing 3(x + 5) as 3x + 5, multiplying only the x by 3.
• B: This comes from dividing by 3 to get x + 5 = 9 and then adding 5 instead of subtracting it.
• C: This subtracts 3 from 27 and then divides by 3, mixing up which number multiplies the parentheses.
• D (correct): Distributing gives 3x + 15 = 27, so 3x = 12 and x = 4.

Answer: A

Correct answer: 76 degrees. An inscribed angle is half its intercepted arc, so the arc is twice the angle: 2 times 38 = 76 degrees.

• A (correct): The arc is twice the inscribed angle, 2 times 38.
• B: This halves the angle; it is the angle that is half the arc, so the arc is double.
• C: This treats the inscribed angle as equal to its arc, which holds only for a central angle.
• D: This subtracts 38 from 180; there is no supplement relationship between an inscribed angle and its arc.

Answer: D

Correct answer: 0 = 5, so the system has no solution. Double the first equation:

Subtract the second equation:

Both variables vanish and a false statement remains, so the lines are parallel and the system has no solution.

• A: The constants do not cancel: 8 − 3 is 5, so the result is false, not 0 = 0.
• B: A false statement means no point works; infinitely many solutions come from a true statement such as 0 = 0.
• C: Both variables cancel here, so no value of x is produced.
• D (correct): Doubling the first equation and subtracting the second leaves the false statement 0 = 5, which signals parallel lines.

Answer: C

Correct answer: 78.5 meters. The line follows the boundary, so use C = πd = 3.14 times 25 = 78.5 meters.

• A: This doubles π times the diameter; 2πr already equals πd, so doubling again is too much.
• B: This multiplies 3.14 by the radius, 12.5, which gives only half the circumference.
• C (correct): Pi times the diameter, 3.14 times 25, is 78.5 meters.
• D: This is π times 12.5 squared, the pad's area, which is not a length.

Answer: C

Correct answer: Angle 7. Corresponding angles sit in the same position at each intersection. Angle 3 is the bottom-left angle at the upper intersection, so its match is the bottom-left angle at the lower intersection, angle 7.

• A: Angles 3 and 6 are alternate interior angles: both between the lines but on opposite sides of the transversal.
• B: Angles 3 and 5 are same-side interior angles, which are supplementary rather than corresponding.
• C (correct): Angle 7 is bottom left at the lower intersection, the same position angle 3 holds at the upper one.
• D: Angle 2 is vertical to angle 3 at the same intersection, not a corresponding angle.

Answer: C

Correct answer: 22.5 square cm. The height must be perpendicular to the base, so use 5 cm, not the slanted 7 cm side.

The area is 22.5 square centimeters.

• A: This uses the slanted 7 cm side as the height.
• B: This leaves out the one-half in the formula.
• C (correct): One-half of base 9 times perpendicular height 5 is 22.5.
• D: This adds 9, 7 and 5 instead of using one-half base times height.

Answer: B

Correct answer: 294 square inches. Find the edge first: s cubed = 343, so s = 7 inches. Each face is 7 times 7, or 49.

• A: This is the area of only one face; a cube has six.
• B (correct): The edge is 7 inches because 7 cubed is 343; six faces of 49 give 294.
• C: This counts only the four side faces and leaves out the top and bottom.
• D: This multiplies the volume by 6 instead of first finding the edge length.

Answer: B

Correct answer: 0.000725 m. For a negative power of ten, move the decimal point left by the size of the exponent. Starting at 7.25 and moving four places left gives 0.000725 m.

• A: This moves the decimal point only three places to the left.
• B (correct): A negative exponent of 4 moves the decimal point four places to the left.
• C: This moves the decimal point five places to the left, one too many.
• D: This moves the decimal point to the right, which is only done for a positive exponent.

Answer: D

Correct answer: 42.75 mm. |L − 42.5| ≤ 0.2 means

Add 42.5 to all parts:

Both endpoints are allowed because the sign is ≤. Only 42.75 mm lies outside this range.

• A: |42.3 − 42.5| = 0.2, which meets the at-most condition; the boundary is included.
• B: |42.7 − 42.5| = 0.2, which is exactly the limit, and ≤ includes the boundary.
• C: |42.45 − 42.5| = 0.05, well within the 0.2 mm allowance.
• D (correct): |42.75 − 42.5| = 0.25, which is more than 0.2, so this part is outside the allowed range.

Answer: A

Correct answer: −4°F. Rises are positive and drops are negative. Total rise =

so the evening temperature was −4°F.

• A (correct): −11 + 4 × 5 − 13 = −11 + 20 − 13 = −4.
• B: This starts at +11 instead of −11: 11 + 20 − 13 = 18.
• C: This adds only one hour's rise of 4 degrees instead of 4 × 5 = 20.
• D: This treats the rise of 20 degrees as a drop: −11 − 20 − 13.

Answer: D

Correct answer: 2x³ + 5x² - 14x + 3. Multiply each term of the first factor by every term of the second. $2x$ gives $2x^3+8x^2-2x$. $-3$ gives $-3x^2-12x+3$. Combine like terms:

so the result is $2x^3+5x^2-14x+3$.

• A: This adds 3x^2 instead of subtracting it; -3 times x^2 is -3x^2.
• B: This leaves out the -12x that comes from -3 times 4x.
• C: This gets the last sign wrong; -3 times -1 is +3.
• D (correct): 2x gives 2x^3 + 8x^2 - 2x; -3 gives -3x^2 - 12x + 3; combining gives 2x^3 + 5x^2 - 14x + 3.

Answer: A

Correct answer: 120 square cm. Each side is

The diagonals bisect each other at right angles, forming right triangles with hypotenuse 13 and one leg 12. The other leg is the square root of

so the second diagonal is 10 cm.

• A (correct): The side is 13, half-diagonals are 12 and 5, so the diagonals are 24 and 10 and the area is half of 240.
• B: This multiplies the diagonals 24 and 10 but leaves out the factor of one half.
• C: This multiplies the side, 13, by the diagonal, 24; a diagonal is not the height of the rhombus.
• D: This multiplies the half-diagonals 12 and 5, which gives the area of only two of the four right triangles.