SAT sample questions, with worked answers

D: mixed. The reviews contained both praise and complaints, and critics were undecided, which is what "mixed" means. "Glowing" and "hostile" each capture only one side.

D: To challenge a common belief about goldfish by presenting evidence against it. The text states the belief, then gives experiments that contradict it ("however"). It does not give training instructions or compare goldfish with other fish.

A: Much of an octopus's nervous system is spread through its arms, which can act on their own.. The text says two-thirds of the neurons are in the arms and that an arm can reach and grasp on its own. The second choice contradicts this, and size comparisons and sight are not discussed.

A: Nests in thick shrubs were raided by predators far less often than nests in open branches.. The hypothesis is about hiding nests from predators, so evidence that sheltered nests are raided less is direct support. Food, location and singing do not address predators.

A: premature. The book "outlived" the harsh first judgment, and its reputation grew later: the judgment came too early. "Premature" means exactly that.

1. Find the clue: the reputation grew later, and the book "outlived" the judgment.
2. Predict: a judgment made too soon.
3. Match: premature.

The trap: Choosing "unanimous" because the reviews were harsh. Harsh is not the same as unanimous, and it does not explain "outlived."

A: Bee visits fell through the day as the measured nectar in the flowers fell.. The hypothesis links visits to nectar. Only the first finding shows visits and nectar falling together. Temperature, flower variety and bees leaving are other possible explanations, not support for this one.

1. Name both parts of the hypothesis: more morning visits, because of more nectar.
2. The right finding must connect visits to nectar.
3. Only "visits fell as nectar fell" does.

The trap: Choosing the temperature finding. It could explain fewer afternoon visits, but by a different cause than the one the ecologist proposed.

D: spice:. A colon introduces a list after a complete sentence. A semicolon must join two complete sentences, and "Including cumin..." is a fragment.

C: is. The subject is "collection" (singular). "Of rare maps" and the phrase between commas do not change it, so the verb is "is."

A: By contrast,. The tern's enormous trip is set against the robins' short ones, so a contrast transition is right. "Likewise" would claim they are similar.

D: While honeybee colonies number in the tens of thousands, bumblebee colonies usually have no more than a few hundred bees.. Only the first choice contrasts the colony sizes (tens of thousands versus a few hundred). The others state a similarity or a different difference.

A: ;. "A single spacecraft could use it to visit several of them" is a complete sentence, and so is the part before it. Two complete sentences can be joined by a semicolon, not by a comma alone or by nothing.

1. Is the part after the blank a complete sentence? Yes: subject "a single spacecraft," verb "could use."
2. Is the part before it complete? Yes.
3. Two complete sentences: a semicolon (or a period, or a comma with "and").

The trap: Picking the comma. A comma alone between two sentences is a comma splice, the error this question type is built around.

A: Ming builders used more brick and stone than earlier builders, whose walls were often packed earth, so much of today's wall dates from the Ming dynasty.. The goal is a reason the Ming sections lasted. Only the first choice contrasts the materials (brick and stone against packed earth) and links that to what stands today.

1. Goal: explain why Ming sections lasted longer.
2. Which notes give a reason? The materials.
3. The answer must contrast the materials and connect them to what survives.

The trap: Choosing the earthen-walls note alone. It is relevant but does not compare it with the Ming builders, so it explains nothing.

B: 2. Distribute first: 6x + 42 = 2x + 50. Collect x on the left and numbers on the right: 6x − 2x = 50 − 42, so 4x = 8 and x = 2. Multiplying only the x by 6 (and not the 7) is the usual slip.

A: −5. Replace every x with −4: 1(−4)² + 4(−4) − 5 = 16 − 16 − 5 = −5. Square the −4 before multiplying by 1; (−n)² is positive.

A: 60. First 25% of 400 = 100 play a sport. Then 60% of those 100 = 60. The second percent is of the sport players, not of the whole school.

D: 21. a² + b² = c²: 29² − 20² = 841 − 400 = 441, so the other leg is 21. Subtracting the sides without squaring gives 9.

A: 64. Write the equation 25 + 0.10t = 31.40. Subtract 25 to get 0.10t = 6.40, so t = 64.

1. Set up: 25 + 0.10t = 31.40.
2. Subtract 25: 0.10t = 6.40.
3. Divide by 0.10: t = 64.

The trap: Dividing the whole bill by 0.10 (314) and forgetting the $25 monthly charge.

A: 4. For ax² + bx + c = 0, the solutions add to -b/a. Here -(-12)/3 = 4. No need to solve the equation.

1. Identify a = 3, b = -12.
2. Sum of roots = -b/a.
3. -(-12)/3 = 4.

The trap: Using b alone (12) or forgetting the sign (-4).

A: 4% lower. Multiply: 1.20 × 0.80 = 0.96, so the final price is 96% of the original, which is 4% lower.

1. A 20% rise multiplies by 1.20.
2. A 20% cut multiplies by 0.80.
3. 1.20 × 0.80 = 0.96: 4% lower.

The trap: Thinking the changes cancel. The cut is 20% of a bigger number, so it removes more than the rise added.

A: Center (-3, 4), radius 6. The form (x - h)² + (y - k)² = r² has center (h, k). x + 3 is x - (-3), so h = -3; k = 4; r² = 36, so r = 6.

1. Rewrite x + 3 as x - (-3): h = -3.
2. y - 4: k = 4.
3. r² = 36, so r = 6.

The trap: Taking the signs as written (3, -4), or giving 36 as the radius instead of its square root.

A: 209. Selection Index = (2 × 690 + 710) ÷ 10 = (1380 + 710) ÷ 10 = 2090 ÷ 10 = 209.

1. Double Reading and Writing: 2 × 690 = 1380.
2. Add Math: 1380 + 710 = 2090.
3. Divide by 10: 209.

The trap: Adding the two scores (1400) or dividing that by 10 (140): Reading and Writing counts twice.