The 2007 AMC 10 Papers A and B emphasized algebraic evaluation and combinatorial counting, with frequent average-speed, coin-outcome, units-digit and counting problems; the back half tested categorization and systematic enumeration more deeply. Scan for the full papers and answer keys.
2007 AMC 10 A/B paper overview and exam highlights.
The 2007 AMC 10 was held in November 2007 in two papers (A and B), with algebraic evaluation and combinatorial counting standing out.
Format: 25 multiple-choice questions, 75 minutes, 150 points max; a blank answer earns 1.5 points and a wrong answer earns 0. The AIME cut-off has recently been around 100 (Paper A).
The 2007 paper set more problems on average speed, coin outcomes, units digits of powers, and combinatorial counting, combining formulas with careful reading.
2007 AMC 10 main topic areas, weights and emphasis.
Evaluation, quadratics, word and speed problems; about 30%.
Rectangle perimeter, triangle area, circles and cylinder surface area; about 22%.
Divisibility, remainders, GCD and divisor counts; about 18%.
Coin outcomes, combinations and ordered counting; about 20%.
Classical probability and dice sums; about 10%.
2007 AMC 10-style mock questions (Basic · Medium · Hard) — submit to grade and view step-by-step solutions.
If x = 5, what is the value of 2x2 - 3x + 4?
Correct answer: A
Substitute x = 5: 2(5)2 - 3(5) + 4 = 2×25 - 15 + 4 = 50 - 15 + 4 = 39. Answer A. Key: direct substitution.The sum of three consecutive integers is 117. What is the largest?
Correct answer: B
Let the middle integer be n: 3n = 117, so n = 39 and the largest is 40. Answer B. Key: model consecutive integers by their middle.How many positive divisors does 72 have?
Correct answer: C
72 = 23×32, so the number of divisors is (3+1)(2+1) = 12. Answer C. Key: divisor-count formula.A rectangle has length 7 and width 4. What is its perimeter?
Correct answer: D
Perimeter = 2(7 + 4) = 2×11 = 22. Answer D. (28 is the area — do not confuse.) Key: rectangle perimeter formula.An item is marked up 20% above cost to a price of $60. What was the cost?
Correct answer: E
cost × 1.2 = 60, so cost = 60 / 1.2 = 50. Answer E. Key: price = cost × (1 + markup).A fair six-sided die is rolled once. What is the probability of rolling at least 5 (5 or 6)?
Correct answer: A
Values at least 5 are 5 and 6 (2 of 6), so the probability is 2/6 = 1/3. Answer A. Key: classical probability = favorable / total.Six coins are tossed at once. How many heads/tails outcomes are possible?
Correct answer: B
Each coin has 2 outcomes, so 6 coins give 26 = 64. Answer B. Key: independent outcomes multiply.What is the remainder when 2007 is divided by 11?
Correct answer: C
11 × 182 = 2002, and 2007 - 2002 = 5, so the remainder is 5. Answer C. Key: division with remainder.If 3x + 4 = 25, what is x?
Correct answer: D
3x = 25 - 4 = 21, so x = 7. Answer D. Key: isolate the variable.A triangle has base 14 and height 5. What is its area?
Correct answer: E
Area = ½×14×5 = 70/2 = 35. Answer E. Key: triangle area formula.If x2 - 13x + 42 = 0, what is the sum of all possible values of x?
Correct answer: A
Factor: (x-6)(x-7) = 0, so x = 6 or 7, and the sum is 13. Answer A. Key: Vieta — sum of roots = -b/a = 13.What is the greatest common divisor of 60 and 90?
Correct answer: B
60 = 22×3×5 and 90 = 2×32×5, so GCD = 2×3×5 = 30. Answer B. Key: take the smallest power of each shared prime.A committee of 2 is chosen from 20 people. How many different committees are possible?
Correct answer: C
C(20,2) = (20×19)/(2×1) = 190. Answer C. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).In a triangle, two angles are 48° and 72°. What is the third angle?
Correct answer: D
Triangle angles sum to 180°, so the third angle = 180 - 48 - 72 = 60°. Answer D. Key: triangle angle-sum theorem.The average of 7 numbers is 24. After removing one number, the average of the remaining 6 is 22. What was the removed number?
Correct answer: E
Sum of 7 = 7×24 = 168; sum of 6 = 6×22 = 132; the removed number = 168 - 132 = 36. Answer E. Key: average = sum / count.What is the units digit of 82007?
Correct answer: A
The units digit of powers of 8 cycles as 8, 4, 2, 6 (period 4). Since 2007 = 4×501 + 3, the remainder is 3, corresponding to the 3rd value, so the units digit is 2. Answer A. Key: cyclic units digits of powers.One worker can finish a job in 5 hours and another in 20 hours. How long does it take them together?
Correct answer: B
Rates: 1/5 + 1/20 = 4/20 + 1/20 = 5/20 = 1/4 per hour, so together they need 1 / (1/4) = 4 hours. Answer B. Key: combined rate = sum of individual rates.A square and an equilateral triangle have the same perimeter. If the triangle side is 28, what is the square side?
Correct answer: C
Triangle perimeter = 3×28 = 84, so the square side = 84 / 4 = 21. Answer C. Key: equal perimeters split by side count.Two fair six-sided dice are rolled. What is the probability the sum is 8?
Correct answer: D
Sums to 8: (2,6),(3,5),(4,4),(5,3),(6,2) — 5 outcomes out of 36, so 5/36. Answer D. Key: enumerate ordered dice pairs.A car travels 120 km at 40 km/h and returns at 60 km/h. What is the average speed for the whole trip (km/h)?
Correct answer: E
Outbound time = 120/40 = 3 h; return = 120/60 = 2 h. Total distance 240 km over 5 h gives 240/5 = 48 km/h. Answer E. Key: average speed = total distance / total time, not the average of speeds.How many positive integers less than 100 are divisible by both 6 and 15?
Correct answer: A
Divisible by both 6 and 15 means divisible by LCM(6,15) = 30. The multiples of 30 below 100 are 30, 60, 90 — 3 of them. Answer A. Key: divisible by both ⟺ divisible by their LCM.A committee of 2 is chosen from 13 people. How many different committees are possible?
Correct answer: B
C(13,2) = (13×12)/(2×1) = 78. Answer B. Key: combinations are order-independent, C(n,k) = n!/(k!(n-k)!).A right cylinder has radius 4 and height 3. What is its total surface area? (in terms of π)
Correct answer: C
Surface area = 2πr2 + 2πrh = 2π(42) + 2π(4)(3) = 32π + 24π = 56π. Answer C. Key: cylinder surface = two bases + lateral area.Given x + y = 26 and xy = 168, what is x2 + y2?
Correct answer: D
x2 + y2 = (x+y)2 - 2xy = 262 - 2×168 = 676 - 336 = 340. Answer D. Key: identity linking sum of squares to sum and product.In how many ways can 28 be written as a sum of three positive integers, where order does not matter?
Correct answer: E
Let a ≤ b ≤ c with a+b+c = 28. For a=1: 13 ways — (1,1,26) to (1,13,14); a=2: 12 ways — (2,2,24) to (2,13,13); a=3: 10 ways — (3,3,22) to (3,12,13); a=4: 9 ways — (4,4,20) to (4,12,12); a=5: 7 ways — (5,5,18) to (5,11,12); a=6: 6 ways — (6,6,16) to (6,11,11); a=7: 4 ways — (7,7,14) to (7,10,11); a=8: 3 ways — (8,8,12) to (8,10,10); a=9: 1 way — (9,9,10). Total 65. Answer E. Key: ordered enumeration to avoid duplicates.Unified AMC 10 specs, consistent across years.
Papers A and B are comparable in difficulty and scope. Students may take either, or both — the higher score is used for awards and AIME qualification.
Four steps · Overview / Topics / Practice / Prep
Read the 2007 AMC 10 A/B overview and format specs to grasp the year’s style.
Review the key topics and weights, and locate your weak areas.
Complete the 25 mock questions (75-minute limit); submit for auto-grading and right/wrong marks.
Open the step-by-step solutions, learn from mistakes, and scan for full papers to push for AIME.
Prep tips and score-boosting advice for the 2007 AMC 10 A/B paper.
Finish all 25 within 75 minutes; skip when stuck, bank the solvable ones, and return to the hard ones.
Average speed = total distance / total time — never the arithmetic mean of the two speeds.
Ordered uses P(n,k); unordered uses C(n,k); check order and repeatability.
Units digits cycle by the base; locate the result via the exponent mod the period.
Aiming above 100? Lock the basics and medium questions, then take the last 5 step by step; scan for full papers and a plan.
Frequent questions about the 2007 AMC 10 papers and answers.
Scan to add the advisor for 2007 AMC 10 A/B past papers, answer keys and solutions, plus a custom prep plan.
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