2026

2026 AMC8 Paper & Solutions New

January 2026 latest exam, 12 sample questions with detailed solutions. Geometry weight increased, new probability types.

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12 Sample Questions

40 Minutes

Max Score 25

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Exam Overview

This exam emphasizes geometry, probability, statistics. Overall difficulty is moderate to hard.

DDifficulty

EasyQ1-10
MediumQ11-20
HardQ21-25

TTopics

Algebra40%

Geometry30%

Number Theory15%

Combinatorics15%

AAwards

Distinguished Honor Roll

Distinguished Honor Roll (Top 1%)

22+

Honor Roll

Honor Roll (Top 5%)

19+

Achievement Roll

Grade 6 and below · 15+ points

15+

Sample Problems

2026 AMC8 Sample Problems (12 questions)

Sample reference problems by difficulty — click an option to check your answer

Q1EasyInteger Ops

Calculate the value of 36 × 25 - 180.

A) 620

B) 680

C) 720

D) 760

E) 800

Steps

36 × 25 = 900

900 - 180 = 720

Answer: C36×25 can be split as 9×4×25 = 9×100 = 900

Q3EasyFraction Ops

Simplify (2/3 + 1/6) ÷ (5/12).

A) 1

B) 6/5

C) 2

D) 12/5

E) 5/2

Steps

2/3 + 1/6 = 4/6 + 1/6 = 5/6

(5/6) ÷ (5/12) = (5/6)×(12/5) = 2

Answer: CDividing by a fraction is the same as multiplying by its reciprocal

Q5EasyDecimal Ops

Calculate the value of 3/4 + 0.25 - 1/8.

A) 7/8

B) 5/8

C) 3/4

D) 1

E) 9/8

Steps

Convert everything to fractions: 0.25 = 1/4

3/4 + 1/4 = 1

1 - 1/8 = 7/8

Answer: AWhen mixing fractions and decimals, it is best to convert everything to fractions first

Q8EasyAverage

The average of five numbers is 24. After one number is removed, the average of the remaining four numbers is 22. What is the number that was removed?

A) 28

B) 30

C) 34

D) 32

E) 36

Steps

Sum of the five numbers = 5 × 24 = 120

Sum of the four numbers = 4 × 22 = 88

The removed number = 120 - 88 = 32

Answer: DThe key to average problems: sum = average × count

Q11MediumLinear Func.

The line y = 2x + b passes through the point (3, 10). Find the value of b.

A) 2

B) 4

C) 3

D) 5

E) 6

Steps

Substitute x=3, y=10: 10 = 2(3) + b

10 = 6 + b

b = 4

Answer: BIf a point lies on a line, its coordinates satisfy the equation

Q13MediumDivisibility

How many numbers from 1 to 60 are divisible by both 3 and 4?

A) 3

B) 4

C) 6

D) 5

E) 7

Steps

Being divisible by both 3 and 4 means being divisible by LCM(3,4)=12

60 ÷ 12 = 5

These numbers are: 12, 24, 36, 48, 60, for a total of 5

Answer: DBeing divisible by both a and b is equivalent to being divisible by LCM(a,b)

Q16MediumTriangle Area

In the coordinate plane, A(0,0), B(4,0), and C(2,3). Find the area of triangle ABC.

A) 4

B) 5

C) 7

D) 6

E) 8

Steps

The base AB lies on the x-axis, with length = 4

The distance from C to AB = the y-coordinate of C = 3

Area = 1/2 × 4 × 3 = 6

Answer: DWhen the base lies on a coordinate axis, you can find the height directly from the vertex coordinates

Q19MediumProbability

Two dice are rolled at the same time. What is the probability that the sum of the numbers is 7?

A) 1/12

B) 1/9

C) 1/6

D) 5/36

E) 1/4

Steps

Total number of outcomes = 6 × 6 = 36

Combinations with a sum of 7: (1,6)(2,5)(3,4)(4,3)(5,2)(6,1) = 6 outcomes

Probability = 6/36 = 1/6

Answer: CListing out the cases is the most reliable method

Q21HardPerm. & Comb.

Three different integers are chosen from 1 to 10 so that their sum is even. How many ways are there to choose them?

A) 40

B) 60

C) 50

D) 70

E) 80

Steps

For the sum of three numbers to be even: all even, or two odd and one even

All even: C(5,3) = 10

Two odd and one even: C(5,2)×C(5,1) = 10×5 = 50

Total: 10 + 50 = 60

Answer: BThe parity of a sum depends on the number of odd addends

Q22HardNumber Theory

In a two-digit number, the tens digit is 2 times the units digit. If the two digits are swapped, the new number is 27 less than the original. What is the original number?

A) 42

B) 63

C) 52

D) 74

E) 84

Steps

Let the units digit be a, and the tens digit be 2a

Original number = 20a + a = 21a, new number = 10a + 2a = 12a

21a - 12a = 9a = 27 → a = 3

Original number = 21 × 3 = 63

Answer: BRepresenting the digits algebraically is the key to solving the problem

Q24HardGeometry

Square ABCD has side length 6. E is the midpoint of BC, and F is a point on CD with DF=2. Find the area of triangle AEF.

A) 12

B) 14

C) 15

D) 16

E) 18

Steps

Area of the square = 36

S(ABE) = 1/2 × 6 × 3 = 9

S(ADF) = 1/2 × 6 × 2 = 6

S(ECF) = 1/2 × 3 × 4 = 6

S(AEF) = 36 - 9 - 6 - 6 = 15

Answer: CSubtract the surrounding triangles from the total area

Q25HardLogic

Among three people, Person A, Person B, and Person C, exactly one is telling the truth. Person A says: "Person B is lying." Person B says: "Person C is lying." Person C says: "Both Person A and Person B are lying." Who is telling the truth?

A) Person A

B) Person B

C) Person C

D) Cannot be determined

E) Both tell the truth

Steps

Suppose Person A tells the truth → Person B is lying → Person C is not lying → Person C's statement is true → Person A is lying, a contradiction

Suppose Person B tells the truth → Person C is lying → Person C's statement is false → at least one of Person A and Person B is not lying ✓

In this case Person A is lying → Person B is not lying ✓, Person C is lying ✓

Only Person B is telling the truth

Answer: BTesting one assumption at a time is the standard method for logical reasoning

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2026 AMC8 Paper & Solutions New

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Exam Overview

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2026 AMC8 Sample Problems (12 questions)

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