2017

2017 AMC8 Paper & Solutions Pick

12 selected sample solutions, moderate difficulty. Algebra focuses on ratios and equations, geometry on triangle classification and area.

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12 Sample Questions

40 Minutes

Max Score 25

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Exam Overview

This exam emphasizes multiple math topics. Overall difficulty is moderate.

DDifficulty

EasyQ1-10
MediumQ11-20
HardQ21-25

TTopics

Algebra40%

Geometry30%

Number Theory15%

Combinatorics15%

AAwards

Distinguished Honor Roll

Distinguished Honor Roll (Top 1%)

20+

Honor Roll

Honor Roll (Top 5%)

17+

Achievement Roll

Grade 6 and below · 15+ points

15+

Sample Problems

2017 AMC8 Sample Problems (12 questions)

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

Q1EasyArithmetic

Calculate the value of (12 + 8) × 3 - 15.

A) 45

B) 35

C) 40

D) 50

E) 55

Steps

20 × 3 - 15 = 60 - 15 = 45

Answer: ACompute inside the parentheses first.

Q4EasyKey concept: ratios

A recipe uses flour and sugar in the ratio 5:2. With 15 cups of flour, how many cups of sugar are needed?

A) 4

B) 5

C) 7

D) 6

E) 8

Steps

15:x = 5:2 → 5x = 30 → x = 6

Answer: DCross-multiply the proportion.

Q6EasyArea

What is the area of a square with side length 9?

A) 81

B) 36

C) 54

D) 63

E) 72

Steps

Area = 9² = 81

Answer: AArea of a square = side².

Q9EasyAverage

The sum of six numbers is 72. What is their average?

A) 10

B) 11

C) 13

D) 12

E) 14

Steps

72 ÷ 6 = 12

Answer: DAverage = sum ÷ count.

Q11MediumKey concept: equations

A father's age is 4 times his son's age. In 6 years, the father's age will be 2.5 times the son's age. How old is the son now?

A) 8

B) 9

C) 6

D) 10

E) 12

Steps

Let the son be x years old and the father 4x years old.

4x + 6 = 2.5(x + 6) → 4x + 6 = 2.5x + 15

1.5x = 9 → x = 6 (Check: father 24→30, son 6→12, 30 = 2.5×12 ✓)

Answer: CAge problems are most direct with an equation.

Q13MediumKey concept: triangles

A triangle has sides 5, 12, 13. What type of triangle is it?

A) Acute angle

B) Right angle

C) Obtuse angle

D) Isosceles

E) Equilateral

Steps

5²+12²=25+144=169=13²

Satisfies the Pythagorean theorem → right triangle.

Answer: B5-12-13 is a common Pythagorean triple.

Q15MediumDivisibility

How many numbers from 1 to 50 are divisible by 4?

A) 10

B) 12

C) 11

D) 13

E) 14

Steps

⌊50/4⌋ = 12

Answer: BThe count of numbers divisible by n is ⌊total/n⌋.

Q17MediumProbability

A bag contains 3 red balls and 2 white balls. One ball is drawn. What is the probability it is red?

A) 1/5

B) 2/5

C) 4/5

D) 3/5

E) 1

Steps

P(red) = 3/5

Answer: DBasic probability = number of favorable outcomes ÷ total number of outcomes.

Q21HardCombinatorics

From {1,2,3,4,5,6,7}, choose 3 distinct numbers whose sum is odd. How many ways are there?

A) 13

B) 14

C) 16

D) 15

E) 17

Steps

4 odd numbers {1,3,5,7}, 3 even numbers {2,4,6}

All odd: C(4,3)=4

One odd and two even: C(4,1)×C(3,2)=12

Total 4+12=16

Answer: CFor the sum to be odd, the number of odd addends must be odd.

Q22HardNumber Theory

A two-digit number has digits that sum to 11. Swapping the digits gives a number that is 27 greater than the original. What is the original number?

A) 38

B) 47

C) 56

D) 65

E) 74

Steps

Let the tens digit be a and the units digit b: a+b=11

(10b+a)-(10a+b) = 27

9b-9a = 27 → b-a = 3

a+b=11, b-a=3 → b=7, a=4

Original number = 47

Answer: BRepresent digit-swapping problems algebraically.

Q24HardArea

A trapezoid has parallel sides of length 6 and 14 and height 8. One diagonal divides it into two triangles. What is the area of the larger triangle?

A) 40

B) 48

C) 64

D) 80

E) 56

Steps

Draw the diagonal from a vertex of the longer parallel side to the shorter parallel side.

The larger triangle has the longer side (14) as its base: S = 1/2 × 14 × 8 = 56

The smaller triangle has the shorter side (6) as its base: S = 1/2 × 6 × 8 = 24

Area of the trapezoid = 80 = 56+24 ✓

Answer: EA diagonal splits a trapezoid into two triangles of equal height.

Q25HardLogic

100 people take an exam with an 80% pass rate. Those who pass average 85 points and those who fail average 45 points. What is the overall average score?

A) 70

B) 73

C) 75

D) 80

E) 77

Steps

80 people pass, 20 people fail.

Total points = 80×85 + 20×45 = 6800 + 900 = 7700

Average = 7700/100 = 77

Answer: EWeighted average = sum of each group's total ÷ total number of people.

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2017 AMC8 Paper & Solutions Pick

Scan to get free 2017 PDF + solutions

Exam Overview

DDifficulty

TTopics

AAwards

2017 AMC8 Sample Problems (12 questions)

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