AMC Math Review

Combo and Probability

100

How many 4-digit numbers greater than 1000 are there that use the four digits of 2012?

What is 9.

200

A three-digit integer contains one of each of the digits 1, 3, and 5. What is the probability that the integer is divisible by 5?

What is 1/3.

300

In the  a middle school football conference, each team plays every other team exactly once. If a total of 21 conference games were played during the 2014 season, how many teams were members of the BIG N conference?

What is 7.

400

What number, when added to the numerator and to the denominator of 2/11, results in a fraction whose value is 0.85?

What is 49.

500

How many whole numbers between 1 and 1000 do not contain the digit 1?

What is 728

Geometry

100

http://www.artofproblemsolving.com/Wiki/index.php/2009_AMC_8_Problems/Problem_4

What is B

200

http://www.artofproblemsolving.com/Wiki/index.php/2009_AMC_8_Problems/Problem_9

What is 23

300

The sides of a triangle have lengths 6.5, 10, and s, where s is a whole number. What is the smallest possible value of s?

What is 4.

400

Points B, D, and J are midpoints of the sides of right triangle ACG. Points K, E, I are midpoints of the sides of triangle JDG, etc. If the dividing and shading process is done 100 times (the first three are shown) and AC=CG=6, then the total area of the shaded triangles is about equal to what integer value? (http://www.artofproblemsolving.com/Wiki/index.php/1999_AMC_8_Problems/Problem_25)

What is 6

500

http://www.artofproblemsolving.com/Wiki/index.php/1996_AJHSME_Problems/Problem_24

What is 115 degrees.

Number Theory

100

Each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is used only once to make two five-digit numbers so that they have the largest possible sum. Which of the following could be one of the numbers? 76531, 86724, 87431, 96240, 97403.

What is 87431.

200

What is the correct ordering of the three numbers 5/19, 7/21, and 9/23, in increasing order?

What is 5/19 < 7/21 < 9/23.

300

What is the units digit of 13²⁰¹²?

What is 1.

400

A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of 8^th-graders to 6^th-graders is 5:3, and the ratio of 8^th-graders to 7^th-graders is 8:5. What is the smallest number of students that could be participating in the project?

What is 89.

500

Find the largest prime number less than 100 that is the sum of two other primes.

What is 73

Word Problems

100

Jose, Thuy, and Kareem each start with the number 10. Jose subtracts 1 from the number 10, doubles his answer, and then adds 2. Thuy doubles the number 10, subtracts 1 from her answer, and then adds 2. Kareem subtracts 1 from the number 10, adds 2 to his number, and then doubles the result. Who gets the largest final answer?

Who is Kareem.

200

Tori's mathematics test had 75 problems: 10 arithmetic, 30 algebra, and 35 geometry problems. Although she answered 70% of the arithmetic, 40% of the algebra, and 60% of the geometry problems correctly, she did not pass the test because she got less than 60% of the problems right. How many more problems would she have needed to answer correctly to earn a 60% passing grade?

What is 5.

300

The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds?

What is 139.

400

John offers cow rides for a small fee. He charges $1.50 for the first mile and $0.90 for each additional mile. All trips must be an integer number of miles in length. How far could Akshar go for $20 if he gives John a $2 tip?

What is 19 miles.

500

Adam has 13 different colors of socks in a drawer, and an infinite number of socks of each color. He wears one sock on each of his five feet, as well as one on each of his two hands and one on his (one) head. What is the minimum number of socks he can blindly pick out of the drawer to be sure that he has a complete set of 8 socks of the same color to wear?

What is 92 socks.

Random Topics!

100

A shop advertises everything is "half price in today's sale." In addition, a coupon gives a 20% discount on sale prices. Using the coupon, the price today represents what percentage off the original price?

What is 60%.

200

Brent has goldfish that quadruple (become four times as many) every month, and Gretel has goldfish that double every month. If Brent has 4 goldfish at the same time that Gretel has 128 goldfish, then in how many months from that time will they have the same number of goldfish?

What is 5 months.

300

Bob has a sequence of five consecutive numbers, the first of which is odd. The sum of the numbers is 35. What is the second number in the sequence?

What is 6.

400

Let x be the answer to this question. What is x² - x + 1?

What is 1

500

On the last day of school, Mrs. Wonderful gave jelly beans to her class. She gave each boy as many jelly beans as there were boys in the class. She gave each girl as many jelly beans as there were girls in the class. She brought 400 jelly beans, and when she finished, she had six jelly beans left. There were two more boys than girls in her class. How many students were in her class?

What is 28.