Euclid
Isaac Newton
Carl Gauss
Emmy Noether
Archimedes
100
Joel took a test consisting of 40 questions. He gets 0.5 points for every correct answer
and loses 1 point for every wrong answer. Joel answered all the questions and
received a score of 2 points. How many questions did he answer correctly?
a. 25
b. 26
c. 27
d. 28
D) 28
100
There is a picture painted on a mosaic made out of 2 ππ π₯ 2 ππ squares (see the
picture). The boundary lines of the figure are made from arcs of circles. What is the
area, in square centimeters, of the shaded region?
a. 32
b. 28
c. 24
d. 20
A) 32
100
Problem:
The function f(x) = 8/(3x^2 - 3k^2), where k is an arbitrary constant, can be expressed as the sum of two functions h(x) and g(x).
If h(x) = A/(3x - 3k), where A is another arbitrary constant, express A in terms of k.
Answer choices:
A) A = 24k
B) A = 4/k
C) A = 3/8k
D) A = 3k^2
E) None of the above
B) A = 4/k
100
What is the measure of the angle formed by the hour hand and minute hand of a clock at 4:40 PM?
100 degrees
100
Evaluate the expression:
((β5 + 1) / 2)^2000 Γ ((β5 - 1) / 2)^2000
A) (5^2000 - 1) / 4
B) (5^2000 + 1) / 4
C) 4^1000
D) 1
D) 1
200
Three of the numbers 2, 4, 16, 25, 50, 125, have a product of 1000. What is the sum of
those three numbers?
a. 131
b. 77
c. 71
d. 143
a) 131
200
Triangle π
ππ is the image of the equilateral triangle πΎππ upon rotation by 130Β°
clockwise around π. What is the measure of β π
πΎπ?
a. 35Β°
b. 25Β°
c. 30Β°
d. 40Β°
A) 35 degrees
200
If two identical right isosceles triangles are overlapped along their hypotenuses in such a way that the resulting triangle's area is 1/8th the length of one of the legs, and the hypotenuses are 12 * 81/2 units long, what is the collective area of the parts of the isosceles triangles that aren't overlapping?
Answer choices:
- 166
- 335
- 477
- 573
- None of the above
573
200
When you divide a natural number n by 7, you get a remainder of 4. When you divide the number n by 11, you also get a remainder of 4. What is the remainder when n is divided by 77?
Answer choices:
A) 1
B) 4
C) 6
D) 7
B) 4
200
21. The average of Joannaβs parents age is 39. Her father is four years older than her
mother. The average age of Joanna and her father is 23. How old is Joanna?
a. 5
b. 7
c. 11
d. 13
A) 5
300
Define 
to be 
for all real numbers 
and 
What is the value of
A) -2
300
Natural numbers 1 to 7 are hidden under the letters π΄, π΅, πΆ, π·, πΈ, πΉ and πΊ in the figure
shown below. The sum of the numbers at the vertices of each of the three
quadrilaterals is equal to 13. What number is hidden under the letter π΄?
a. 1
b. 2
c. 4
d. 5
A) 1
300
2024 AMC 10A
A rectangle is partitioned into 
regions as shown. Each region is to be painted a solid color - red, orange, yellow, blue, or green - so that regions that touch are painted different colors, and colors can be used more than once. How many different colorings are possible?
D) 540
300
A sequence starts with the terms:
1, -1, -1, 1, -1. After the fifth term, every term is equal to the product of the two preceding terms.
For example, the sixth term is the product of the fourth and fifth terms.
What is the sum of the first 2023 terms of the sequence?
A) 674
B) 0
C) -674
D) 1011
C) -674
300
Which of the following line segments in the quadrilateral πππ
π (shown in the picture
below) is the longest?
a. ππ
b. ππ
c. ππ
d. ππ
A) ππ
400
The number 2024 is written as the sum of not necessarily distinct two-digit numbers.
What is the least number of two-digit numbers needed to write this sum?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
B) 21
400
What is the sum of the digits of the smallest prime that can be written as a sum of 5 distinct primes?
(A) 5
(B) 7
(C) 8
(D) 10
(E) 13
B) 7
400
AMC 10A 2011 Problem 15
Roy bought a new battery-gasoline hybrid car. On a trip the car ran exclusively on its battery for the first 
miles, then ran exclusively on gasoline for the rest of the trip, using gasoline at a rate of 
gallons per mile. On the whole trip he averaged 
miles per gallon. How long was the trip in miles?
(C) 440
We know that 
. Let be the distance the car traveled during the time it ran on gasoline, then the amount of gas used is 
. The total distance traveled is 
, so we get 
. Solving this equation, we get 
, so the total distance is 
.
400
AMC 10A 2021 Problem 8
When a student multiplied the number 
by the repeating decimal, 
where 
and 
are digits, he did not notice the notation and just multiplied times 
Later he found that his answer is 
less than the correct answer. What is the 
-digit number 
(E) 75
We are given that 
from which
400
In rhombus 
, point 
lies on segment 
so that 
, 
, and 
. What is the area of ? (Note: The figure is not drawn to scale.)
.
is a rhombus, so 
.
is a 
right triangle, hence 
.
The area of the rhombus is base times height: 