Account Sign in Sign up

Free classroom resource

Math worksheet generator

Build a printable AMC-style set by topic and difficulty. Every worksheet includes multiple-choice questions and a worked answer key.

Mathbound · Contest practice

Mixed topics worksheet

Mixed difficulty

Name

Date

1.
A committee of $4$ is chosen from $13$ people. How many committees?
- A.495
- B.52
- C.715
- D.728
- E.286
2.
What is the maximum product of positive integers that sum to $37$ ?
- A.708586
- B.708589
- C.262144
- D.531441
- E.708588
3.
Compute $2^{100}+3^{100}$ modulo $13$ .
- A.0
- B.1
- C.3
- D.6
- E.12
4.
Compute $5^{10}\bmod 11$ .
- A.4
- B.1
- C.5
- D.2
- E.3
5.
Lattice paths $(0,0)\to(7,7)$ with steps $(1,0),(0,1)$ avoiding $(4,5)$ . How many?
- A.3432
- B.1260
- C.2207
- D.2172
- E.2162
6.
$\binom{9}{2}=$
- A.27
- B.45
- C.36
- D.72
- E.18
7.
Two fair dice are rolled. Probability the sum equals $9$ ?
- A.1/6
- B.5/36
- C.4/12
- D.4/18
- E.4/36
8.
Lattice points strictly inside the right triangle with vertices $(0,0)$ , $(17,0)$ , $(0,11)$ ?
- A.93.5
- B.80
- C.79
- D.81
- E.28
9.
Fifteen equally spaced points on a circle form a regular $15$ -gon. Three distinct vertices are chosen to form a triangle. How many of these triangles contain the center of the $15$ -gon in their interior?
- A.120
- B.132
- C.140
- D.148
- E.156
10.
Right triangle with legs $6$ and $8$ . Hypotenuse?
- A.11
- B.8
- C.14
- D.10
- E.9

Answer key · worked solutions

1. C. 715
$\binom{m}{k}$ . $\binom{13}{4}$ . $715$ .
2. E. 708588
Prefer parts equal to $3$ (use $2$ s when needed; avoid $1$ s). Partition $37$ optimally. $708588$ .
3. D. 6
Fermat: reduce exponents modulo $12$ . $2^{12}\equiv1$ , $3^{12}\equiv1\pmod{13}$ . $6$ .
4. B. 1
Successive squaring / cycles. Reduce powers modulo 11. $1$ .
5. D. 2172
$\binom{2n}{n}$ minus paths through the obstacle. Subtract product of binomials. $2172$ .
6. C. 36
$n(n-1)/2$ . $36$ . $36$ .
7. E. 4/36
Count ordered pairs out of $36$ . $4$ favorable. $4/36$ .
8. B. 80
$\frac{(A-1)(B-1)}{2}$ for this triangle. Formula. $80$ .
9. C. 140
Center inside iff each arc between chosen vertices has length $<7.5$ , i.e. $\le7$ . Same arc method as smaller regular polygons — scaled carefully. $140$ .
10. D. 10
Pythagorean theorem / scaled triples. $\sqrt{(6)^2+(8)^2}$ . $10$ .

Teaching a class or club? Find classroom-ready starting sets on the teacher resources page.

Free AMC Math Worksheet Generator — Mathbound