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.
Compute $6^{10}\bmod 11$ .
- A.4
- B.1
- C.6
- D.2
- E.3
2.
How many positive integers $n\le 150$ are divisible by $6$ ?
- A.21
- B.26
- C.144
- D.24
- E.25
3.
Right triangle with legs $24$ and $45$ . Hypotenuse?
- A.45
- B.69
- C.51
- D.50
- E.52
4.
How many positive integers $k\le 120$ satisfy $\gcd(k,120)=1$ ?
- A.32
- B.24
- C.42
- D.119
- E.60
5.
Lattice points strictly inside the right triangle with vertices $(0,0)$ , $(17,0)$ , $(0,14)$ ?
- A.104
- B.103
- C.105
- D.31
- E.119
6.
How many $3$ -digit positive integers have **distinct** digits and have digit sum equal to $12$ ?
- A.54
- B.61
- C.66
- D.72
- E.78
7.
Right triangle with legs $27$ and $36$ . Hypotenuse?
- A.46
- B.36
- C.63
- D.45
- E.44
8.
A frog starts at pad $0$ and jumps $+1$ or $+2$ each move. Pad $13$ is unsafe. How many jump sequences reach pad $20$ without landing on pad $13$ ?
- A.3029
- B.3031
- C.3030
- D.10946
- E.3028
9.
How many ways can a committee of $2$ be chosen from $7$ people?
- A.22
- B.7
- C.20
- D.14
- E.21
10.
How many positive integers $n\le 100$ satisfy $n\equiv 4\pmod{5}$ ?
- A.20
- B.22
- C.21
- D.23
- E.19

Answer key · worked solutions

1. B. 1
Successive squaring / cycles. Reduce powers modulo 11. $1$ .
2. E. 25
Count multiples. $\lfloor 150/6\rfloor$ . $25$ .
3. C. 51
Pythagorean theorem / scaled triples. $\sqrt{(24)^2+(45)^2}$ . $51$ .
4. A. 32
Euler totient $\varphi(n)$ . Factor 120. $32$ .
5. A. 104
$\frac{(A-1)(B-1)}{2}$ for this triangle. Formula. $104$ .
6. C. 66
Casework on hundreds digit with distinctness and sum constraint. Systematic enumeration by leading digit — not a single formula. $66$ .
7. D. 45
Pythagorean theorem / scaled triples. $\sqrt{(27)^2+(36)^2}$ . $45$ .
8. A. 3029
Fibonacci with a zeroed forbidden state. DP with $F(13)=0$ . $3029$ .
9. E. 21
$\binom{n}{k}$ . $\binom{7}{2}$ . $21$ .
10. A. 20
Arithmetic progression. First 4, step 5. $20$ .

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

Free AMC Math Worksheet Generator — Mathbound