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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.
Solve for $x$ : $3x+12=33$ .
- A.8
- B.12
- C.6
- D.7
- E.33
2.
How many pairs of positive integers $(x,y)$ with $x\le y$ satisfy $\dfrac1x+\dfrac1y=\dfrac1{17}$ ?
- A.2
- B.3
- C.17
- D.1
- E.z4
3.
A committee of $3$ is chosen from $15$ people. How many committees?
- A.470
- B.105
- C.364
- D.45
- E.455
4.
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
5.
If $x+\dfrac1x=10$ , then $x^2+\dfrac1{x^2}=$
- A.20
- B.99
- C.98
- D.100
- E.z4
6.
Positive integer solutions to $x_1+\cdots+x_{8}=16$ with each $x_i\le 8$ ?
- A.245157
- B.6435
- C.6428
- D.6422
- E.6427
7.
Regular $10$ -gon vertices labeled. How many triangles formed by three vertices contain the center?
- A.20
- B.15
- C.120
- D.100
- E.30
8.
How many positive integers $n\le 50$ satisfy $n\equiv 2\pmod{8}$ ?
- A.8
- B.9
- C.6
- D.7
- E.z4
9.
Compute $3^{12}\bmod 11$ .
- A.3
- B.10
- C.0
- D.1
- E.9
10.
How many positive integers $n\le 200$ satisfy $n\equiv 1\pmod{7}$ ?
- A.30
- B.31
- C.28
- D.29
- E.z4

Answer key · worked solutions

1. D. 7
Isolate $x$ . $3x=33-12$ . $7$ .
2. A. 2
$(x-t)(y-t)=t^2$ . Divisors $d\le t$ of $t^2$ . $2$ .
3. E. 455
$\binom{m}{k}$ . $\binom{15}{3}$ . $455$ .
4. D. 2172
$\binom{2n}{n}$ minus paths through the obstacle. Subtract product of binomials. $2172$ .
5. C. 98
Square both sides. $10^2-2$ . $98$ .
6. E. 6427
Inclusion-exclusion after $y_i=x_i-1$ . Upper bound 8. $6427$ .
7. A. 20
Each arc between vertices $<n/2$ . Count valid triples. $20$ .
8. D. 7
Arithmetic progression. First 2, step 8. $7$ .
9. E. 9
Successive squaring / cycles. Reduce powers modulo 11. $9$ .
10. D. 29
Arithmetic progression. First 1, step 7. $29$ .

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Free AMC Math Worksheet Generator — Mathbound