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.
What is $\operatorname{lcm}(36,48)$ ?
- A.12
- B.180
- C.144
- D.96
- E.1728
2.
Compute $3^{10}\bmod 7$ .
- A.6
- B.0
- C.4
- D.3
- E.5
3.
Lattice points strictly inside the right triangle with vertices $(0,0)$ , $(7,0)$ , $(0,16)$ ?
- A.46
- B.23
- C.56
- D.45
- E.44
4.
If $r$ and $s$ are roots of $x^2+10x+18=0$ , find $r^3+s^3$ (without solving).
- A.460
- B.442
- C.470
- D.180
- E.1000
5.
Arithmetic sequence: first term $5$ , common difference $2$ . Sum of first $25$ terms?
- A.725
- B.723
- C.750
- D.125
- E.53
6.
Lattice paths $(0,0)\to(10,10)$ with steps $(1,0),(0,1)$ avoiding $(6,3)$ . How many?
- A.157246
- B.157036
- C.157026
- D.184756
- E.27720
7.
Solve $5x-3=2x+12$ .
- A.6
- B.5
- C.7
- D.3
- E.4
8.
Solve for $x$ : $3x+4=13$ .
- A.2
- B.3
- C.13
- D.4
- E.z4
9.
Solve for $x$ : $3x+8=41$ .
- A.11
- B.41
- C.12
- D.8
- E.10
10.
Solve for $x$ : $3x+2=8$ .
- A.2
- B.8
- C.3
- D.5
- E.1

Answer key · worked solutions

1. C. 144
$\operatorname{lcm}(a,b)=ab/\gcd(a,b)$ . $\gcd=12$ . $144$ .
2. C. 4
Successive squaring / cycles. Reduce powers modulo 7. $4$ .
3. D. 45
$\frac{(A-1)(B-1)}{2}$ for this triangle. Formula. $45$ .
4. A. 460
$r^3+s^3=(r+s)((r+s)^2-3rs)$ . Vieta: $r+s=10$ , $rs=18$ . $460$ .
5. A. 725
$S_n=\frac n2(2a+(n-1)d)$ . Plug values. $725$ .
6. B. 157036
$\binom{2n}{n}$ minus paths through the obstacle. Subtract product of binomials. $157036$ .
7. B. 5
Isolate $x$ . $3x=15$ . $5$ .
8. B. 3
Isolate $x$ . $3x=13-4$ . $3$ .
9. A. 11
Isolate $x$ . $3x=41-8$ . $11$ .
10. A. 2
Isolate $x$ . $3x=8-2$ . $2$ .

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

Free AMC Math Worksheet Generator — Mathbound