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.
How many positive integers $n\le 150$ satisfy $n\equiv 2\pmod{5}$ ?
- A.29
- B.30
- C.32
- D.31
- E.33
2.
A square has side length $14$ . What is its perimeter?
- A.56
- B.57
- C.196
- D.55
- E.28
3.
Lattice points strictly inside the right triangle with vertices $(0,0)$ , $(10,0)$ , $(0,9)$ ?
- A.37
- B.19
- C.45
- D.36
- E.35
4.
What is the sum of the first $40$ positive integers?
- A.860
- B.80
- C.1600
- D.820
- E.819
5.
What is the sum of the first $27$ positive integers?
- A.378
- B.377
- C.405
- D.54
- E.729
6.
An item costs $56$ . After a $10\%$ discount (no tax), how much is paid?
- A.51.40
- B.6
- C.50.40
- D.46
- E.56
7.
Positive integer solutions to $x_1+\cdots+x_{6}=14$ with each $x_i\le 8$ ?
- A.1282
- B.1276
- C.1281
- D.11628
- E.1287
8.
What is $\operatorname{lcm}(24,48)$ ?
- A.72
- B.48
- C.0
- D.1152
- E.24
9.
Two fair dice are rolled. Probability the sum equals $11$ ?
- A.2/36
- B.1/6
- C.3/36
- D.2/12
- E.2/18
10.
Lattice points strictly inside the right triangle with vertices $(0,0)$ , $(16,0)$ , $(0,13)$ ?
- A.91
- B.29
- C.104
- D.90
- E.89

Answer key · worked solutions

1. B. 30
Arithmetic progression. First 2, step 5. $30$ .
2. A. 56
Perimeter $4s$ . $4\cdot14$ . $56$ .
3. D. 36
$\frac{(A-1)(B-1)}{2}$ for this triangle. Formula. $36$ .
4. D. 820
$n(n+1)/2$ . $40(40+1)/2$ . $820$ .
5. A. 378
$n(n+1)/2$ . $27(27+1)/2$ . $378$ .
6. C. 50.40
Multiply by $(1-d)$ . $56(1-10/100)$ . $50.40$ .
7. C. 1281
Inclusion-exclusion after $y_i=x_i-1$ . Upper bound 8. $1281$ .
8. B. 48
$\operatorname{lcm}(a,b)=ab/\gcd(a,b)$ . $\gcd=24$ . $48$ .
9. A. 2/36
Count ordered pairs out of $36$ . $2$ favorable. $2/36$ .
10. D. 90
$\frac{(A-1)(B-1)}{2}$ for this triangle. Formula. $90$ .

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

Free AMC Math Worksheet Generator — Mathbound