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.
An item costs $76$ . After a $20\%$ discount (no tax), how much is paid?
- A.56
- B.76
- C.61.80
- D.15
- E.60.80
2.
How many positive integers $k\le 75$ have exactly three positive divisors?
- A.5
- B.7
- C.3
- D.4
- E.8
3.
Solve for $x$ : $3x+1=25$ .
- A.8
- B.25
- C.9
- D.1
- E.7
4.
What is $\operatorname{lcm}(14,66)$ ?
- A.462
- B.476
- C.924
- D.396
- E.2
5.
Arithmetic sequence: first term $4$ , common difference $4$ . Sum of first $12$ terms?
- A.312
- B.308
- C.324
- D.48
- E.z4
6.
An item costs $65$ . It is discounted $20\%$ , then $5\%$ tax is applied to the discounted price. How much is paid?
- A.68
- B.56.60
- C.54.60
- D.53.10
- E.52
7.
Positive integer solutions to $x_1+\cdots+x_{5}=14$ ?
- A.710
- B.3060
- C.2002
- D.716
- E.715
8.
What is $\operatorname{lcm}(8,24)$ ?
- A.0
- B.8
- C.24
- D.32
- E.192
9.
How many positive integers $n\le 100$ satisfy $n\equiv 1\pmod{7}$ ?
- A.17
- B.16
- C.14
- D.15
- E.alt4
10.
How many positive integers $n\le 100$ satisfy $n\equiv 3\pmod{7}$ ?
- A.14
- B.16
- C.15
- D.17
- E.13

Answer key · worked solutions

1. E. 60.80
Multiply by $(1-d)$ . $76(1-20/100)$ . $60.80$ .
2. D. 4
Exactly three divisors $\iff k=p^2$ . Primes $p\le\sqrt{75}$ . $4$ .
3. A. 8
Isolate $x$ . $3x=25-1$ . $8$ .
4. A. 462
$\operatorname{lcm}=ab/\gcd$ . $\gcd=2$ . $462$ .
5. A. 312
$S_n=\frac n2(2a+(n-1)d)$ . Plug values. $312$ .
6. C. 54.60
Discount first, then tax. $65\cdot(1-20/100)\cdot(1+5/100)$ . $54.60$ .
7. E. 715
$\binom{N-1}{k-1}$ . $\binom{13}{4}$ . $715$ .
8. C. 24
$\operatorname{lcm}=ab/\gcd$ . $\gcd=8$ . $24$ .
9. D. 15
Count an arithmetic progression. First 1, common difference 7. $15$ .
10. A. 14
Arithmetic progression. First 3, step 7. $14$ .

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

Free AMC Math Worksheet Generator — Mathbound