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.
Lattice points strictly inside the triangle with vertices $(0,0)$ , $(12,0)$ , $(0,9)$ ?
- A.44
- B.48
- C.54
- D.40
- E.61
2.
An item costs $45$ . It is discounted $10\%$ , then $8\%$ tax is applied to the discounted price. How much is paid?
- A.49
- B.45.74
- C.43.74
- D.42.24
- E.41
3.
How many positive divisors does $42$ have?
- A.11
- B.9
- C.10
- D.7
- E.8
4.
How many positive integers $n\le 100$ are divisible by $7$ ?
- A.14
- B.12
- C.15
- D.93
- E.13
5.
If $r$ and $s$ are roots of $x^2+8x+10=0$ , find $r^3+s^3$ (without solving).
- A.272
- B.262
- C.280
- D.80
- E.512
6.
What is $\operatorname{lcm}(27,57)$ ?
- A.3
- B.540
- C.513
- D.456
- E.1539
7.
Positive integer solutions to $x_1+\cdots+x_{4}=13$ ?
- A.221
- B.220
- C.216
- D.560
- E.715
8.
Lattice paths $(0,0)\to(8,8)$ with steps $(1,0),(0,1)$ avoiding $(4,5)$ . How many?
- A.8460
- B.8450
- C.12870
- D.4410
- E.8530
9.
Solve for $x$ : $3x+2=26$ .
- A.8
- B.26
- C.9
- D.2
- E.7
10.
Positive integer solutions to $x_1+\cdots+x_{4}=23$ with each $x_i\le 8$ ?
- A.1540
- B.205
- C.199
- D.204
- E.2600

Answer key · worked solutions

1. A. 44
$\frac{(a-1)(b-1)}{2}$ for this right triangle. Formula. $44$ .
2. C. 43.74
Discount first, then tax. $45\cdot(1-10/100)\cdot(1+8/100)$ . $43.74$ .
3. E. 8
Factor and use $\prod(e_i+1)$ . Count divisors of $42$ . $8$ .
4. A. 14
Count multiples. $\lfloor 100/7\rfloor$ . $14$ .
5. A. 272
$r^3+s^3=(r+s)((r+s)^2-3rs)$ . Vieta: $r+s=8$ , $rs=10$ . $272$ .
6. C. 513
$\operatorname{lcm}(a,b)=ab/\gcd(a,b)$ . $\gcd=3$ . $513$ .
7. B. 220
$\binom{N-1}{k-1}$ . $\binom{12}{3}$ . $220$ .
8. A. 8460
$\binom{2n}{n}$ minus paths through the obstacle. Subtract product of binomials. $8460$ .
9. A. 8
Isolate $x$ . $3x=26-2$ . $8$ .
10. D. 204
Inclusion-exclusion after $y_i=x_i-1$ . Upper bound 8. $204$ .

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

Free AMC Math Worksheet Generator — Mathbound