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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.
Arithmetic sequence: first term $4$ , common difference $2$ . Sum of first $10$ terms?
- A.140
- B.40
- C.22
- D.130
- E.128
2.
Positive integer solutions to $x_1+\cdots+x_{6}=17$ ?
- A.12376
- B.4369
- C.4368
- D.4362
- E.26334
3.
Lattice paths $(0,0)\to(9,9)$ with steps $(1,0),(0,1)$ avoiding $(7,7)$ . How many?
- A.48620
- B.20592
- C.28064
- D.28028
- E.28018
4.
What is $\operatorname{lcm}(21,33)$ ?
- A.693
- B.3
- C.252
- D.231
- E.198
5.
An item costs $52$ . After a $10\%$ discount (no tax), how much is paid?
- A.47.80
- B.5
- C.46.80
- D.42
- E.52
6.
A committee of $2$ is chosen from $15$ people. How many committees?
- A.30
- B.105
- C.120
- D.15
- E.91
7.
Lattice points strictly inside the right triangle with vertices $(0,0)$ , $(12,0)$ , $(0,11)$ ?
- A.55
- B.54
- C.56
- D.23
- E.66
8.
An item costs $50$ . It is discounted $25\%$ , then $10\%$ tax is applied to the discounted price. How much is paid?
- A.55
- B.43.25
- C.41.25
- D.39.75
- E.38
9.
How many involutions (bijections $f$ with $f\circ f=\mathrm{id}$ ) exist on a set of $9$ elements?
- A.2611
- B.2882
- C.2620
- D.512
- E.2629
10.
Positive integer solutions to $x_1+\cdots+x_{5}=13$ ?
- A.496
- B.495
- C.490
- D.2380
- E.1287

Answer key · worked solutions

1. D. 130
$S_n=\frac n2(2a+(n-1)d)$ . Plug values. $130$ .
2. C. 4368
$\binom{N-1}{k-1}$ . $\binom{16}{5}$ . $4368$ .
3. D. 28028
$\binom{2n}{n}$ minus paths through the obstacle. Subtract product of binomials. $28028$ .
4. D. 231
$\operatorname{lcm}(a,b)=ab/\gcd(a,b)$ . $\gcd=3$ . $231$ .
5. C. 46.80
Multiply by $(1-d)$ . $52(1-10/100)$ . $46.80$ .
6. B. 105
$\binom{m}{k}$ . $\binom{15}{2}$ . $105$ .
7. A. 55
$\frac{(A-1)(B-1)}{2}$ for this triangle. Formula. $55$ .
8. C. 41.25
Discount first, then tax. $50\cdot(1-25/100)\cdot(1+10/100)$ . $41.25$ .
9. C. 2620
$I_n=I_{n-1}+(n-1)I_{n-2}$ — not a $4$ -element listing drill. Compute the recurrence up to $n=9$ . $2620$ .
10. B. 495
$\binom{N-1}{k-1}$ . $\binom{12}{4}$ . $495$ .

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