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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 $6$ . Sum of first $15$ terms?
- A.690
- B.684
- C.705
- D.60
- E.88
2.
Lattice points strictly inside the right triangle with vertices $(0,0)$ , $(14,0)$ , $(0,5)$ ?
- A.35
- B.26
- C.25
- D.27
- E.19
3.
Triangle $ABC$ has side lengths $AB=13$ , $BC=14$ , and $CA=15$ . Let $r$ be the inradius of $\triangle ABC$ . What is $r^{2}$ ?
- A.12
- B.14
- C.16
- D.18
- E.20
4.
An item costs $50$ . It is discounted $25\%$ , then $8\%$ tax is applied to the discounted price. How much is paid?
- A.42.50
- B.40.50
- C.39.00
- D.38
- E.54
5.
What is the maximum product of positive integers that sum to $36$ ?
- A.262144
- B.531439
- C.531441
- D.531444
- E.531442
6.
If $r$ and $s$ are roots of $x^2+7x+8=0$ , find $r^3+s^3$ (without solving).
- A.182
- B.56
- C.343
- D.175
- E.167
7.
What is the maximum product of positive integers that sum to $30$ ?
- A.59047
- B.59049
- C.59052
- D.59050
- E.32768
8.
Positive integer solutions to $x_1+\cdots+x_{4}=20$ ?
- A.965
- B.1771
- C.4845
- D.970
- E.969
9.
Solve for $x$ : $3x+8=23$ .
- A.5
- B.23
- C.6
- D.8
- E.4
10.
Solve for $x$ : $3x+7=22$ .
- A.5
- B.22
- C.6
- D.7
- E.4

Answer key · worked solutions

1. A. 690
$S_n=\frac n2(2a+(n-1)d)$ . Plug values. $690$ .
2. B. 26
$\frac{(A-1)(B-1)}{2}$ for this triangle. Formula. $26$ .
3. C. 16
Heron: area $K=84$ ; semiperimeter $s=21$ ; $r=K/s=4$ . Compute $K=\sqrt{21\cdot8\cdot7\cdot6}=84$ first. $r^{2}=16$ .
4. B. 40.50
Discount first, then tax. $50\cdot(1-25/100)\cdot(1+8/100)$ . $40.50$ .
5. C. 531441
Prefer parts equal to $3$ (use $2$ s when needed; avoid $1$ s). Partition $36$ optimally. $531441$ .
6. D. 175
$r^3+s^3=(r+s)((r+s)^2-3rs)$ . Vieta: $r+s=7$ , $rs=8$ . $175$ .
7. B. 59049
Prefer parts equal to $3$ (use $2$ s when needed; avoid $1$ s). Partition $30$ optimally. $59049$ .
8. E. 969
$\binom{N-1}{k-1}$ . $\binom{19}{3}$ . $969$ .
9. A. 5
Isolate $x$ . $3x=23-8$ . $5$ .
10. A. 5
Isolate $x$ . $3x=22-7$ . $5$ .

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Free AMC Math Worksheet Generator — Mathbound