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Math worksheet generator

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Mathbound · Contest practice

Mixed topics worksheet

Mixed difficulty

Name

Date

1.
Arithmetic sequence: first term $3$ , common difference $5$ . Sum of first $10$ terms?
- A.265
- B.30
- C.48
- D.255
- E.250
2.
Arithmetic sequence: first term $4$ , common difference $7$ . Sum of first $15$ terms?
- A.810
- B.60
- C.102
- D.795
- E.788
3.
An item costs $60$ . It is discounted $15\%$ , then $5\%$ tax is applied to the discounted price. How much is paid?
- A.52.05
- B.51
- C.63
- D.55.55
- E.53.55
4.
Arithmetic sequence: first term $5$ , common difference $2$ . Sum of first $10$ terms?
- A.140
- B.138
- C.150
- D.50
- E.23
5.
A square has side length $12$ . What is its perimeter?
- A.48
- B.49
- C.144
- D.47
- E.24
6.
A square has side length $22$ . What is its perimeter?
- A.88
- B.89
- C.484
- D.87
- E.44
7.
How many positive integers $n\le 100$ are divisible by $4$ ?
- A.20
- B.26
- C.96
- D.24
- E.25
8.
How many positive divisors does $29$ have?
- A.2
- B.4
- C.3
- D.29
- E.1
9.
Lattice paths $(0,0)\to(10,10)$ with steps $(1,0),(0,1)$ avoiding $(5,5)$ . How many?
- A.184756
- B.63504
- C.121504
- D.121252
- E.121242
10.
An item costs $100$ . After a $25\%$ discount (no tax), how much is paid?
- A.78
- B.25
- C.75
- D.76.00
- E.100

Answer key · worked solutions

1. D. 255
$S_n=\frac n2(2a+(n-1)d)$ . Plug values. $255$ .
2. D. 795
$S_n=\frac n2(2a+(n-1)d)$ . Plug values. $795$ .
3. E. 53.55
Discount first, then tax. $60\cdot(1-15/100)\cdot(1+5/100)$ . $53.55$ .
4. A. 140
$S_n=\frac n2(2a+(n-1)d)$ . Plug values. $140$ .
5. A. 48
Perimeter $4s$ . $4\cdot12$ . $48$ .
6. A. 88
Perimeter $4s$ . $4\cdot22$ . $88$ .
7. E. 25
Count multiples. $\lfloor 100/4\rfloor$ . $25$ .
8. A. 2
Factor and use $\prod(e_i+1)$ . Count divisors of $29$ . $2$ .
9. D. 121252
$\binom{2n}{n}$ minus paths through the obstacle. Subtract product of binomials. $121252$ .
10. C. 75
Multiply by $(1-d)$ . $100(1-25/100)$ . $75$ .

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