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Mini mock 1

15 problems matching a real contest's position mix, 45 minutes

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Mini mock 1AMC 10 Step by Step

Name: Date: September 13, 2026

15 problems · 45 minutes · 6 / 1.5 / 0

1.2019 AMC 10A #2
What is the hundreds digit of $(20!-15!)?$
1. A)
  $0$
2. B)
  $1$
3. C)
  $2$
4. D)
  $4$
5. E)
  $5$
2.2014 AMC 10A #5
On an algebra quiz, $10\%$ of the students scored $70$ points, $35\%$ scored $80$ points, $30\%$ scored $90$ points, and the rest scored $100$ points. What is the difference between the mean and median score of the students' scores on this quiz?
1. A)
  $1$
2. B)
  $2$
3. C)
  $3$
4. D)
  $4$
5. E)
  $5$
3.2021 AMC Fall 10B #5
Let $n=8^{2022}$ . Which of the following is equal to $\frac{n}{4}?$
1. A)
  $4^{1010}$
2. B)
  $2^{2022}$
3. C)
  $8^{2018}$
4. D)
  $4^{3031}$
5. E)
  $4^{3032}$
4.2013 AMC 10A #8
What is the value of $\frac{2^{2014}+2^{2012}}{2^{2014}-2^{2012}} ?$
1. A)
  $-1$
2. B)
  $1$
3. C)
  $\frac{5}{3}$
4. D)
  $2013$
5. E)
  $2^{4024}$
5.2021 AMC 10B #8
Mr. Zhou places all the integers from $1$ to $225$ into a $15$ by $15$ grid. He places $1$ in the middle square (eighth row and eighth column) and places other numbers one by one clockwise, as shown in part in the diagram below. What is the sum of the greatest number and the least number that appear in the second row from the top?
1. A)
  $367$
2. B)
  $368$
3. C)
  $369$
4. D)
  $379$
5. E)
  $380$
6.2020 AMC 10A #10
Seven cubes, whose volumes are $1$ , $8$ , $27$ , $64$ , $125$ , $216$ , and $343$ cubic units, are stacked vertically to form a tower in which the volumes of the cubes decrease from bottom to top. Except for the bottom cube, the bottom face of each cube lies completely on top of the cube below it. What is the total surface area of the tower (including the bottom) in square units?
1. A)
  $644$
2. B)
  $658$
3. C)
  $664$
4. D)
  $720$
5. E)
  $749$
7.2018 AMC 10A #12
How many ordered pairs of real numbers $(x,y)$ satisfy the following system of equations? \begin{align} x+3y&=3 \\ \big||x|-|y|\big|&=1 \end{align}
1. A)
  $1$
2. B)
  $2$
3. C)
  $3$
4. D)
  $4$
5. E)
  $8$
8.2011 AMC 10A #13
How many even integers are there between 200 and 700 whose digits are all different and come from the set {1, 2, 5, 7, 8, 9}?
1. A)
  $12$
2. B)
  $20$
3. C)
  $72$
4. D)
  $120$
5. E)
  $200$
9.2025 AMC 10A #15
In the figure below, $ABEF$ is a rectangle, $\overline{AD}\perp\overline{DE}$ , $AF=7$ , $AB=1$ , and $AD=5$ . What is the area of $\triangle ABC$ ?
1. A)
  $\frac{3}{8}$
2. B)
  $\frac{4}{9}$
3. C)
  $\frac{1}{8}\sqrt{13}$
4. D)
  $\frac{7}{15}$
5. E)
  $\frac{1}{8}\sqrt{15}$
10.2014 AMC 10B #17
What is the greatest power of $2$ that is a factor of $10^{1002} - 4^{501}$ ?
1. A)
  $2^{1002}$
2. B)
  $2^{1003}$
3. C)
  $2^{1004}$
4. D)
  $2^{1005}$
5. E)
  $2^{1006}$
11.2015 AMC 10A #17
A line that passes through the origin intersects both the line $x=1$ and the line $y=1+\frac{\sqrt{3}}{3}x$ . The three lines create an equilateral triangle. What is the perimeter of the triangle?
1. A)
  $2\sqrt{6}$
2. B)
  $2+2\sqrt{3}$
3. C)
  $6$
4. D)
  $3+2\sqrt{3}$
5. E)
  $6+\frac{\sqrt{3}}{3}$
12.2016 AMC 10B #17
All the numbers $2, 3, 4, 5, 6, 7$ are assigned to the six faces of a cube, one number to each face. For each of the eight vertices of the cube, a product of three numbers is computed, where the three numbers are the numbers assigned to the three faces that include that vertex. What is the greatest possible value of the sum of these eight products?
1. A)
  $312$
2. B)
  $343$
3. C)
  $625$
4. D)
  $729$
5. E)
  $1680$
13.2011 AMC 10A #20
Two points on the circumference of a circle of radius $r$ are selected independently and at random. From each point a chord of length $r$ is drawn in a clockwise direction. What is the probability that the two chords intersect?
1. A)
  $\frac{1}{6}$
2. B)
  $\frac{1}{5}$
3. C)
  $\frac{1}{4}$
4. D)
  $\frac{1}{3}$
5. E)
  $\frac{1}{2}$
14.2014 AMC 10A #22
In rectangle $ABCD$ , $AB=20$ and $BC=10$ . Let $E$ be a point on $\overline{CD}$ such that $\angle CBE=15^\circ$ . What is $AE$ ?
1. A)
  $\dfrac{20\sqrt3}3$
2. B)
  $10\sqrt3$
3. C)
  $18$
4. D)
  $11\sqrt3$
5. E)
  $20$
15.2014 AMC 10B #25
In a small pond there are eleven lily pads in a row labeled $0$ through $10$ . A frog is sitting on pad $1$ . When the frog is on pad $N$ , $0<N<10$ , it will jump to pad $N-1$ with probability $\frac{N}{10}$ and to pad $N+1$ with probability $1-\frac{N}{10}$ . Each jump is independent of the previous jumps. If the frog reaches pad $0$ it will be eaten by a patiently waiting snake. If the frog reaches pad $10$ it will exit the pond, never to return. What is the probability that the frog will escape without being eaten by the snake?
1. A)
  $\frac{32}{79}$
2. B)
  $\frac{161}{384}$
3. C)
  $\frac{63}{146}$
4. D)
  $\frac{7}{16}$
5. E)
  $\frac{1}{2}$