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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)
  $\frac{1}{2}$

Mini mock 1 — answersAMC 10 Step by Step

Name: Date: September 13, 2026

Keep this page separate from the problems.

Answers

#	Answer	Topic and the idea it turns on
1	A	Divisibility & Factors — Both 15! and 20! contain the factors 2, 5, 10 and more, so each is a multiple of 1000; their difference ends in three zeros.
2	C	Statistics & Data — The cumulative percentages 10, 45, 75 show the middle student is in the 90 group, so the median is 90, while the weighted mean is 87.
3	E	Exponents, Logarithms & Radicals — Convert everything to base 2: 8^2022 = 2^6066, dividing by 4 gives 2^6064, and 6064/2 = 3032 turns it into a power of 4.
4	C	Exponents, Logarithms & Radicals — Factor 2^2012 out of the numerator and denominator; what remains is (4+1)/(4-1).
5	A	Paths & Grids — Odd squares sit at top-right corners: 169 ends the 13×13 block at row 2, so that row holds 157–169, then 170 and 210 at its ends.
6	B	Solid Geometry — Seen from above the tower shows exactly a 7-by-7 square of exposed top faces, and likewise from below; only the side faces need summing.
7	C	Absolute Value & Inequalities — On the line x = 3 - 3y the sign of x is fixed by y, so only three sign regions remain, each giving two linear equations.
8	A	Basic Counting — Hundreds digit is 2 or 5, units digit is 2 or 8, and hundreds digit 2 leaves only 8 for the units place.
9	A	Similar & Congruent Triangles — Draw AE: it is the hypotenuse of both right triangles ABE and ADE, so DE = 5 and triangles ABC and EDC are similar in ratio 1 : 5.
10	D	Divisibility & Factors — Pull out the common 2^1002, then find how many 2s divide 5^1002 - 1 by factoring it as (5^501 - 1)(5^501 + 1).
11	D	Coordinate Geometry — Slope sqrt(3)/3 means a 30-degree line, so the third line is its mirror image y = -x/sqrt(3); they meet x = 1 at points 1 + 2/sqrt(3) apart.
12	D	Algebraic Manipulation — Each vertex takes one face from each pair of opposite faces, so the eight products sum to (a+b)(c+d)(e+f); the pair sums total 27, so the max is 9^3.
13	D	Geometric Probability — A chord of length r spans 60 degrees; fix the first point, and the chords cross exactly when the second point lands within 60 degrees on either side.
14	E	Triangles: Area & Pythagorean — Reflect the 30-60-90 triangle to get tan 15 = 2 - sqrt 3; then CE = 20 - 10 sqrt 3, DE = 10 sqrt 3, and AE = 20.
15	C	Conditional Probability & States — Consecutive differences of the escape probabilities satisfy d_N = N/(10-N) d_{N-1}, so d_N = d_0 / C(9,N), and the differences sum to 1.