AMC 8 Readiness Comprehensive Model Check (16 Problems)
Covers: Counting/Probability, Number Theory, Geometry, Ratios/Percent/Average
Time: 35 50 minutes No calculator Show your first step for each problem
R1) Impurities A 100-unit package is 12% impurities. You remove only impurities. After removal,
impurities are 8%. What fraction of the original impurities was removed?
R2) Class Average
A class has 19 tests with an average score of 80. After adding one more test,
the average becomes 81. What is the score of the new test?
R3) Mix & Replace
A 10-liter drink is 40% juice. Remove 2 liters of the drink and replace with
water. What is the new percentage of juice in the mixture?
R4) Proportional Recipe
Sugar : Flour = 2 : 5. If a recipe originally uses 80 g of flour, how many
grams of sugar are needed after adding 30 g more flour while keeping the same ratio? How many
additional grams of sugar must be added?
C1) How many 3-digit numbers have no repeated digits?
C2) A fair coin is flipped 4 times. What is the probability of getting at least 3 heads?
C3) How many distinct permutations can be made from the letters of the word LEVEL?
C4) On a 3×3 grid, you move only right or up from the southwest corner to the northeast corner. How
many shortest paths are there?
AMC 8 Readiness Comprehensive Model Check (cont.)
N1) What is the remainder when 2025 is divided by 9?
N2) Two positive integers have GCD 6 and LCM 60. If one of the integers is 12, what is the other?
N3) Find the smallest positive integer n such that n 3 (mod 5) and n 1 (mod 4).
N4) What is the units digit of 7^2025?
G1) The angles of a triangle are in the ratio 2 : 3 : 4. What is the largest angle (in degrees)?
G2) A right triangle has legs 6 and 8. What is its area?
G3) A square has side length 10. A smaller square is formed by joining the midpoints of the sides of
the original square. What is the area of the smaller square?
G4) A rectangle has opposite vertices at (0, 0) and (6, 4). What is the length of its diagonal?
Answer Key AMC 8 Readiness Comprehensive Model Check
R1) 25/69
R2) 100
R3) 26 2/3%
R4) New flour = 110 g, sugar must be 44 g; additional sugar = 12 g
C1) 648
C2) 5/16
C3) 30
C4) 20
N1) 0
N2) 30
N3) 13
N4) 7
G1) 80°
G2) 24
G3) 50
G4) 2 13
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