Continental Math League (CML) Advanced Practice Questions
Grades 4, 5 & 6 – Elementary School
100 Advanced CML Practice Problems – Prepare for Continental Math League elementary school competitions with challenging problems covering algebra, geometry, probability, number theory, and more!
π What’s Included:
- β 100 Advanced CML-style questions for grades 4-6
- β Algebra, Geometry, Probability and more
- β Downloadable PDF for offline practice
- β Complete answer key included
- β Elementary school level – Perfect for competitive math prep
π CML Advanced Practice Questions (1β50)
These advanced questions cover topics for grades 4-6. Take your time and show all your work!
π’ Algebra & Equations
1) The product of two consecutive odd integers is 483. What is the sum of these two integers?
2) If 3x – 7 = 2x + 11, what is the value of x?
3) Solve for y: 5(y – 3) = 2(y + 6)
4) If 3Λ£ = 27 and 2ΚΈ = 32, what is the value of x + y?
5) If x + y = 12 and xy = 32, what is the value of xΒ² + yΒ²?
6) What is the value of x if 2xΒ² – 8 = 10?
7) If nΒ² + 5n – 36 = 0, what is the positive value of n?
π’ Number Theory & Patterns
8) How many positive divisors does 1800 have?
9) What is the least common multiple of 24, 36, and 40?
10) How many prime numbers are there between 40 and 60?
11) What is the greatest common factor of 126 and 180?
12) The sum of three consecutive multiples of 7 is 168. What is the smallest of these three numbers?
13) Find the units digit of 7Β²β°Β²β΅.
14) What is the sum of all positive even integers less than 50?
15) The average of five consecutive integers is 23. What is the largest of these integers?
16) How many positive integers less than 100 are divisible by both 6 and 8?
π Sequences & Series
17) In a sequence, each term after the first two is the sum of the previous two terms. If the 4th term is 17 and the 6th term is 44, what is the 3rd term?
18) The sum of the first n positive integers is 210. What is n?
19) In an arithmetic sequence, the first term is 5 and the common difference is 3. What is the 20th term?
20) What is the sum of the first 10 terms of the sequence: 2, 5, 8, 11, …?
21) A sequence follows the pattern: 3, 9, 27, 81, … What is the 8th term?
π Fractions, Decimals & Percents
22) What is 3/8 of 120?
23) Express 0.375 as a fraction in lowest terms.
24) What percent of 80 is 24?
25) A number is increased by 20%, then decreased by 20%. What is the overall percent change?
26) If 35% of a number is 70, what is the number?
27) What is the decimal equivalent of 7/16?
28) Simplify: (2/3 + 1/4) Γ· (1/2 – 1/6)
π Geometry – Perimeter & Area
29) A rectangle has a perimeter of 84 cm. If the length is 3 times the width, what is the area of the rectangle in square centimeters?
30) A triangle has sides of length 13, 14, and 15. What is the area of this triangle?
31) An equilateral triangle has a perimeter of 48 cm. What is its area in square centimeters? (Round to the nearest whole number)
32) A regular hexagon has a perimeter of 54 cm. What is the length of one side?
33) The diagonal of a rectangle is 25 cm and one side is 15 cm. What is the perimeter of the rectangle?
34) A trapezoid has parallel sides of lengths 8 and 12, and a height of 5. What is its area?
35) A parallelogram has a base of 14 cm and a height of 9 cm. What is its area?
β Geometry – Circles
36) A circle is inscribed in a square with side length 16. What is the area of the region inside the square but outside the circle? (Express in terms of Ο)
37) Two circles have radii of 8 and 6. What is the difference between their areas? (Express in terms of Ο)
38) A circle has a circumference of 62.8 cm. What is its radius? (Use Ο = 3.14)
39) A square is inscribed in a circle with radius 10. What is the area of the square?
40) What is the area of a sector of a circle with radius 6 and central angle 60Β°? (Express in terms of Ο)
π¦ Geometry – Solid Figures
41) A cylinder has a radius of 5 cm and a height of 12 cm. What is its volume in cubic centimeters? (Use Ο = 3.14)
42) A rectangular box has dimensions 4 by 6 by 8. What is its surface area?
43) A cube has a volume of 216 cubic cm. What is the length of one edge?
44) A sphere has a radius of 3 cm. What is its volume? (Use Ο = 3.14 and V = 4/3ΟrΒ³)
45) A rectangular box has integer dimensions. Its volume is 120 cubic units and its surface area is 184 square units. What is the sum of its three dimensions?
π° Word Problems – Money & Shopping
46) A store offers a 25% discount on an item, then adds 8% sales tax. If the final price is $40.50, what was the original price before discount and tax?
47) John has twice as many dimes as quarters. If he has $4.50 in total, how many dimes does he have?
48) A shirt costs $24 after a 20% discount. What was the original price?
49) Sarah bought 3 books at $8 each and 2 pens at $1.50 each. How much change did she receive from a $50 bill?
50) A store marks up an item by 40% and then offers a 25% discount. If the final price is $42, what was the original cost?
π― Ready for More Challenge?
Continue with Questions 51-100 covering Age & Time, Distance Rate & Time, Mixtures & Ratios, Probability, and more advanced topics!
π Continue to Part 2 (Q51-100) βπ Answer Key (Questions 1-50)
Check your answers below. Remember: showing your work is essential for full credit!
1) 44
2) 18
3) 9
4) 8
5) 80
6) 3
7) 4
8) 36
9) 360
10) 5
11) 18
12) 49
13) 7
14) 600
15) 25
16) 4
17) 10
18) 20
19) 62
20) 155
21) 6561
22) 45
23) 3/8
24) 30%
25) -4%
26) 200
27) 0.4375
28) 11/4 or 2.75
29) 243
30) 84
31) 111
32) 9
33) 70
34) 50
35) 126
36) 256 – 64Ο
37) 28Ο
38) 10
39) 200
40) 6Ο
41) 942
42) 208
43) 6
44) 113.04
45) 17
46) $50
47) 12
48) $30
49) $23
50) $40
π CML Competition Success Tips
- Master Fundamentals: Strong arithmetic, algebra and geometry skills are key
- Practice Multi-Step Problems: Break complex problems into manageable parts
- Time Management: CML contests are timed – practice under pressure
- Show All Work: Develop clear, logical solution strategies
- Learn from Mistakes: Review incorrect answers thoroughly
- Use Mental Math: Develop shortcuts for common calculations
π More CML Practice Resources
βΉοΈ About Continental Math League (CML) for Elementary School
The Continental Math League elementary division challenges students in grades 4-6 with advanced mathematical concepts. These competitions help students develop problem-solving skills in algebra, geometry, number theory, and more.
Success in CML competitions at this level requires mastery of fundamental concepts and the ability to apply them creatively to complex, multi-step problems. Regular practice with challenging questions builds the confidence and skills needed to excel.
π Ready to Excel in Advanced CML?
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