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Grade 6

20260723.Thu first session - mostly quiz

Patterns/Sequences

20260827.Thu basic hw
20260829.Sat
Score Pct 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
26.5/36 73.6 c a a a cb c c c d c a d c a c a c d b c c b c a a a a ad a a a a a a a a
20260831.Mon Patterns/Sequences - matchstick rearrangement problems
20260910.Thu Advanced patterns hw
20260914.Mon Advanced patterns part 1
Score Pct 01 02 03 04 05 06 07
6/7 85.7 c a b a b a b
20260914.Mon Advanced patterns part 2
Score Pct 8 9 10 11 12 13 14 15 16 17 18 19 20
10.75/13 82.7 b c b Sat Thu Mon a b b c b ab thu not oct Mon c
20260910.Thu Advanced patterns hw
20260918.Fri More patterns part 1
Score Pct 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
a b c d a b
11.25/25 45.0 70 56+984=1040 654+104=758 285661-5=2856 376+428=804 9 0 1156235 65115321 666198 3 not possible7 41130(1,0), (4,0), (7,0), (2,5), (5,5), (8,5) 4 (1,0) 1087 397 ?17, 54, 91 not possible23 ?Composite None 73931 579 37 58
20260918.Fri More calendar patterns part 2
Score Pct 22 23 24 25 26
0.0/5 0.0 WednesdayTuesday Thursday ab da ?2




Algebra and Number Theory

1) Divisibility Rules (2, 3, 4, 5, 6, 8, 9, 11)

20260908.Tue hw answers
202609XX
Score Pct 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
a b c d 111 221 1111 100001 107107 1234554321 1 2 3 4 1 2 3 4 5 6 1 2 3 4
19.5/38 51.3 7 (5,2)7,0), (2,5) (5,0), (0,5), (9,5) (2,0), (7,4)No solution 3 13.17 11 11 911.9737 311.112232211 c 120 No 8 3 4 3 3, 6, 9 0, 5 10 to 9 31 to 9 20 to 9 1 to 9 3 3 8 4 c a c b 529 is a multiple of 3c a d 5 1230432 2232, 2532, 2832, 2136, 2436, 2736 1
202609XX
Score Pct 1 2 3
1 2 3 4 1 2 3 4 1 2 3 4
3.25/12 27.1 ?No 262,161 196,621 idk589,863 Lari 1 74 2 4 ?13 tetri ?33 tetri ?21 ?23
202609XX
Score Pct 4 5 6 7 8 9 10 11 12 13
1 2
7.5/11 68.2 a b c 11 with Alx14 with Alx42 25 18, 38 62 301 5


2) Greatest Common Divisor (GCD) & Least Common Multiple (LCM)

20260921.Mon hw answers
20260921.Mon
Score Pct 1 2 3 4 5 W1 W2 W3 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10
1 2 3 4 1 2 3 4 1 2 34,48 120,150 50,540 14,20,48 36,54,72 88,240,300 8,28 64,96 240,360 480,540 48,72 48,72,80 150,300,600 3 5 9 18
29.0/39 74.4 6 48120 1680840 3090 60 120 73828 6500 135 98 2 30 90 2 18 4 56 192 720 4320 144 720 450600 48 2 9 Let d = gcd(n, n+1), so d divides (n+1) - n = 1, hence d = 1 143 144 100 75 1 gcd(a, a+2) is 1 or 2, it equals 2 if and only if a is even (16,135) (8,270) (4,540), (2,1080)2, 180), (36, 60) 1,3 1,5 1,93,9 1,2,3,186,9,18 7
20260921.Mon Revised
Score Pct 1 2 3 4 5 W1 W2 W3 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10
1 2 3 4 1 2 3 4 1 2 34,48 120,150 50,540 14,20,48 36,54,72 88,240,300 8,28 64,96 240,360 480,540 48,72 48,72,80 150,300,600 3 5 9 18
35.25/39 90.4 6 120 840 90 60 120 728 6500 135 98 2 30 90 2 18 4 56 192 720 4320 144 720 600 48 2 9 Let d = gcd(n, n+1), so d divides (n+1) - n = 1, hence d = 1 143 144 100 75 1 gcd(a, a+2) is 1 or 2, it equals 2 if and only if a is even (16,135) (8,270) (4,540), (2,1080)2, 180), (36, 60) 1,3 1,5 1,93,9 1,2,3,186,9,18 7

3) Powers of Numbers & Exponent Rules

20260918.Fri hw answers
20260919.Sat
Score Pct 1 2 3 4 5 6 7 8
88 96 124 144 460 588 1140 2400 24 77 128 4128 28 99 200 532 12 13 50 120 15 19 27 48
25.75/27 95.4 2^3 x 11 = 2^5 x 3 = 2^2 x 31 = 2^4 x 3^2 = 2^2 x 5 x 23 = 2^3 x 712 x 3 x 7^2 = 2^2 x 3 x 5 x 19 = 2^5 x 3 x 5^2 2 7 2 2 7 11 5 19 2 1 2 3 16 4 2 4 10 9 2

20260921.Mon
Score Pct 1 2 3 4 5 6 7 8 9
180 504 1080 2520
9.5/12 79.2 2^2 x 3^2 x 5 2^3 x 3^2 x 7 2^3 x 3^3 x 5 2^3 x 3^2 x 5 x 7 ?5 2^{60} 3^{40} 2 5 9 3 72 ?48

4) Algebraic Equations & Systems of Variables (Most important)

20260925.Fri hw
20260929 operation order
Score Pct 1 2 3 4 5 6 7 8 9 10
7.5/10 75.0 27 400 53 115 8475 30 56 1 876 104

20260929 basic equations
Score Pct 1 2 3 4 5 6 7 8 9 10
8.75/10 87.5 3549 7 3 9 14 55 40 72 8 6

20260929 equations with brackets
Score Pct 1 2 3 4
a b c d e f g h a b c d e f a b c d e a b c d e
20.25/24 84.4 2 2 14 710 4 2 2-2 -32 2 1 2 1 4 5 2 3 5 3 1 2 1 3 2 0

20260929 challenge questions
Score Pct 1 2 3 4 5
2.5/5 50.0 2 10/3 ?53/7 ?37/9 2.5

20261002.Fri hw
20261002.Fri practice systems of equations
Score Pct 1 2 3 4 5 6 7 8
8/8 100.0 x=5, y=1 x=1, y=3 infinitely many solutions (y = 3x - 1) no solution x=3, y=-1/6 x=3, y=1 x=3, y=4 x=7, y=5

20261002.Fri word problems
Score Pct 1 2 3 4 5
3.75/5 75.0 jeans: $20, blouses: $10 30 two-point questions, 10 four-point questions 21 child tickets, 67 adult tickets width = 22 cm, length = 66 cm11 cm, length = 33 cm 36 sundaes

20261002.Fri 3-variable systems & visual puzzles
Score Pct C1 C2 C3 C4
1.5/4 37.5 ?x=1, y=2, z=3 x=1, y=2, z=3 85599 6 touchdowns, 5 PATs, 3 field goals

5) Working with Fractions & Ratios (4 involved)

20261013.Tue hw
20261016.Fri basic operations & comparison
Score Pct 1 2 3 4
a b a b a b c d
6.5/9 72.2 4/11 < 6/11 11/15 < 27/31 7/8 127/130 1/24 < 1/4 = 3/12 < 5/12 < 11/24 < 1/2 = 3/6 = 12/24 < 15/24 < 2/3 = 16/24 < 22/24 5 1/1231/6 4 8/15 15 10/3320 2

20261016.Fri multi-step multi-operation expressions
Score Pct 5 6 7
a b c a b a b
4.5/7 64.3 845 11/12 198 2/5147/15 1408/770 293142/5 1 8/5 6/5

20261016.Fri decimals & exponents
Score Pct 8 9 10 11 12 13 14 15 16 17 18 19 20
a b c d a b c d a b c d
9.5/22 43.2 0.6 0.875 0.04 0.2 3/8 23/100 29/25 25/8 2 0.000001 500 0.3 800,000100000 4 with dad 1/4 with dad 1/2 with dad -16/9 with dad 3 with dad 30 with dad5 40.94 with dad80 5 with dad with dad101/84

20261016.Fri word problems, speeds & rates
Score Pct W1 W2 W3 W4
a b
1.25/5 25.0 8/84 < 9/84First tourist walked faster by 7/6 km/h 12/40 < 25/40 > 2/40Dato 3.5 tons = 1 hectare 1 ton = 2/7 hectares The bus is the slowest and takes 2.058888888...(infinite 8s)Car, 1.5 hours

20261016.Fri algebraic integer variable analysis
Score Pct A1 A2 A3 A4
0.25/4 6.2 17/24, 18/24, 19/24, 20/24 8, 9, 10, 11, 12, 137, 8, 9, 10, 11, 12, 13 6, 7, 8, 9, 10, 11 3027

6) Base-10 Structure (1, 10, 100, 1000) (4 involved)

20261006.Tue hw
20261006.Tue two-digit problems
Score Pct 1 2 3 4 5 6 7 8 9 10 11 12 13
8.0/13 61.5 57 83 82 ?20 6859 ?36 18 97 58 52 (c) 72 1827 39

20261006.Tue three-digit & page numbering problems
Score Pct 14 15 16 17 18
0.0/5 0.0 (a) 342 (d) 7, 8b) 11, 12 ?357 ?258 624835

20261006.Tue digits appended to left or right
Score Pct A1 A2 A3
0.5/3 16.7 (e) 100x+11 10x + 7, and it is larger by 9x + 6 ?375

7) Averages & Statistical Mean


Rates and Kinematics

8) Work, Time & Capacity (Working Hours)

9) Velocity & Motion Kinematics

10) Clock Angles & Time Calculation


Combinatorics and Set theory

11) Bipartite Matching (Match People with Things) (Most simple)

12) Venn Diagrams & Overlapping Sets (Really important)

13) Fundamental Counting Principle & Combinatorics

14) Logic of Truth-Telling & Lying Games (Simple) (Can be combined with 11)

15) Pigeonhole Principle & Worst-Case Scenarios


Game Theory and Tournaments

16) Tournament Structure & Results

17) Balance Scale Logic & Weighings

18) Combinatorial Strategy Games (Hard)


Geometry

19) Perimeter & Planar Dissections (Hard)

20) 2D Geometry & Area (Hard)

21) 3D Geometry & Surface Area


Bonus

22) Match Sticks

23) Constructions




Grade 7

Algebra

1) Variables & Expressions

2) Natural Powers & Prime Factorization (including GCD & LCM, Total number of h3isors of a number)

3) Divisibility Rules & Properties (including last-digit arithmetic, modular arithmetic/arithmetic of remainders, number formulas e.g., odd n = 2k + 1, Euclidean algorithm)

4) Custom Operations (New/binary operators and custom operations)

5) Set Theory (subsets, equality of two sets, empty sets; operations: union, intersection, set difference, symmetric difference)

6) Number Line & Decimals (The number line, negative numbers, periodic and non-periodic decimals, converting repeating decimals into fractions)

7) Absolute Value (Absolute value (module) of a number)

8) Percentages

9) Proportions (directly proportional and inversely proportional quantities)

10) Averages & Mixture Problems (Solving problems using arithmetic mean)

11) Distributive Property (expanding/opening brackets)

12) Linear Equations

13) Exponent Rules (Natural exponents and properties of powers with natural exponents)

14) Monomials (Monomials, operations on monomials: multiplication, exponentiation/raising to a power, degree of a standard monomial)

15) Polynomials (Polynomials, standard polynomials, degree of a polynomial, operations on polynomials: addition, subtraction, multiplying a monomial by a polynomial, multiplying polynomials)

16) Algebraic Identities (square of sum and difference of two expressions, square of sum of three or more expressions, sum and difference of cubes, sum and difference of $n$-th powers, cube of sum and difference of two expressions)

17) Quadratic Trinomials (completing the square, finding maximum and minimum values)

18) Identities (Proofs of algebraic identities)

19) Polynomial Division

20) Factoring Polynomials factoring out common factors, grouping method, using algebraic identities, a^n - b^n, a^n + b^n, factoring trinomials where a = 1 with rational roots)

21) Cartesian Coordinate System (The coordinate plane, coordinates of a point)

22) Functions & Graphs (Definition of a function, methods of representing functions, function graphs)

23) Linear Functions (position of linear function graphs relative to coordinate axes and each other, parallel and perpendicular lines).

24) Graphical Solution of Equations

25) Linear Equations in Two Variables

26) Systems of Linear Equations (solving systems using substitution and elimination/addition methods).

27) Reducible Systems

28) System Applications (Solving word problems by constructing systems of linear equations)



Geometry

1) Foundations of Geometry: Introduction to geometry (primitive concepts, axioms), relative positions of points and lines, relative positions of lines.

2) Line Segments: Segments, segment construction axiom, segment measurement axiom.

3) Half-Planes: Concept of a half-plane.

4) Rays: Concept of a ray.

5) Angles: Angle measurement, angle measurement axiom.

6) Angle Bisectors

7) Supplementary & Vertical Angles

8) Perpendicular Lines: Angle between two lines, perpendicularity of lines

9) Congruence: Congruence/equality of geometric figures.

10) Parallel Lines: Criteria for parallel lines, properties of parallel lines

11) Triangles: General concepts of triangles

12) Triangle Angle Sum: Sum of angles in a triangle

13) Triangle Cevians: Altitudes, bisectors, and medians of a triangle

14) Triangle Congruence Rules (SAS & ASA & SSS)

15) Isosceles Triangles

16) Perpendicular Bisectors

17) Exterior Angles

18) Triangle Inequality

19) Distance & Right Triangles: Distance from a point to a line, distance between two parallel lines, right triangles, criteria for right triangle congruence.

20) Properties of Right Triangles: Property of a 30 angle's opposite side, property of the median to the hypotenuse, angle bisector properties, angles formed between the altitude, median, and bisector drawn from the right-angle vertex).

21) Circles & Lines: Circles (radius, diameter, chord, tangent line)

22) Perpendicular Diameter Property

23) Intersections of Circles

24) Inscribed & Circumscribed Triangles

25) Arcs & Central Angles

26) Inscribed Angles

27) Intersecting Chords & Secants