Abacus learning is one of the best ways to improve arithmetic skills and number fluency. Abacus math also helps develop an interest and passion in math for many students as their confidence and understanding grows from an early age. After all, most students prefer the subjects they perform well in!
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Practicing math offers students numerous benefits, including improved problem-solving, critical thinking, and logical reasoning skills.

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1. Pythagorean theorem: a² + b² = c²

2. Quadratic formula: x = (-b ± √(b² - 4ac)) / 2a

3. Distance formula: d = √((x₂ - x₁)² + (y₂ - y₁)²)

4. Slope-intercept form of a line: y = mx + b

5. Point-slope form of a line: y - y₁ = m(x - x₁)

6. Midpoint formula: ((x₁ + x₂)/2, (y₁ + y₂)/2)

7. Law of sines: a/sin A = b/sin B = c/sin C

8. Law of cosines: c² = a² + b² - 2ab cos C

9. Sum of angles in a triangle: A + B + C = 180°

10. Area of a triangle: A = (1/2)bh

11. Volume of a sphere: V = (4/3)πr³

12. Volume of a cylinder: V = πr²h

13. Volume of a cone: V = (1/3)πr²h

14. Surface area of a sphere: A = 4πr²

15. Surface area of a cylinder: A = 2πr² + 2πrh

16. Surface area of a cone: A = πr² + πrs, where s is the slant height

17. Binomial theorem: (a + b)ⁿ = Σ(n choose k)a^(n-k)b^k, where Σ is the sum from k=0 to n, and (n choose k) is the binomial coefficient

18. Fundamental theorem of calculus: ∫a^b f(x) dx = F(b) - F(a), where F is the antiderivative of f

19. Derivative of a constant: d/dx(c) = 0

20. Power rule for derivatives: d/dx(xⁿ) = nx^(n-1)

21. Product rule for derivatives: d/dx(fg) = f'g + fg'

22. Quotient rule for derivatives: d/dx(f/g) = (f'g - fg')/g²

23. Chain rule for derivatives: d/dx(f(g(x))) = f'(g(x))g'(x)

24. Mean value theorem: if f is continuous on [a,b] and differentiable on (a,b), then there exists c in (a,b) such that f'(c) = (f(b) - f(a))/(b-a)

25. Intermediate value theorem: if f is continuous on [a,b], then for any y between f(a) and f(b), there exists c in [a,b] such that f(c) = y

26. Rolle's theorem: if f is continuous on [a,b] and differentiable on (a,b), and if f(a) = f(b), then there exists c in (a,b) such that f'(c) = 0

27. Integration by substitution: ∫f(g(x))g'(x) dx = ∫f(u) du, where u = g(x)

28. Integration by parts: ∫u dv = uv - ∫v du

29. L'Hopital's rule: if lim(x → a) f(x)/g(x) = 0/0 or ∞/∞, then lim(x → a) f(x)/g(x) = lim(x → a) f'(x)/g'(x)

30. Taylor series: f(x) = Σ(n=0 to ∞) f^(n)(a)/n!(x-a)^n, where f^(n) is the nth derivative of f

31. Euler's formula: e^(ix) = cos(x) + i sin(x)

32. De Moivre's theorem: (cos x + i sin x)^n = cos(nx) + i sin(nx)

33. Fundamental trigonometric identities: sin² x + cos² x = 1, 1 + tan² x = sec² x, 1 + cot² x = csc² x

34. Double angle formulas: sin 2x = 2sin x cos x, cos 2x = cos² x - sin² x, tan 2x = (2tan x)/(1 - tan² x)

35. Half angle formulas: sin(x/2) = ±√((1 - cos x)/2), cos(x/2) = ±√((1 + cos x)/2), tan(x/2) = ±√((1 - cos x)/(1 + cos x))

36. Sum-to-product formulas: sin A + sin B = 2sin((A+B)/2)cos((A-B)/2), cos A + cos B = 2cos((A+B)/2)cos((A-B)/2), sin A - sin B = 2cos((A+B)/2)sin((A-B)/2), cos A - cos B = -2sin((A+B)/2)sin((A-B)/2)

37. Product-to-sum formulas: cos A cos B = (1/2)(cos(A-B) + cos(A+B)), sin A sin B = (1/2)(cos(A-B) - cos(A+B)), sin A cos B = (1/2)(sin(A+B) + sin(A-B)), cos A sin B = (1/2)(sin(A+B) - sin(A-B))

38. Hyperbolic functions: sinh x = (e^x - e^-x)/2, cosh x = (e^x + e^-x)/2, tanh x = sinh x/cosh x

39. Inverse trigonometric functions: arcsin x, arccos x, arctan x

40. Logarithmic identities: log(xy) = log x + log y, log(x/y) = log x - log y, log x^n = n log x

41. Exponential identities: e^x+y = e^x e^y, (e^x)^n = e^(nx), e^0 = 1

42. Binomial coefficients: (n choose k) = n!/(k!(n-k)!)

It is good video to understand the concept of abacus.

It is for you

https://vm.tiktok.com/ZMB3oa4W7
Trigonometry basic for grade 8 and above

Four digit calculate using abacus

PREPARING TO SUCCEED ON TESTS
 
What to Study, How to Study

1.
What to study:

✍Notes from class lessons
✍Homework
👌Textbook readings
👌Worksheets, maps, charts, graphs, labs, diagrams, formulas
✍Vocabulary words
2.
How to study
:
✍Read all notes.
✍Say notes aloud.
✍Rewrite notes in a briefer form (note shrink).
✍Write margin questions.
✍Make flash cards for your notes and any unfamiliar vocabulary, 
then quiz yourself.
✍Review any worksheets, maps, charts, graphs, labs, diagrams, 
formulas.
✍Reread pages from textbook.
Find a “study-buddy” and quiz each other.
✍Create your own practice quizzes.
✍Check the computer for helpful tutorials.
✍Come for extra help!!
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For grade 9 student..
Basic concept of Trigonometry

Quadrant and Trig sign value
Above grade 8

Mental calculation using abacus
#for bold students
Addition and subtraction practice using abacus