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SAT Math Formulas

Subjects : sat, math

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Answer 50 questions in 15 minutes.
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1. Percents
360
(area of base)*height
Middle number (or average of 2) of set from smallest to largest
Part/whole = %/100

2. Exponent Rules
A=S^2 - P=4S - Diagonal is root2 times side
Negative number raised to even power will be positive - negative number raised to odd power will be negative - numbers with absolute values between 0 and 1 will be a smaller distance from 0 the higher the power to which they are raised
([old-new]/old)*100%
S-S-S - S-A-S - A-S-A

3. Square
A=1/2bh
Negative number raised to even power will be positive - negative number raised to odd power will be negative - numbers with absolute values between 0 and 1 will be a smaller distance from 0 the higher the power to which they are raised
A=S^2 - P=4S - Diagonal is root2 times side
= (x degree / 360) C

4. Area Hexagon
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
(1/3)pir^2*h
A=S^2 - P=4S - Diagonal is root2 times side
A=(3root3/2)r^2

5. Real Wheel Formula
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
A=S^2 - P=4S - Diagonal is root2 times side
Factor out the common value - 4^a + 4^a + 4^a + 4^a - 4^a (1+1+1+1) - 4^a * 4^1 - 4^a+1
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

6. Similar Triangles
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
x1/y1 = x2/y2
0 - -2 - -4 - ...

7. Area of a Sector
Negative number raised to even power will be positive - negative number raised to odd power will be negative - numbers with absolute values between 0 and 1 will be a smaller distance from 0 the higher the power to which they are raised
The most frequently occurring number in a set
Consists of all of the elements that appear in either set without repeating elements
= (x degree / 360) pi*r^2

8. Geometric Sequences
An=A1(r)^n-1
0 - -2 - -4 - ...
x1y1 = x2y2
A=S^2 - P=4S - Diagonal is root2 times side

9. Right Triangle
Positive and negative whole numbers
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
A=[(B1+B2)*H]/2

10. Same Rate
Multiply number of choices available in each option to get total number of options
The sum of the lengths of any two sides is greater than the length of the third side - AB + AC > BC - [AB - AC] < BC < AB + AC
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

11. Distance/Work Formula
A=L*W - P=2L+2W - Diagonals equal length
(1/3)pir^2*h
D=R*T - W=R*T
The sum of the lengths of any two sides is greater than the length of the third side - AB + AC > BC - [AB - AC] < BC < AB + AC

12. Extension of the Pythagorean Theorem
An=A1(r)^n-1
Consists of all the elements that appear in both sets
(distance between opposite vertices) - square root(L^2+W^2+H^2)
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

13. Mixture Formula
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
#successful events / total# possible outcomes
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
S=180(n-2)

14. Direct Variation
A=S^2 - P=4S - Diagonal is root2 times side
x1/y1 = x2/y2
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Middle number (or average of 2) of set from smallest to largest

15. Equilateral Triangle
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Factor out the common value - 4^a + 4^a + 4^a + 4^a - 4^a (1+1+1+1) - 4^a * 4^1 - 4^a+1
Volume=(4/3)pir^3
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

16. Sum of Interior Angles
360
S=180(n-2)
D/W= (R1+R2)*T
Part/whole = %/100

17. Weighted Averages
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
A=L*W - P=2L+2W - Diagonals equal length
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
Part/whole = %/100

18. Same Work
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Part/whole = %/100
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Positive and negative whole numbers

19. Congruent Triangles
S-S-S - S-A-S - A-S-A
0 - -2 - -4 - ...
S=180(n-2)
Order matters - nPr=n! / (n-r)!

20. Volume of Pyramid
Multiply number of choices available in each option to get total number of options
Part/whole = %/100
(1/3)LW*H
(distance between opposite vertices) - square root(L^2+W^2+H^2)

21. Even/Odd Results
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
An=A1+(n-1)d
S-S-S - S-A-S - A-S-A

22. Adding/Subtracting Exponents
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Factor out the common value - 4^a + 4^a + 4^a + 4^a - 4^a (1+1+1+1) - 4^a * 4^1 - 4^a+1
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Positive and negative whole numbers

23. Combinations

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24. Intersection
Consists of all the elements that appear in both sets
A=1/2bh
S-S-S - S-A-S - A-S-A
Positive and negative whole numbers

25. Even Numbers
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
0 - -2 - -4 - ...
Positive and negative whole numbers
#successful events / total# possible outcomes

26. Same Time
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
(distance between opposite vertices) - square root(L^2+W^2+H^2)
D/W= (R1+R2)*T
Order doesn't matter - nCr=n! / r!(n-r)!

27. Volume of Prism
(area of base)*height
Factor out the common value - 4^a + 4^a + 4^a + 4^a - 4^a (1+1+1+1) - 4^a * 4^1 - 4^a+1
An=A1+(n-1)d
x1/y1 = x2/y2

28. Rational Number
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
([old-new]/old)*100%
2 equal sides - 2 equal angles
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

29. Volume of Cone
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
A=[(B1+B2)*H]/2
(1/3)pir^2*h
2 equal sides - 2 equal angles

30. Area of a Triangle
A=1/2bh
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
D/W= (R1+R2)*T
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

31. Rectangles
A=L*W - P=2L+2W - Diagonals equal length
The sum of the lengths of any two sides is greater than the length of the third side - AB + AC > BC - [AB - AC] < BC < AB + AC
Negative number raised to even power will be positive - negative number raised to odd power will be negative - numbers with absolute values between 0 and 1 will be a smaller distance from 0 the higher the power to which they are raised
Consists of all of the elements that appear in either set without repeating elements

32. Mode
Negative number raised to even power will be positive - negative number raised to odd power will be negative - numbers with absolute values between 0 and 1 will be a smaller distance from 0 the higher the power to which they are raised
The most frequently occurring number in a set
Consists of all of the elements that appear in either set without repeating elements
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

33. Cylinders
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A=(3root3/2)r^2
(area of base)*height
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

34. Volume of Sphere
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Volume=(4/3)pir^3
1 - 3 - 5 - ...
Order doesn't matter - nCr=n! / r!(n-r)!

35. Distance Formula
A=L*W - P=2L+2W - Diagonals equal length
Square root[(x2-x1)^2 + (y2-y1)^2]
Positive and negative whole numbers
S-S-S - S-A-S - A-S-A

36. Median
Middle number (or average of 2) of set from smallest to largest
An=A1(r)^n-1
x1y1 = x2y2
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

37. Indirect Variation
Square root[(x2-x1)^2 + (y2-y1)^2]
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
x1y1 = x2y2
S-S-S - S-A-S - A-S-A

38. Same Distance
Part/whole = %/100
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
360

39. Odd Numbers
1 - 3 - 5 - ...
A=1/2bh
x1/y1 = x2/y2
Order doesn't matter - nCr=n! / r!(n-r)!

40. Fundamental Counting Principle
Multiply number of choices available in each option to get total number of options
Consists of all the elements that appear in both sets
S=180(n-2)
S-S-S - S-A-S - A-S-A

41. Triangle Inequality
(1/3)pir^2*h
A=(3root3/2)r^2
The sum of the lengths of any two sides is greater than the length of the third side - AB + AC > BC - [AB - AC] < BC < AB + AC
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

42. Special Right Triangles
x1y1 = x2y2
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
Consists of all the elements that appear in both sets
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

43. Integer
The most frequently occurring number in a set
Positive and negative whole numbers
A=[(B1+B2)*H]/2
Negative number raised to even power will be positive - negative number raised to odd power will be negative - numbers with absolute values between 0 and 1 will be a smaller distance from 0 the higher the power to which they are raised

44. Parallelograms
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Part/whole = %/100
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

45. Combined Rates
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
D/W=R1T1 + R2T2
2 equal sides - 2 equal angles
(1/3)pir^2*h

46. Length on an Arc
(area of base)*height
= (x degree / 360) C
(distance between opposite vertices) - square root(L^2+W^2+H^2)
A=[(B1+B2)*H]/2

47. Sum of Exterior Angles
(distance between opposite vertices) - square root(L^2+W^2+H^2)
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
S-S-S - S-A-S - A-S-A
360

48. Probability
#successful events / total# possible outcomes
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Middle number (or average of 2) of set from smallest to largest
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

49. Area Trapezoid
Factor out the common value - 4^a + 4^a + 4^a + 4^a - 4^a (1+1+1+1) - 4^a * 4^1 - 4^a+1
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Square root[(x2-x1)^2 + (y2-y1)^2]
A=[(B1+B2)*H]/2

50. Arithmetic Sequence
The most frequently occurring number in a set
An=A1+(n-1)d
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

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SAT Math Formulas

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