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SAT Math Formulas

Subjects : sat, math

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Answer 50 questions in 15 minutes.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. Sum of Interior Angles
Volume=(4/3)pir^3
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Order doesn't matter - nCr=n! / r!(n-r)!
S=180(n-2)

2. Volume of Pyramid
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
(1/3)LW*H
(1/3)pir^2*h
D/W= (R1+R2)*T

3. Same Time
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
An=A1+(n-1)d
D/W= (R1+R2)*T
Positive and negative whole numbers

4. Permutations
x1/y1 = x2/y2
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
Order matters - nPr=n! / (n-r)!
Part/whole = %/100

5. Indirect Variation
x1y1 = x2y2
#successful events / total# possible outcomes
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
(1/3)pir^2*h

6. Area Hexagon
A=(3root3/2)r^2
An=A1+(n-1)d
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

7. Percents
2 equal sides - 2 equal angles
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
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
Part/whole = %/100

8. Distance/Work Formula
A=[(B1+B2)*H]/2
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
D=R*T - W=R*T
(area of base)*height

9. Sum of Exterior Angles
D=R*T - W=R*T
360
Volume=(4/3)pir^3
S=180(n-2)

10. Adding/Subtracting Exponents
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
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
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

11. Mixture Formula
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
360
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

12. Fundamental Counting Principle
Multiply number of choices available in each option to get total number of options
Consists of all of the elements that appear in either set without repeating elements
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
= (x degree / 360) pi*r^2

13. Geometric Sequences
The most frequently occurring number in a set
An=A1(r)^n-1
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
D/W=R1T1 + R2T2

14. Probability
#successful events / total# possible outcomes
([old-new]/old)*100%
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
(1/3)pir^2*h

15. Average Rate
0 - -2 - -4 - ...
An=A1(r)^n-1
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
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

16. Parallelograms
(1/3)LW*H
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Square root[(x2-x1)^2 + (y2-y1)^2]

17. Direct Variation
x1/y1 = x2/y2
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
A=L*W - P=2L+2W - Diagonals equal length
An=A1(r)^n-1

18. Percentage Change
0 - -2 - -4 - ...
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
360
([old-new]/old)*100%

19. Triangle Inequality
Middle number (or average of 2) of set from smallest to largest
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
D/W= (R1+R2)*T
Positive and negative whole numbers

20. Weighted Average
1 - 3 - 5 - ...
Volume=(4/3)pir^3
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

21. Weighted Averages
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
A=[(B1+B2)*H]/2
S=180(n-2)
A=S^2 - P=4S - Diagonal is root2 times side

22. Same Rate
1 - 3 - 5 - ...
Square root[(x2-x1)^2 + (y2-y1)^2]
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Multiply number of choices available in each option to get total number of options

23. Mode
The most frequently occurring number in a set
360
S=180(n-2)
D=R*T - W=R*T

24. Length on an Arc
S=180(n-2)
= (x degree / 360) C
([old-new]/old)*100%
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

25. Even/Odd Results
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
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]
(area of base)*height

26. Odd Numbers
(1/3)pir^2*h
1 - 3 - 5 - ...
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
A=L*W - P=2L+2W - Diagonals equal length

27. Combined Rates
(1/3)pir^2*h
An=A1(r)^n-1
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
D/W=R1T1 + R2T2

28. Combinations
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
Order doesn't matter - nCr=n! / r!(n-r)!
Consists of all of the elements that appear in either set without repeating elements
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

29. Union
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A=S^2 - P=4S - Diagonal is root2 times side
Consists of all of the elements that appear in either set without repeating elements
A=[(B1+B2)*H]/2

30. Same Work
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)
#successful events / total# possible outcomes
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

31. Cylinders
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
(1/3)LW*H
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

32. Area of a Triangle
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
A=1/2bh
Order doesn't matter - nCr=n! / r!(n-r)!
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

33. Special Right Triangles
= (x degree / 360) pi*r^2
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
D=R*T - W=R*T

34. Exponent Rules
(distance between opposite vertices) - square root(L^2+W^2+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
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
(1/3)pir^2*h

35. Real Wheel Formula
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
Positive and negative whole numbers
D/W=R1T1 + R2T2

36. Rational Number
([old-new]/old)*100%
(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

37. Volume of Prism
D/W=R1T1 + R2T2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
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
(area of base)*height

38. Right Triangle
2 equal sides - 2 equal angles
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
S-S-S - S-A-S - A-S-A
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

39. Volume of Sphere
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Volume=(4/3)pir^3
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

40. Distance Formula
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
D/W= (R1+R2)*T
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Square root[(x2-x1)^2 + (y2-y1)^2]

41. Square
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
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A=S^2 - P=4S - Diagonal is root2 times side
D/W= (R1+R2)*T

42. Intersection
(1/3)pir^2*h
Consists of all the elements that appear in both sets
S=180(n-2)
x1y1 = x2y2

43. Same Distance
x1/y1 = x2/y2
D/W=R1T1 + R2T2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
1 - 3 - 5 - ...

44. Area of a Sector
= (x degree / 360) pi*r^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
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
(distance between opposite vertices) - square root(L^2+W^2+H^2)

45. Integer
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Multiply number of choices available in each option to get total number of options
([old-new]/old)*100%
Positive and negative whole numbers

46. Similar Triangles
x1y1 = x2y2
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
x1/y1 = x2/y2

47. Volume of Cone
(1/3)pir^2*h
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
(area of base)*height
Positive and negative whole numbers

48. Area Trapezoid
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
([old-new]/old)*100%
A=[(B1+B2)*H]/2
x1y1 = x2y2

49. Median
Middle number (or average of 2) of set from smallest to largest
Square root[(x2-x1)^2 + (y2-y1)^2]
S=180(n-2)
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

50. Rectangles
([old-new]/old)*100%
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
A=L*W - P=2L+2W - Diagonals equal length
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

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