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SAT Math Formulas

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Special Right Triangles
([old-new]/old)*100%
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Order doesn't matter - nCr=n! / r!(n-r)!
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

2. Mixture Formula
x1y1 = x2y2
A=(3root3/2)r^2
D/W=R1T1 + R2T2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

3. Weighted Averages
A=1/2bh
An=A1+(n-1)d
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
An=A1(r)^n-1

4. Union
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
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
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

5. Congruent Triangles
S-S-S - S-A-S - A-S-A
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Order matters - nPr=n! / (n-r)!
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

6. Same Work
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
0 - -2 - -4 - ...
x1y1 = x2y2

7. Volume of Pyramid
Multiply number of choices available in each option to get total number of options
#successful events / total# possible outcomes
(1/3)LW*H
A=1/2bh

8. Real Wheel Formula
Consists of all of the elements that appear in either set without repeating elements
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
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=[(B1+B2)*H]/2

9. Probability
An=A1(r)^n-1
#successful events / total# possible outcomes
(1/3)LW*H
A=S^2 - P=4S - Diagonal is root2 times side

10. Isosceles Triangle
An=A1(r)^n-1
x1y1 = x2y2
2 equal sides - 2 equal angles
A=1/2bh

11. Permutations
Order matters - nPr=n! / (n-r)!
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
An=A1+(n-1)d
x1y1 = x2y2

12. Average Rate
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
S=180(n-2)
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

13. Combinations

14. Fundamental Counting Principle
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
x1/y1 = x2/y2
Multiply number of choices available in each option to get total number of options
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

15. Rectangles
(1/3)pir^2*h
Order matters - nPr=n! / (n-r)!
A=L*W - P=2L+2W - Diagonals equal length
360

16. Cylinders
= (x degree / 360) pi*r^2
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

17. Percents
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Part/whole = %/100
A=(3root3/2)r^2
Multiply number of choices available in each option to get total number of options

18. Intersection
= (x degree / 360) C
(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
Consists of all the elements that appear in both sets

19. Right Triangle
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Multiply number of choices available in each option to get total number of options
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

20. Odd Numbers
([old-new]/old)*100%
x1/y1 = x2/y2
= (x degree / 360) pi*r^2
1 - 3 - 5 - ...

21. Exponent Rules
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Consists of all the elements that appear in both sets
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
x1/y1 = x2/y2

22. Volume of Cone
D/W= (R1+R2)*T
(1/3)pir^2*h
A=1/2bh
(area of base)*height

23. Similar Triangles
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
Middle number (or average of 2) of set from smallest to largest
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Volume=(4/3)pir^3

24. Area Hexagon
A=(3root3/2)r^2
= (x degree / 360) C
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Square root[(x2-x1)^2 + (y2-y1)^2]

25. Even Numbers
D/W=R1T1 + R2T2
A=(3root3/2)r^2
0 - -2 - -4 - ...
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

26. Area Trapezoid
D/W= (R1+R2)*T
0 - -2 - -4 - ...
A=[(B1+B2)*H]/2
Positive and negative whole numbers

27. Extension of the Pythagorean Theorem
(distance between opposite vertices) - square root(L^2+W^2+H^2)
A=S^2 - P=4S - Diagonal is root2 times side
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

28. Weighted Average
A=S^2 - P=4S - Diagonal is root2 times side
Square root[(x2-x1)^2 + (y2-y1)^2]
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A=(3root3/2)r^2

29. Equilateral Triangle
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
A=S^2 - P=4S - Diagonal is root2 times side
(1/3)pir^2*h
An=A1(r)^n-1

30. Sum of Exterior Angles
360
= (x degree / 360) pi*r^2
Consists of all of the elements that appear in either set without repeating elements
([old-new]/old)*100%

31. Length on an Arc
= (x degree / 360) C
Multiply number of choices available in each option to get total number of options
Square root[(x2-x1)^2 + (y2-y1)^2]
0 - -2 - -4 - ...

32. Even/Odd Results
S-S-S - S-A-S - A-S-A
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

33. Percentage Change
A=L*W - P=2L+2W - Diagonals equal length
([old-new]/old)*100%
= (x degree / 360) pi*r^2
(1/3)pir^2*h

34. Adding/Subtracting Exponents
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
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
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
A=1/2bh

35. Integer
Positive and negative whole numbers
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
x1y1 = x2y2
Consists of all the elements that appear in both sets

36. Sum of Interior Angles
S=180(n-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
D=R*T - W=R*T
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

37. Square
2 equal sides - 2 equal angles
A=S^2 - P=4S - Diagonal is root2 times side
([old-new]/old)*100%
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

38. Volume of Sphere
#successful events / total# possible outcomes
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=L*W - P=2L+2W - Diagonals equal length
Volume=(4/3)pir^3

39. Geometric Sequences
An=A1(r)^n-1
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Consists of all the elements that appear in both sets
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

40. Same Rate
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
x1y1 = x2y2

41. Distance/Work Formula
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
An=A1+(n-1)d
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
D=R*T - W=R*T

42. Direct Variation
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
(area of base)*height
x1/y1 = x2/y2

43. Mode
A=L*W - P=2L+2W - Diagonals equal length
The most frequently occurring number in a set
([old-new]/old)*100%
360

44. Indirect Variation
x1y1 = x2y2
#successful events / total# possible outcomes
Order doesn't matter - nCr=n! / r!(n-r)!
The most frequently occurring number in a set

45. Median
Middle number (or average of 2) of set from smallest to largest
(distance between opposite vertices) - square root(L^2+W^2+H^2)
x1/y1 = x2/y2
(1/3)LW*H

46. Combined Rates
2 equal sides - 2 equal angles
The most frequently occurring number in a set
D/W=R1T1 + R2T2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

47. Area of a Sector
#successful events / total# possible outcomes
= (x degree / 360) pi*r^2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Order matters - nPr=n! / (n-r)!

48. Arithmetic Sequence
2 equal sides - 2 equal angles
Consists of all of the elements that appear in either set without repeating elements
An=A1+(n-1)d
(1/3)pir^2*h

49. Triangle Inequality
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
Consists of all of the elements that appear in either set without repeating elements
S=180(n-2)

50. Same Time
S-S-S - S-A-S - A-S-A
A=S^2 - P=4S - Diagonal is root2 times side
D/W= (R1+R2)*T
An=A1(r)^n-1