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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. Union
= (x degree / 360) C
1 - 3 - 5 - ...
Consists of all of the elements that appear in either set without repeating elements
x1/y1 = x2/y2

2. Sum of Exterior Angles
A=L*W - P=2L+2W - Diagonals equal length
Multiply number of choices available in each option to get total number of options
An=A1(r)^n-1
360

3. Even Numbers
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
0 - -2 - -4 - ...
D/W= (R1+R2)*T
Part/whole = %/100

4. Volume of Pyramid
Multiply number of choices available in each option to get total number of options
(1/3)LW*H
An=A1+(n-1)d
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

5. Length on an Arc
= (x degree / 360) C
(area of base)*height
(1/3)pir^2*h
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

6. Volume of Cone
A=1/2bh
= (x degree / 360) C
(1/3)pir^2*h
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

7. Even/Odd Results
D/W= (R1+R2)*T
([old-new]/old)*100%
Part/whole = %/100
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

8. Exponent Rules
Volume=(4/3)pir^3
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
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

9. Probability
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Order doesn't matter - nCr=n! / r!(n-r)!
#successful events / total# possible outcomes
Middle number (or average of 2) of set from smallest to largest

10. Volume of Sphere
Volume=(4/3)pir^3
0 - -2 - -4 - ...
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

11. Area Trapezoid
x1/y1 = x2/y2
A=[(B1+B2)*H]/2
S-S-S - S-A-S - A-S-A
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

12. Permutations
An=A1(r)^n-1
Order doesn't matter - nCr=n! / r!(n-r)!
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Order matters - nPr=n! / (n-r)!

13. Cylinders
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
0 - -2 - -4 - ...
Volume=(4/3)pir^3
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

14. Odd Numbers
(1/3)LW*H
1 - 3 - 5 - ...
D=R*T - W=R*T
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

15. Direct Variation
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
An=A1(r)^n-1
x1/y1 = x2/y2
= (x degree / 360) C

16. Isosceles Triangle
Volume=(4/3)pir^3
2 equal sides - 2 equal angles
Multiply number of choices available in each option to get total number of options
Middle number (or average of 2) of set from smallest to largest

17. Combined Rates
2 equal sides - 2 equal angles
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
Consists of all of the elements that appear in either set without repeating elements
D/W=R1T1 + R2T2

18. Volume of Prism
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
(area of base)*height
0 - -2 - -4 - ...
An=A1+(n-1)d

19. Same Time
Multiply number of choices available in each option to get total number of options
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

20. Integer
Middle number (or average of 2) of set from smallest to largest
Positive and negative whole numbers
2 equal sides - 2 equal angles
1 - 3 - 5 - ...

21. Arithmetic Sequence
Square root[(x2-x1)^2 + (y2-y1)^2]
A=[(B1+B2)*H]/2
An=A1+(n-1)d
A=1/2bh

22. Intersection
Consists of all the elements that appear in both sets
([old-new]/old)*100%
A=(3root3/2)r^2
Order matters - nPr=n! / (n-r)!

23. Area of a Sector
= (x degree / 360) pi*r^2
The most frequently occurring number in a set
A=L*W - P=2L+2W - Diagonals equal length
S=180(n-2)

24. Indirect Variation
x1y1 = x2y2
(area of base)*height
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Volume=(4/3)pir^3

25. Rectangles
A=L*W - P=2L+2W - Diagonals equal length
Positive and negative whole numbers
A=[(B1+B2)*H]/2
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

26. Area Hexagon
A=(3root3/2)r^2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Order matters - nPr=n! / (n-r)!
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

27. Weighted Averages
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Order matters - nPr=n! / (n-r)!
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
= (x degree / 360) pi*r^2

28. Triangle Inequality
360
S=180(n-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
Positive and negative whole numbers

29. Adding/Subtracting Exponents
Order doesn't matter - nCr=n! / r!(n-r)!
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
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

30. Percentage Change
([old-new]/old)*100%
Middle number (or average of 2) of set from smallest to largest
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
2 equal sides - 2 equal angles

31. Mode
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
The most frequently occurring number in a set
x1/y1 = x2/y2
2 equal sides - 2 equal angles

32. Average Rate
(area of base)*height
An=A1(r)^n-1
Volume=(4/3)pir^3
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

33. Equilateral Triangle
1 - 3 - 5 - ...
Square root[(x2-x1)^2 + (y2-y1)^2]
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
A=(3root3/2)r^2

34. Area of a Triangle
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=1/2bh
A=(3root3/2)r^2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

35. Median
A=L*W - P=2L+2W - Diagonals equal length
= (x degree / 360) pi*r^2
Middle number (or average of 2) of set from smallest to largest
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

36. Same Rate
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
x1/y1 = x2/y2
A=(3root3/2)r^2

37. Real Wheel Formula
A=[(B1+B2)*H]/2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A=1/2bh
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

38. Weighted Average
Order matters - nPr=n! / (n-r)!
A=S^2 - P=4S - Diagonal is root2 times side
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Square root[(x2-x1)^2 + (y2-y1)^2]

39. Geometric Sequences
Part/whole = %/100
An=A1(r)^n-1
(1/3)pir^2*h
Volume=(4/3)pir^3

40. Similar Triangles
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
D/W= (R1+R2)*T

41. Parallelograms
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Order doesn't matter - nCr=n! / r!(n-r)!
x1y1 = x2y2

42. Percents
360
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
2 equal sides - 2 equal angles
Part/whole = %/100

43. Fundamental Counting Principle
Order doesn't matter - nCr=n! / r!(n-r)!
Part/whole = %/100
Middle number (or average of 2) of set from smallest to largest
Multiply number of choices available in each option to get total number of options

44. Distance/Work Formula
= (x degree / 360) pi*r^2
D=R*T - W=R*T
x1y1 = x2y2
Volume=(4/3)pir^3

45. Same Distance
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Middle number (or average of 2) of set from smallest to largest
Square root[(x2-x1)^2 + (y2-y1)^2]
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

46. Same Work
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
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
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
(distance between opposite vertices) - square root(L^2+W^2+H^2)

47. Mixture Formula
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Middle number (or average of 2) of set from smallest to largest
2 equal sides - 2 equal angles

48. Extension of the Pythagorean Theorem
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)
Positive and negative whole numbers
Order doesn't matter - nCr=n! / r!(n-r)!

49. Distance Formula
Square root[(x2-x1)^2 + (y2-y1)^2]
Positive and negative whole numbers
Part/whole = %/100
x1/y1 = x2/y2

50. Rational Number
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
Order matters - nPr=n! / (n-r)!
A=L*W - P=2L+2W - Diagonals equal length