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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. Same Work
0 - -2 - -4 - ...
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
A=L*W - P=2L+2W - Diagonals equal length
S=180(n-2)

2. Similar Triangles
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Positive and negative whole numbers
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

3. Equilateral Triangle
Order doesn't matter - nCr=n! / r!(n-r)!
#successful events / total# possible outcomes
A=L*W - P=2L+2W - Diagonals equal length
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

4. Distance/Work Formula
A=L*W - P=2L+2W - Diagonals equal length
An=A1+(n-1)d
D=R*T - W=R*T
Multiply number of choices available in each option to get total number of options

5. Union
Order matters - nPr=n! / (n-r)!
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Consists of all of the elements that appear in either set without repeating elements

6. Fundamental Counting Principle
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
Square root[(x2-x1)^2 + (y2-y1)^2]
Multiply number of choices available in each option to get total number of options
Positive and negative whole numbers

7. Congruent Triangles
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
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
S-S-S - S-A-S - A-S-A
([old-new]/old)*100%

8. Volume of Pyramid
S=180(n-2)
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
(1/3)LW*H
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

9. Area Hexagon
Consists of all of the elements that appear in either set without repeating elements
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A=(3root3/2)r^2
The most frequently occurring number in a set

10. Sum of Exterior Angles
([old-new]/old)*100%
360
A=S^2 - P=4S - Diagonal is root2 times side
Positive and negative whole numbers

11. Same Distance
An=A1(r)^n-1
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
A=(3root3/2)r^2

12. Even/Odd Results
Positive and negative whole numbers
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
(area of base)*height
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

13. Volume of Prism
(1/3)LW*H
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(area of base)*height
0 - -2 - -4 - ...

14. Same Rate
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
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Middle number (or average of 2) of set from smallest to largest
The most frequently occurring number in a set

15. Mode
([old-new]/old)*100%
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
The most frequently occurring number in a set
2 equal sides - 2 equal angles

16. Weighted Averages
D/W=R1T1 + R2T2
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
(area of base)*height
Middle number (or average of 2) of set from smallest to largest

17. Volume of Sphere
Order doesn't matter - nCr=n! / r!(n-r)!
A=1/2bh
Volume=(4/3)pir^3
Order matters - nPr=n! / (n-r)!

18. Isosceles Triangle
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
2 equal sides - 2 equal angles
360
Order matters - nPr=n! / (n-r)!

19. Same Time
S-S-S - S-A-S - A-S-A
D/W= (R1+R2)*T
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/W=R1T1 + R2T2

20. Probability
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Square root[(x2-x1)^2 + (y2-y1)^2]
(distance between opposite vertices) - square root(L^2+W^2+H^2)
#successful events / total# possible outcomes

21. Arithmetic Sequence
An=A1+(n-1)d
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
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

22. Exponent Rules
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
#successful events / total# possible outcomes
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
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

23. Rational Number
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
A=[(B1+B2)*H]/2
Square root[(x2-x1)^2 + (y2-y1)^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

24. Geometric Sequences
An=A1(r)^n-1
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
(area of base)*height
Middle number (or average of 2) of set from smallest to largest

25. Median
Volume=(4/3)pir^3
Middle number (or average of 2) of set from smallest to largest
D/W=R1T1 + R2T2
S-S-S - S-A-S - A-S-A

26. Percents
S-S-S - S-A-S - A-S-A
= (x degree / 360) C
(area of base)*height
Part/whole = %/100

27. Length on an Arc
= (x degree / 360) C
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
= (x degree / 360) pi*r^2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

28. Even Numbers
S-S-S - S-A-S - A-S-A
Positive and negative whole numbers
0 - -2 - -4 - ...
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

29. Real Wheel Formula
Positive and negative whole numbers
Volume=(4/3)pir^3
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

30. Area of a Triangle
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
A=1/2bh
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

31. Average Rate
D/W= (R1+R2)*T
Positive and negative whole numbers
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Middle number (or average of 2) of set from smallest to largest

32. Direct Variation
S=180(n-2)
([old-new]/old)*100%
x1/y1 = x2/y2
A=L*W - P=2L+2W - Diagonals equal length

33. Sum of Interior Angles
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
S=180(n-2)
(1/3)LW*H
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

34. Extension of the Pythagorean Theorem
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
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
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Order matters - nPr=n! / (n-r)!

35. Percentage Change
([old-new]/old)*100%
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
= (x degree / 360) pi*r^2
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

36. Parallelograms
x1/y1 = x2/y2
S=180(n-2)
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

37. Combinations

38. Adding/Subtracting Exponents
An=A1+(n-1)d
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

39. Cylinders
#successful events / total# possible outcomes
D=R*T - W=R*T
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

40. Mixture Formula
x1y1 = x2y2
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%
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

41. Weighted Average
A=L*W - P=2L+2W - Diagonals equal length
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
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

42. Square
0 - -2 - -4 - ...
#successful events / total# possible outcomes
A=S^2 - P=4S - Diagonal is root2 times side
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

43. Distance Formula
A=(3root3/2)r^2
Square root[(x2-x1)^2 + (y2-y1)^2]
Order matters - nPr=n! / (n-r)!
(distance between opposite vertices) - square root(L^2+W^2+H^2)

44. Indirect Variation
A=[(B1+B2)*H]/2
An=A1+(n-1)d
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
x1y1 = x2y2

45. Permutations
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Volume=(4/3)pir^3
Order matters - nPr=n! / (n-r)!
x1y1 = x2y2

46. Right Triangle
A=(3root3/2)r^2
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
A=L*W - P=2L+2W - Diagonals equal length

47. Integer
x1/y1 = x2/y2
A=1/2bh
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Positive and negative whole numbers

48. Volume of Cone
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
(1/3)pir^2*h
S-S-S - S-A-S - A-S-A
= (x degree / 360) pi*r^2

49. Area Trapezoid
(1/3)pir^2*h
Order doesn't matter - nCr=n! / r!(n-r)!
A=1/2bh
A=[(B1+B2)*H]/2

50. Rectangles
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
= (x degree / 360) C
A=L*W - P=2L+2W - Diagonals equal length
D/W= (R1+R2)*T