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SAT Math Formulas

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
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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. Area of a Sector
The most frequently occurring number in a set
= (x degree / 360) pi*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
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

2. Union
Multiply number of choices available in each option to get total number of options
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
Consists of all of the elements that appear in either set without repeating elements
Part/whole = %/100

3. Similar 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
(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
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

4. Special Right Triangles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
360
An=A1+(n-1)d
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

5. Rational Number
Multiply number of choices available in each option to get total number of options
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=(3root3/2)r^2
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

6. Even Numbers
Order doesn't matter - nCr=n! / r!(n-r)!
S-S-S - S-A-S - A-S-A
(1/3)LW*H
0 - -2 - -4 - ...

7. Real Wheel Formula
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
(1/3)pir^2*h
The most frequently occurring number in a set
A=[(B1+B2)*H]/2

8. Adding/Subtracting Exponents
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
Consists of all the elements that appear in both sets
Volume=(4/3)pir^3

9. Area Hexagon
Order matters - nPr=n! / (n-r)!
Positive and negative whole numbers
(distance between opposite vertices) - square root(L^2+W^2+H^2)
A=(3root3/2)r^2

10. Percentage Change
D/W=R1T1 + R2T2
A=S^2 - P=4S - Diagonal is root2 times side
([old-new]/old)*100%
#successful events / total# possible outcomes

11. Isosceles Triangle
0 - -2 - -4 - ...
2 equal sides - 2 equal angles
(area of base)*height
A=(3root3/2)r^2

12. Permutations
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
0 - -2 - -4 - ...
Order matters - nPr=n! / (n-r)!
D/W=R1T1 + R2T2

13. Direct Variation
S-S-S - S-A-S - A-S-A
D=R*T - W=R*T
= (x degree / 360) C
x1/y1 = x2/y2

14. Integer
Part/whole = %/100
= (x degree / 360) pi*r^2
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Positive and negative whole numbers

15. Weighted Averages
S-S-S - S-A-S - A-S-A
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
(area of base)*height
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

16. Cylinders
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
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
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

17. Sum of Exterior Angles
(area of base)*height
360
S-S-S - S-A-S - A-S-A
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

18. Exponent Rules
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Square root[(x2-x1)^2 + (y2-y1)^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
Part/whole = %/100

19. Equilateral Triangle
Volume=(4/3)pir^3
S=180(n-2)
A=L*W - P=2L+2W - Diagonals equal length
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

20. Congruent Triangles
S-S-S - S-A-S - A-S-A
The most frequently occurring number in a set
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

21. Extension of the Pythagorean Theorem
360
A=1/2bh
(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

22. Same Work
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
A=S^2 - P=4S - Diagonal is root2 times side
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

23. Same Distance
A=(3root3/2)r^2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
([old-new]/old)*100%
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

24. Fundamental Counting Principle
Multiply number of choices available in each option to get total number of options
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

25. Volume of Pyramid
Order matters - nPr=n! / (n-r)!
Consists of all the elements that appear in both sets
2 equal sides - 2 equal angles
(1/3)LW*H

26. Area of a Triangle
S=180(n-2)
A=1/2bh
x1y1 = x2y2
Middle number (or average of 2) of set from smallest to largest

27. Even/Odd Results
D/W=R1T1 + R2T2
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
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

28. Odd Numbers
0 - -2 - -4 - ...
1 - 3 - 5 - ...
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
S-S-S - S-A-S - A-S-A

29. Weighted Average
1 - 3 - 5 - ...
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)
Square root[(x2-x1)^2 + (y2-y1)^2]

30. Probability
#successful events / total# possible outcomes
1 - 3 - 5 - ...
(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

31. Triangle Inequality
(distance between opposite vertices) - square root(L^2+W^2+H^2)
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
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

32. Average Rate
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
S-S-S - S-A-S - A-S-A
Volume=(4/3)pir^3
A=S^2 - P=4S - Diagonal is root2 times side

33. Same Time
D/W= (R1+R2)*T
([old-new]/old)*100%
#successful events / total# possible outcomes
2 equal sides - 2 equal angles

34. Distance Formula
S=180(n-2)
Square root[(x2-x1)^2 + (y2-y1)^2]
(area of base)*height
An=A1(r)^n-1

35. Mixture Formula
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Order doesn't matter - nCr=n! / r!(n-r)!
x1/y1 = x2/y2
An=A1+(n-1)d

36. Geometric Sequences
360
An=A1(r)^n-1
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
A=(3root3/2)r^2

37. Sum of Interior Angles
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
S=180(n-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
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

38. Median
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
D/W=R1T1 + R2T2
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

39. Volume of Sphere
S=180(n-2)
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
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
Volume=(4/3)pir^3

40. Mode
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
The most frequently occurring number in a set
#successful events / total# possible outcomes

41. Volume of Cone
(1/3)pir^2*h
([old-new]/old)*100%
360
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

42. Parallelograms
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
An=A1+(n-1)d
D=R*T - W=R*T
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

43. Same Rate
A=1/2bh
An=A1+(n-1)d
D/W= (R1+R2)*T
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

44. Combinations

45. Percents
A=(3root3/2)r^2
Part/whole = %/100
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
D/W=R1T1 + R2T2

46. Arithmetic Sequence
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
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
An=A1+(n-1)d
An=A1(r)^n-1

47. Rectangles
A=L*W - P=2L+2W - Diagonals equal length
= (x degree / 360) pi*r^2
Square root[(x2-x1)^2 + (y2-y1)^2]
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

48. Square
The most frequently occurring number in a set
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Order matters - nPr=n! / (n-r)!
A=S^2 - P=4S - Diagonal is root2 times side

49. Volume of Prism
An=A1(r)^n-1
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=1/2bh
(area of base)*height

50. Combined Rates
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
D/W=R1T1 + R2T2
= (x degree / 360) pi*r^2
An=A1+(n-1)d