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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.
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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. Mode
An=A1+(n-1)d
S=180(n-2)
The most frequently occurring number in a set
Consists of all the elements that appear in both sets

2. Volume of Pyramid
= (x degree / 360) C
(1/3)LW*H
A=1/2bh
2 equal sides - 2 equal angles

3. Even Numbers
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
x1y1 = x2y2
0 - -2 - -4 - ...
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

4. Rational Number
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
A=[(B1+B2)*H]/2
An=A1+(n-1)d

5. Permutations
Order matters - nPr=n! / (n-r)!
Positive and negative whole numbers
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
D=R*T - W=R*T

6. Extension of the Pythagorean Theorem
An=A1(r)^n-1
Multiply number of choices available in each option to get total number of options
(distance between opposite vertices) - square root(L^2+W^2+H^2)
S=180(n-2)

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

8. Triangle Inequality
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
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
A=L*W - P=2L+2W - Diagonals equal length
D=R*T - W=R*T

9. Rectangles
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
A=L*W - P=2L+2W - Diagonals equal length
Volume=(4/3)pir^3
360

10. Area Hexagon
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
A=(3root3/2)r^2
A=1/2bh
Consists of all of the elements that appear in either set without repeating elements

11. Similar Triangles
360
Middle number (or average of 2) of set from smallest to largest
Consists of all of the elements that appear in either set without repeating elements
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

12. Same Time
360
S-S-S - S-A-S - A-S-A
(1/3)pir^2*h
D/W= (R1+R2)*T

13. Equilateral Triangle
D/W=R1T1 + R2T2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
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

14. Same Distance
1 - 3 - 5 - ...
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
(area of base)*height

15. Weighted Averages
S=180(n-2)
(area of base)*height
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

16. Percents
Volume=(4/3)pir^3
An=A1+(n-1)d
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Part/whole = %/100

17. Weighted Average
D=R*T - W=R*T
0 - -2 - -4 - ...
Positive and negative whole numbers
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

18. Area Trapezoid
A=[(B1+B2)*H]/2
S-S-S - S-A-S - A-S-A
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

19. Volume of Sphere
Volume=(4/3)pir^3
An=A1+(n-1)d
360
(area of base)*height

20. Geometric Sequences
([old-new]/old)*100%
An=A1(r)^n-1
D=R*T - W=R*T
Volume=(4/3)pir^3

21. Isosceles Triangle
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
2 equal sides - 2 equal angles
A=[(B1+B2)*H]/2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

22. Distance/Work Formula
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
0 - -2 - -4 - ...
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
D=R*T - W=R*T

23. Combined Rates
1 - 3 - 5 - ...
Middle number (or average of 2) of set from smallest to largest
#successful events / total# possible outcomes
D/W=R1T1 + R2T2

24. Cylinders
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
An=A1(r)^n-1
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Middle number (or average of 2) of set from smallest to largest

25. 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
Volume=(4/3)pir^3
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

26. Sum of Interior Angles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
(distance between opposite vertices) - square root(L^2+W^2+H^2)
S=180(n-2)
Consists of all the elements that appear in both sets

27. Area of a Sector
Order matters - nPr=n! / (n-r)!
0 - -2 - -4 - ...
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
= (x degree / 360) pi*r^2

28. Even/Odd Results
(1/3)LW*H
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
x1y1 = x2y2
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

29. Combinations

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30. Arithmetic Sequence
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
x1y1 = x2y2
1 - 3 - 5 - ...
An=A1+(n-1)d

31. Union
D/W=R1T1 + R2T2
0 - -2 - -4 - ...
Consists of all of the elements that appear in either set without repeating elements
A=(3root3/2)r^2

32. Fundamental Counting Principle
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Multiply number of choices available in each option to get total number of options
= (x degree / 360) pi*r^2

33. Mixture Formula
2 equal sides - 2 equal angles
A=1/2bh
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
A=L*W - P=2L+2W - Diagonals equal length

34. Adding/Subtracting Exponents
(1/3)pir^2*h
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
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

35. Probability
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
#successful events / total# possible outcomes
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

36. Intersection
S-S-S - S-A-S - A-S-A
A=(3root3/2)r^2
D/W= (R1+R2)*T
Consists of all the elements that appear in both sets

37. Distance Formula
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
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]
A=S^2 - P=4S - Diagonal is root2 times side

38. Volume of Cone
Part/whole = %/100
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
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

39. Direct Variation
x1/y1 = x2/y2
A=S^2 - P=4S - Diagonal is root2 times side
= (x degree / 360) C
D/W=R1T1 + R2T2

40. Sum of Exterior Angles
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
The most frequently occurring number in a set
360
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

41. Volume of Prism
A=(3root3/2)r^2
(area of base)*height
(1/3)LW*H
1 - 3 - 5 - ...

42. Indirect Variation
Multiply number of choices available in each option to get total number of options
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
(distance between opposite vertices) - square root(L^2+W^2+H^2)
x1y1 = x2y2

43. Length on an Arc
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
= (x degree / 360) C
Middle number (or average of 2) of set from smallest to largest

44. Integer
(area of base)*height
Positive and negative whole numbers
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Middle number (or average of 2) of set from smallest to largest

45. Median
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
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
(area of base)*height

46. Area of a Triangle
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
A=1/2bh
An=A1(r)^n-1

47. Right Triangle
1 - 3 - 5 - ...
(1/3)LW*H
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(distance between opposite vertices) - square root(L^2+W^2+H^2)

48. Average Rate
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
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

49. Special Right Triangles
x1/y1 = x2/y2
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
D=R*T - W=R*T
An=A1(r)^n-1

50. Parallelograms
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
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
2 equal sides - 2 equal angles