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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. Parallelograms
The most frequently occurring number in a set
(distance between opposite vertices) - square root(L^2+W^2+H^2)
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

2. Indirect Variation
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
x1y1 = x2y2
A=L*W - P=2L+2W - Diagonals equal length
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

3. Adding/Subtracting Exponents
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
Order doesn't matter - nCr=n! / r!(n-r)!
A=L*W - P=2L+2W - Diagonals equal length

4. Union
Consists of all of the elements that appear in either set without repeating elements
D=R*T - W=R*T
#successful events / total# possible outcomes
0 - -2 - -4 - ...

5. Distance/Work Formula
D=R*T - W=R*T
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

6. Probability
Middle number (or average of 2) of set from smallest to largest
D/W=R1T1 + R2T2
#successful events / total# possible outcomes
S=180(n-2)

7. Special Right Triangles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Middle number (or average of 2) of set from smallest to largest
A=(3root3/2)r^2
0 - -2 - -4 - ...

8. Similar Triangles
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
A=1/2bh
A=S^2 - P=4S - Diagonal is root2 times side
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

9. Mode
The most frequently occurring number in a set
#successful events / total# possible outcomes
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

10. Extension of the Pythagorean Theorem
(distance between opposite vertices) - square root(L^2+W^2+H^2)
([old-new]/old)*100%
D/W= (R1+R2)*T
(area of base)*height

11. Area Trapezoid
360
Part/whole = %/100
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
A=[(B1+B2)*H]/2

12. Volume of Pyramid
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
= (x degree / 360) pi*r^2
(1/3)LW*H
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

13. Percentage Change
([old-new]/old)*100%
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
S-S-S - S-A-S - A-S-A
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

14. Real Wheel Formula
#successful events / total# possible outcomes
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

15. Length on an Arc
A=L*W - P=2L+2W - Diagonals equal length
= (x degree / 360) C
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
A=S^2 - P=4S - Diagonal is root2 times side

16. Percents
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Part/whole = %/100
#successful events / total# possible outcomes
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

17. Volume of Sphere
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=(4/3)pir^3
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

18. Same Time
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)
D/W= (R1+R2)*T
A=(3root3/2)r^2

19. Combined Rates
Volume=(4/3)pir^3
D/W=R1T1 + R2T2
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
S-S-S - S-A-S - A-S-A

20. Equilateral Triangle
S-S-S - S-A-S - A-S-A
(1/3)LW*H
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

21. Odd Numbers
(1/3)pir^2*h
1 - 3 - 5 - ...
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

22. Combinations

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23. Average Rate
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
A=L*W - P=2L+2W - Diagonals equal length
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

24. Area of a Triangle
A=1/2bh
An=A1+(n-1)d
Consists of all of the elements that appear in either set without repeating elements
2 equal sides - 2 equal angles

25. Volume of Cone
(1/3)pir^2*h
(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
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

26. 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
x1/y1 = x2/y2
Multiply number of choices available in each option to get total number of options
Part/whole = %/100

27. Even/Odd Results
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
1 - 3 - 5 - ...
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Square root[(x2-x1)^2 + (y2-y1)^2]

28. Congruent Triangles
S-S-S - S-A-S - A-S-A
#successful events / total# possible outcomes
D=R*T - W=R*T
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

29. Exponent Rules
Middle number (or average of 2) of set from smallest to largest
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
2 equal sides - 2 equal angles
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

30. Same Distance
Volume=(4/3)pir^3
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
(area of base)*height
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

31. Geometric Sequences
An=A1(r)^n-1
A=L*W - P=2L+2W - Diagonals equal length
Order matters - nPr=n! / (n-r)!
x1/y1 = x2/y2

32. Integer
Order doesn't matter - nCr=n! / r!(n-r)!
Positive and negative whole numbers
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
D/W=R1T1 + R2T2

33. Isosceles Triangle
2 equal sides - 2 equal angles
D/W= (R1+R2)*T
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

34. Distance Formula
A=[(B1+B2)*H]/2
D/W=R1T1 + R2T2
Square root[(x2-x1)^2 + (y2-y1)^2]
S-S-S - S-A-S - A-S-A

35. Direct Variation
1 - 3 - 5 - ...
= (x degree / 360) C
A=S^2 - P=4S - Diagonal is root2 times side
x1/y1 = x2/y2

36. Same Work
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
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
#successful events / total# possible outcomes

37. Same Rate
Part/whole = %/100
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
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

38. Intersection
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
S=180(n-2)
Square root[(x2-x1)^2 + (y2-y1)^2]
Consists of all the elements that appear in both sets

39. Median
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Middle number (or average of 2) of set from smallest to largest
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
A=[(B1+B2)*H]/2

40. 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
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
0 - -2 - -4 - ...
(area of base)*height

41. Permutations
Square root[(x2-x1)^2 + (y2-y1)^2]
(1/3)pir^2*h
Order matters - nPr=n! / (n-r)!
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

42. Sum of Exterior Angles
A=(3root3/2)r^2
D/W=R1T1 + R2T2
360
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

43. Sum of Interior Angles
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
(1/3)pir^2*h
D=R*T - W=R*T
S=180(n-2)

44. Weighted Averages
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
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)(number1) + (avg2)(number2) = (avgT)(numberT)

45. Even Numbers
D/W= (R1+R2)*T
A=L*W - P=2L+2W - Diagonals equal length
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
0 - -2 - -4 - ...

46. Rectangles
([old-new]/old)*100%
#successful events / total# possible outcomes
Multiply number of choices available in each option to get total number of options
A=L*W - P=2L+2W - Diagonals equal length

47. Arithmetic Sequence
The most frequently occurring number in a set
An=A1+(n-1)d
A=L*W - P=2L+2W - Diagonals equal length
S-S-S - S-A-S - A-S-A

48. Mixture Formula
= (x degree / 360) pi*r^2
(1/3)LW*H
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

49. Area Hexagon
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
A=(3root3/2)r^2

50. Volume of Prism
D/W=R1T1 + R2T2
(area of base)*height
x1y1 = x2y2
A=[(B1+B2)*H]/2