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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. Volume of Prism
1 - 3 - 5 - ...
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
(area of base)*height
S=180(n-2)

2. Extension of the Pythagorean Theorem
An=A1+(n-1)d
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Volume=(4/3)pir^3
A=(3root3/2)r^2

3. Real Wheel Formula
0 - -2 - -4 - ...
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Consists of all of the elements that appear in either set without repeating elements
([old-new]/old)*100%

4. Cylinders
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Consists of all the elements that appear in both sets
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
([old-new]/old)*100%

5. Sum of Exterior Angles
360
Consists of all the elements that appear in both sets
(area of base)*height
= (x degree / 360) pi*r^2

6. Area of a Sector
x1/y1 = x2/y2
Order doesn't matter - nCr=n! / r!(n-r)!
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
= (x degree / 360) pi*r^2

7. Distance Formula
Square root[(x2-x1)^2 + (y2-y1)^2]
#successful events / total# possible outcomes
A=1/2bh
D=R*T - W=R*T

8. Average Rate
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
(1/3)pir^2*h
An=A1+(n-1)d
A=[(B1+B2)*H]/2

9. Length on an Arc
= (x degree / 360) C
D=R*T - W=R*T
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

10. Sum of Interior Angles
Volume=(4/3)pir^3
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
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=180(n-2)

11. Congruent Triangles
A=L*W - P=2L+2W - Diagonals equal length
S-S-S - S-A-S - A-S-A
Volume=(4/3)pir^3
A=(3root3/2)r^2

12. Parallelograms
Volume=(4/3)pir^3
An=A1+(n-1)d
S=180(n-2)
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

13. Same Rate
1 - 3 - 5 - ...
The most frequently occurring number in a set
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
A=L*W - P=2L+2W - Diagonals equal length

14. Combinations
D=R*T - W=R*T
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
= (x degree / 360) C
Order doesn't matter - nCr=n! / r!(n-r)!

15. Volume of Sphere
Volume=(4/3)pir^3
The most frequently occurring number in a set
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
([old-new]/old)*100%

16. Same Work
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
0 - -2 - -4 - ...
(1/3)pir^2*h
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

17. Fundamental Counting Principle
2 equal sides - 2 equal angles
Multiply number of choices available in each option to get total number of options
A=[(B1+B2)*H]/2
A=S^2 - P=4S - Diagonal is root2 times side

18. Odd Numbers
Part/whole = %/100
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
1 - 3 - 5 - ...
Consists of all the elements that appear in both sets

19. Similar Triangles
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
#successful events / total# possible outcomes
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

20. Isosceles Triangle
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
2 equal sides - 2 equal angles
Middle number (or average of 2) of set from smallest to largest

21. Arithmetic Sequence
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
An=A1+(n-1)d
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
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

22. Permutations
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Order matters - nPr=n! / (n-r)!
A=S^2 - P=4S - Diagonal is root2 times side
Part/whole = %/100

23. Distance/Work Formula
Part/whole = %/100
S-S-S - S-A-S - A-S-A
D=R*T - W=R*T
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

24. Probability
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
An=A1(r)^n-1
#successful events / total# possible outcomes

25. Square
A=(3root3/2)r^2
S=180(n-2)
A=S^2 - P=4S - Diagonal is root2 times side
(1/3)pir^2*h

26. Even/Odd Results
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
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
= (x degree / 360) C

27. Weighted Average
x1y1 = x2y2
Square root[(x2-x1)^2 + (y2-y1)^2]
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

28. Percents
An=A1(r)^n-1
Part/whole = %/100
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Multiply number of choices available in each option to get total number of options

29. Rational Number
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
x1y1 = x2y2
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

30. Right Triangle
= (x degree / 360) C
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(area of base)*height
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

31. Intersection
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Consists of all the elements that appear in both sets
Multiply number of choices available in each option to get total number of options
An=A1(r)^n-1

32. Median
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Middle number (or average of 2) of set from smallest to largest
360
A=L*W - P=2L+2W - Diagonals equal length

33. Integer
2 equal sides - 2 equal angles
Positive and negative whole numbers
D=R*T - W=R*T
A=[(B1+B2)*H]/2

34. Mode
Multiply number of choices available in each option to get total number of options
The most frequently occurring number in a set
A=(3root3/2)r^2
([old-new]/old)*100%

35. Even Numbers
Part/whole = %/100
A=S^2 - P=4S - Diagonal is root2 times side
Multiply number of choices available in each option to get total number of options
0 - -2 - -4 - ...

36. Exponent Rules
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
= (x degree / 360) C
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
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

37. Volume of Cone
Multiply number of choices available in each option to get total number of options
(1/3)pir^2*h
2 equal sides - 2 equal angles
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

38. Direct Variation
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
x1y1 = x2y2
x1/y1 = x2/y2
A=1/2bh

39. Equilateral Triangle
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
360
D/W=R1T1 + R2T2
2 equal sides - 2 equal angles

40. Volume of Pyramid
D/W= (R1+R2)*T
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
(1/3)LW*H

41. 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
A=1/2bh
An=A1(r)^n-1
2 equal sides - 2 equal angles

42. Special Right Triangles
#successful events / total# possible outcomes
= (x degree / 360) pi*r^2
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Square root[(x2-x1)^2 + (y2-y1)^2]

43. Geometric Sequences
An=A1(r)^n-1
([old-new]/old)*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
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

44. Rectangles
A=L*W - P=2L+2W - Diagonals equal length
A=S^2 - P=4S - Diagonal is root2 times side
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
The most frequently occurring number in a set

45. Union
Consists of all of the elements that appear in either set without repeating elements
(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
(1/3)pir^2*h

46. Weighted Averages
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
The most frequently occurring number in a set
= (x degree / 360) C
S=180(n-2)

47. Percentage Change
([old-new]/old)*100%
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
360

48. Indirect Variation
x1y1 = x2y2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
= (x degree / 360) pi*r^2
(distance between opposite vertices) - square root(L^2+W^2+H^2)

49. Combined Rates
D/W=R1T1 + R2T2
2 equal sides - 2 equal angles
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Order matters - nPr=n! / (n-r)!

50. Area Trapezoid
Consists of all of the elements that appear in either set without repeating elements
360
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=[(B1+B2)*H]/2

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