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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 Cone
An=A1+(n-1)d
(1/3)pir^2*h
S=180(n-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

2. Mixture Formula
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Consists of all the elements that appear in both sets
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Square root[(x2-x1)^2 + (y2-y1)^2]

3. Direct Variation
x1/y1 = x2/y2
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

4. Sum of Exterior Angles
Order doesn't matter - nCr=n! / r!(n-r)!
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
1 - 3 - 5 - ...
360

5. Weighted Average
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
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^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(area of base)*height

6. Same Distance
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
(1/3)pir^2*h
([old-new]/old)*100%
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

7. Parallelograms
Consists of all of the elements that appear in either set without repeating elements
(area of base)*height
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

8. Rational Number
(1/3)pir^2*h
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

9. Distance Formula
Square root[(x2-x1)^2 + (y2-y1)^2]
Consists of all the elements that appear in both sets
= (x degree / 360) C
D=R*T - W=R*T

10. Area Hexagon
A=(3root3/2)r^2
([old-new]/old)*100%
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
0 - -2 - -4 - ...

11. Area Trapezoid
= (x degree / 360) pi*r^2
x1y1 = x2y2
Consists of all of the elements that appear in either set without repeating elements
A=[(B1+B2)*H]/2

12. Even Numbers
([old-new]/old)*100%
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
0 - -2 - -4 - ...
Positive and negative whole numbers

13. Indirect Variation
1 - 3 - 5 - ...
x1y1 = x2y2
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

14. Special Right Triangles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A=L*W - P=2L+2W - Diagonals equal length
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

15. Area of a Sector
(1/3)LW*H
(1/3)pir^2*h
= (x degree / 360) pi*r^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

16. Arithmetic Sequence
([old-new]/old)*100%
An=A1+(n-1)d
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
D=R*T - W=R*T

17. Odd Numbers
1 - 3 - 5 - ...
A=L*W - P=2L+2W - Diagonals equal length
Order doesn't matter - nCr=n! / r!(n-r)!
Positive and negative whole numbers

18. Congruent Triangles
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
S-S-S - S-A-S - A-S-A
Positive and negative whole numbers
1 - 3 - 5 - ...

19. Fundamental Counting Principle
= (x degree / 360) C
Multiply number of choices available in each option to get total number of options
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
#successful events / total# possible outcomes

20. Distance/Work Formula
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
D=R*T - W=R*T
Multiply number of choices available in each option to get total number of options
A=S^2 - P=4S - Diagonal is root2 times side

21. Real Wheel Formula
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
S=180(n-2)
Volume=(4/3)pir^3

22. Volume of Pyramid
Square root[(x2-x1)^2 + (y2-y1)^2]
Order matters - nPr=n! / (n-r)!
Consists of all of the elements that appear in either set without repeating elements
(1/3)LW*H

23. Percentage Change
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
A=L*W - P=2L+2W - Diagonals equal length
The most frequently occurring number in a set
([old-new]/old)*100%

24. Triangle Inequality
Consists of all of the elements that appear in either set without repeating elements
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
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
Multiply number of choices available in each option to get total number of options

25. Union
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
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
Consists of all of the elements that appear in either set without repeating elements
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

26. Square
2 equal sides - 2 equal angles
S=180(n-2)
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A=S^2 - P=4S - Diagonal is root2 times side

27. Intersection
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
#successful events / total# possible outcomes
Multiply number of choices available in each option to get total number of options
Consists of all the elements that appear in both sets

28. Integer
2 equal sides - 2 equal angles
Volume=(4/3)pir^3
Positive and negative whole numbers
(area of base)*height

29. Permutations
A=S^2 - P=4S - Diagonal is root2 times side
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
Order matters - nPr=n! / (n-r)!

30. Median
D/W=R1T1 + R2T2
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

31. Cylinders
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
0 - -2 - -4 - ...
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

32. Length on an Arc
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
= (x degree / 360) C
Multiply number of choices available in each option to get total number of options
= (x degree / 360) pi*r^2

33. Same Time
D/W= (R1+R2)*T
An=A1+(n-1)d
Positive and negative whole numbers
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

34. Even/Odd Results
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Square root[(x2-x1)^2 + (y2-y1)^2]
A=L*W - P=2L+2W - Diagonals equal length
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

35. Similar Triangles
x1/y1 = x2/y2
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
S-S-S - S-A-S - A-S-A

36. Exponent Rules
2 equal sides - 2 equal angles
(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
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

37. Equilateral Triangle
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
= (x degree / 360) C
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

38. Mode
An=A1+(n-1)d
The most frequently occurring number in a set
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

39. Geometric Sequences
#successful events / total# possible outcomes
Part/whole = %/100
Order matters - nPr=n! / (n-r)!
An=A1(r)^n-1

40. Same Rate
Consists of all the elements that appear in both sets
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
D=R*T - W=R*T
360

41. Combinations

42. Isosceles Triangle
2 equal sides - 2 equal angles
S-S-S - S-A-S - A-S-A
Consists of all the elements that appear in both sets
1 - 3 - 5 - ...

43. Area of a Triangle
A=1/2bh
A=(3root3/2)r^2
(area of base)*height
360

44. Rectangles
A=L*W - P=2L+2W - Diagonals equal length
An=A1+(n-1)d
= (x degree / 360) C
D/W= (R1+R2)*T

45. Adding/Subtracting Exponents
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
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
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(area of base)*height

46. Same Work
Order doesn't matter - nCr=n! / r!(n-r)!
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(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

47. Probability
D/W=R1T1 + R2T2
#successful events / total# possible outcomes
D/W= (R1+R2)*T
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

48. Combined Rates
Part/whole = %/100
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
D/W=R1T1 + R2T2

49. Right Triangle
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
D/W= (R1+R2)*T
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
Part/whole = %/100

50. Sum of Interior Angles
1 - 3 - 5 - ...
S=180(n-2)
Order matters - nPr=n! / (n-r)!
Square root[(x2-x1)^2 + (y2-y1)^2]