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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 Pyramid
#successful events / total# possible outcomes
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
(1/3)LW*H

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

3. Even/Odd Results
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
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Middle number (or average of 2) of set from smallest to largest

4. Isosceles Triangle
Part/whole = %/100
Volume=(4/3)pir^3
2 equal sides - 2 equal angles
x1y1 = x2y2

5. Percentage Change
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
([old-new]/old)*100%
(1/3)LW*H
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

6. Equilateral Triangle
D/W= (R1+R2)*T
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Part/whole = %/100
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

7. Permutations
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
Part/whole = %/100
Order matters - nPr=n! / (n-r)!
S-S-S - S-A-S - A-S-A

8. Mode
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
A=1/2bh
1 - 3 - 5 - ...
The most frequently occurring number in a set

9. Right Triangle
= (x degree / 360) pi*r^2
The most frequently occurring number in a set
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

10. Even Numbers
0 - -2 - -4 - ...
An=A1+(n-1)d
(distance between opposite vertices) - square root(L^2+W^2+H^2)
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

11. Direct Variation
x1/y1 = x2/y2
([old-new]/old)*100%
= (x degree / 360) C
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

12. Volume of Cone
360
A=L*W - P=2L+2W - Diagonals equal length
= (x degree / 360) pi*r^2
(1/3)pir^2*h

13. Volume of Prism
(area of base)*height
Consists of all the elements that appear in both sets
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

14. Parallelograms
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Square root[(x2-x1)^2 + (y2-y1)^2]
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

15. Square
Part/whole = %/100
Volume=(4/3)pir^3
The most frequently occurring number in a set
A=S^2 - P=4S - Diagonal is root2 times side

16. Weighted Average
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
D/W=R1T1 + R2T2
x1/y1 = x2/y2

17. Integer
Order matters - nPr=n! / (n-r)!
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
Positive and negative whole numbers
A=[(B1+B2)*H]/2

18. Area Trapezoid
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
= (x degree / 360) pi*r^2
A=[(B1+B2)*H]/2

19. Area of a Sector
Multiply number of choices available in each option to get total number of options
= (x degree / 360) pi*r^2
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
Positive and negative whole numbers

20. Percents
#successful events / total# possible outcomes
(area of base)*height
Part/whole = %/100
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

21. Sum of Exterior Angles
D/W= (R1+R2)*T
Volume=(4/3)pir^3
360
An=A1(r)^n-1

22. Distance/Work Formula
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
([old-new]/old)*100%
Order matters - nPr=n! / (n-r)!

23. Same Work
D/W=R1T1 + R2T2
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Square root[(x2-x1)^2 + (y2-y1)^2]
Positive and negative whole numbers

24. Probability
#successful events / total# possible outcomes
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

25. Mixture Formula
A=S^2 - P=4S - Diagonal is root2 times side
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
= (x degree / 360) pi*r^2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

26. Special Right Triangles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
An=A1(r)^n-1
A=L*W - P=2L+2W - Diagonals equal length
D/W=R1T1 + R2T2

27. Same Distance
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Order doesn't matter - nCr=n! / r!(n-r)!
x1y1 = x2y2
Middle number (or average of 2) of set from smallest to largest

28. Geometric Sequences
Multiply number of choices available in each option to get total number of options
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=S^2 - P=4S - Diagonal is root2 times side
An=A1(r)^n-1

29. Exponent Rules
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
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)LW*H

30. Real Wheel Formula
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
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Positive and negative whole numbers
Consists of all of the elements that appear in either set without repeating elements

31. Rational Number
x1y1 = x2y2
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
A=1/2bh
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

32. Same Rate
= (x degree / 360) pi*r^2
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
(area of base)*height

33. Sum of Interior Angles
2 equal sides - 2 equal angles
= (x degree / 360) pi*r^2
S=180(n-2)
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

34. Volume of Sphere
S-S-S - S-A-S - A-S-A
Multiply number of choices available in each option to get total number of options
([old-new]/old)*100%
Volume=(4/3)pir^3

35. Average Rate
A=1/2bh
(area of base)*height
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
= (x degree / 360) C

36. Cylinders
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
= (x degree / 360) pi*r^2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
S-S-S - S-A-S - A-S-A

37. Adding/Subtracting Exponents
An=A1+(n-1)d
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
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

38. Distance Formula
Square root[(x2-x1)^2 + (y2-y1)^2]
Part/whole = %/100
An=A1(r)^n-1
A=L*W - P=2L+2W - Diagonals equal length

39. Length on an Arc
Square root[(x2-x1)^2 + (y2-y1)^2]
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
= (x degree / 360) C
x1/y1 = x2/y2

40. Union
D/W=R1T1 + R2T2
Consists of all of the elements that appear in either set without repeating elements
S-S-S - S-A-S - A-S-A
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

41. Similar Triangles
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
Positive and negative whole numbers
An=A1(r)^n-1
Order doesn't matter - nCr=n! / r!(n-r)!

42. Extension of the Pythagorean Theorem
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
D=R*T - W=R*T
(distance between opposite vertices) - square root(L^2+W^2+H^2)
A=1/2bh

43. Area Hexagon
(1/3)LW*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
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A=(3root3/2)r^2

44. Triangle Inequality
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
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
= (x degree / 360) pi*r^2

45. Combined Rates
Multiply number of choices available in each option to get total number of options
Positive and negative whole numbers
D/W=R1T1 + R2T2
A=[(B1+B2)*H]/2

46. Congruent Triangles
S-S-S - S-A-S - A-S-A
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
A=1/2bh
= (x degree / 360) pi*r^2

47. Weighted Averages
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
0 - -2 - -4 - ...
S=180(n-2)
Consists of all the elements that appear in both sets

48. Intersection
The most frequently occurring number in a set
= (x degree / 360) C
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
Consists of all the elements that appear in both sets

49. Odd Numbers
Consists of all the elements that appear in both sets
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
1 - 3 - 5 - ...
A=L*W - P=2L+2W - Diagonals equal length

50. Combinations

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