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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. Odd Numbers
1 - 3 - 5 - ...
A=(3root3/2)r^2
An=A1+(n-1)d
An=A1(r)^n-1

2. Combined Rates
A=[(B1+B2)*H]/2
A=S^2 - P=4S - Diagonal is root2 times side
Consists of all the elements that appear in both sets
D/W=R1T1 + R2T2

3. Real Wheel Formula
360
= (x degree / 360) pi*r^2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

4. Adding/Subtracting Exponents
([old-new]/old)*100%
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
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=L*W - P=2L+2W - Diagonals equal length

5. Volume of Cone
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
A=(3root3/2)r^2
(1/3)pir^2*h
Multiply number of choices available in each option to get total number of options

6. 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
0 - -2 - -4 - ...
Positive and negative whole numbers

7. Percentage Change
([old-new]/old)*100%
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
Part/whole = %/100
A=S^2 - P=4S - Diagonal is root2 times side

8. Cylinders
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
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Positive and negative whole numbers

9. Sum of Interior Angles
S=180(n-2)
1 - 3 - 5 - ...
A=S^2 - P=4S - Diagonal is root2 times side
A=(3root3/2)r^2

10. Fundamental Counting Principle
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Multiply number of choices available in each option to get total number of options
Order doesn't matter - nCr=n! / r!(n-r)!
#successful events / total# possible outcomes

11. Mode
A=[(B1+B2)*H]/2
(1/3)LW*H
The most frequently occurring number in a set
1 - 3 - 5 - ...

12. Mixture Formula
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
360

13. Distance Formula
Square root[(x2-x1)^2 + (y2-y1)^2]
([old-new]/old)*100%
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
A=(3root3/2)r^2

14. Union
Consists of all of the elements that appear in either set without repeating elements
#successful events / total# possible outcomes
0 - -2 - -4 - ...
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

15. Right Triangle
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
A=S^2 - P=4S - Diagonal is root2 times side

16. Same Rate
1 - 3 - 5 - ...
#successful events / total# possible outcomes
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Positive and negative whole numbers

17. Geometric Sequences
An=A1(r)^n-1
D=R*T - W=R*T
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

18. Even Numbers
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
0 - -2 - -4 - ...
Order doesn't matter - nCr=n! / r!(n-r)!
= (x degree / 360) pi*r^2

19. Probability
(distance between opposite vertices) - square root(L^2+W^2+H^2)
#successful events / total# possible outcomes
An=A1+(n-1)d
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

20. Area of a Triangle
(area of base)*height
A=1/2bh
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
#successful events / total# possible outcomes

21. Intersection
Consists of all the elements that appear in both sets
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
(distance between opposite vertices) - square root(L^2+W^2+H^2)
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

22. Even/Odd Results
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
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
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

23. Permutations
Order matters - nPr=n! / (n-r)!
Order doesn't matter - nCr=n! / r!(n-r)!
S=180(n-2)
Square root[(x2-x1)^2 + (y2-y1)^2]

24. Extension of the Pythagorean Theorem
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Middle number (or average of 2) of set from smallest to largest
S=180(n-2)

25. Parallelograms
The most frequently occurring number in a set
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Volume=(4/3)pir^3

26. Average Rate
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Part/whole = %/100
A=1/2bh
x1y1 = x2y2

27. Rational Number
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
The most frequently occurring number in a set
Middle number (or average of 2) of set from smallest to largest
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

28. Volume of Prism
D=R*T - W=R*T
(1/3)LW*H
(area of base)*height
Middle number (or average of 2) of set from smallest to largest

29. Area Trapezoid
D/W= (R1+R2)*T
Multiply number of choices available in each option to get total number of options
A=[(B1+B2)*H]/2
A=L*W - P=2L+2W - Diagonals equal length

30. Volume of Sphere
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
x1/y1 = x2/y2
#successful events / total# possible outcomes
Volume=(4/3)pir^3

31. Sum of Exterior Angles
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
360
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Positive and negative whole numbers

32. Median
Middle number (or average of 2) of set from smallest to largest
x1y1 = x2y2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Volume=(4/3)pir^3

33. Equilateral Triangle
= (x degree / 360) pi*r^2
Order doesn't matter - nCr=n! / r!(n-r)!
x1/y1 = x2/y2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

34. Area of a Sector
= (x degree / 360) pi*r^2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
S-S-S - S-A-S - A-S-A
The most frequently occurring number in a set

35. Arithmetic Sequence
([old-new]/old)*100%
An=A1+(n-1)d
A=[(B1+B2)*H]/2
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

36. Exponent Rules
x1/y1 = x2/y2
(1/3)LW*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
The most frequently occurring number in a set

37. 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
S-S-S - S-A-S - A-S-A
The most frequently occurring number in a set
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

38. Length on an Arc
D/W= (R1+R2)*T
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
(1/3)LW*H
= (x degree / 360) C

39. Special Right Triangles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
(1/3)pir^2*h
The most frequently occurring number in a set
= (x degree / 360) C

40. Distance/Work Formula
An=A1(r)^n-1
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
2 equal sides - 2 equal angles

41. Weighted Average
(1/3)pir^2*h
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
The most frequently occurring number in a set
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

42. Square
Order matters - nPr=n! / (n-r)!
(1/3)pir^2*h
A=S^2 - P=4S - Diagonal is root2 times side
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

43. Rectangles
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
A=(3root3/2)r^2
A=L*W - P=2L+2W - Diagonals equal length

44. Same Distance
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
A=[(B1+B2)*H]/2
Consists of all of the elements that appear in either set without repeating elements

45. Volume of Pyramid
(1/3)LW*H
x1/y1 = x2/y2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

46. Isosceles Triangle
2 equal sides - 2 equal angles
360
0 - -2 - -4 - ...
Consists of all of the elements that appear in either set without repeating elements

47. Percents
An=A1(r)^n-1
Order doesn't matter - nCr=n! / r!(n-r)!
D/W= (R1+R2)*T
Part/whole = %/100

48. Congruent Triangles
0 - -2 - -4 - ...
S-S-S - S-A-S - A-S-A
(area of base)*height
An=A1+(n-1)d

49. Weighted Averages
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Consists of all of the elements that appear in either set without repeating elements
Middle number (or average of 2) of set from smallest to largest
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

50. Same Work
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
= (x degree / 360) C
A=S^2 - P=4S - Diagonal is root2 times side
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

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