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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. Distance Formula
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
#successful events / total# possible outcomes
Square root[(x2-x1)^2 + (y2-y1)^2]

2. Same Work
(1/3)pir^2*h
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
360
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

3. Right Triangle
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
A=(3root3/2)r^2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

4. Triangle Inequality
(distance between opposite vertices) - square root(L^2+W^2+H^2)
x1/y1 = x2/y2
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
An=A1(r)^n-1

5. Distance/Work Formula
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
D=R*T - W=R*T
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
S=180(n-2)

6. Mode
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
The most frequently occurring number in a set
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

7. Odd Numbers
1 - 3 - 5 - ...
(1/3)LW*H
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Volume=(4/3)pir^3

8. Permutations
A=L*W - P=2L+2W - Diagonals equal length
([old-new]/old)*100%
Order matters - nPr=n! / (n-r)!
Square root[(x2-x1)^2 + (y2-y1)^2]

9. Congruent Triangles
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
A=[(B1+B2)*H]/2
S-S-S - S-A-S - A-S-A
= (x degree / 360) pi*r^2

10. Area Hexagon
Consists of all the elements that appear in both sets
A=(3root3/2)r^2
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
A=L*W - P=2L+2W - Diagonals equal length

11. Isosceles Triangle
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
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Part/whole = %/100
2 equal sides - 2 equal angles

12. Arithmetic Sequence
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
An=A1+(n-1)d
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=[(B1+B2)*H]/2

13. Mixture Formula
D=R*T - W=R*T
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
360

14. Same Time
Order matters - nPr=n! / (n-r)!
D/W= (R1+R2)*T
A=(3root3/2)r^2
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

15. Similar Triangles
S-S-S - S-A-S - A-S-A
Order matters - nPr=n! / (n-r)!
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
1 - 3 - 5 - ...

16. Combinations

17. Exponent Rules
D/W=R1T1 + R2T2
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
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

18. Equilateral Triangle
(distance between opposite vertices) - square root(L^2+W^2+H^2)
([old-new]/old)*100%
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

19. Weighted Averages
D=R*T - W=R*T
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Consists of all of the elements that appear in either set without repeating elements
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

20. Rectangles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
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
An=A1+(n-1)d
A=L*W - P=2L+2W - Diagonals equal length

21. Extension of the Pythagorean Theorem
Consists of all the elements that appear in both sets
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Positive and negative whole numbers
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

22. Volume of Pyramid
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
(1/3)LW*H
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
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

23. Rational Number
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
Middle number (or average of 2) of set from smallest to largest
Multiply number of choices available in each option to get total number of options

24. Probability
x1y1 = x2y2
Part/whole = %/100
#successful events / total# possible outcomes
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

25. 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
Consists of all the elements that appear in both sets
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
An=A1+(n-1)d

26. Area of a Triangle
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A=1/2bh
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
x1/y1 = x2/y2

27. Median
A=[(B1+B2)*H]/2
Middle number (or average of 2) of set from smallest to largest
2 equal sides - 2 equal angles
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

28. Geometric Sequences
(1/3)pir^2*h
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A=L*W - P=2L+2W - Diagonals equal length
An=A1(r)^n-1

29. Indirect Variation
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Volume=(4/3)pir^3
Order matters - nPr=n! / (n-r)!
x1y1 = x2y2

30. Intersection
Consists of all the elements that appear in both sets
Positive and negative whole numbers
A=[(B1+B2)*H]/2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

31. Volume of Cone
(1/3)pir^2*h
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
A=L*W - P=2L+2W - Diagonals equal length
x1y1 = x2y2

32. Fundamental Counting Principle
Order doesn't matter - nCr=n! / r!(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
A=L*W - P=2L+2W - Diagonals equal length
Multiply number of choices available in each option to get total number of options

33. Combined Rates
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
D/W=R1T1 + R2T2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

34. Union
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Consists of all of the elements that appear in either set without repeating elements
Multiply number of choices available in each option to get total number of options
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

35. Same Distance
= (x degree / 360) pi*r^2
Order matters - nPr=n! / (n-r)!
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

36. Area Trapezoid
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
(area of base)*height
A=[(B1+B2)*H]/2
Consists of all of the elements that appear in either set without repeating elements

37. Even Numbers
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
([old-new]/old)*100%
2 equal sides - 2 equal angles
0 - -2 - -4 - ...

38. Parallelograms
= (x degree / 360) C
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)
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

39. Real Wheel Formula
360
#successful events / total# possible outcomes
Multiply number of choices available in each option to get total number of options
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

40. Length on an Arc
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
An=A1+(n-1)d
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
= (x degree / 360) C

41. Percents
Part/whole = %/100
(distance between opposite vertices) - square root(L^2+W^2+H^2)
(1/3)LW*H
= (x degree / 360) pi*r^2

42. Sum of Exterior Angles
2 equal sides - 2 equal angles
360
An=A1+(n-1)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

43. Cylinders
(1/3)LW*H
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
Square root[(x2-x1)^2 + (y2-y1)^2]

44. Average Rate
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

45. Volume of Sphere
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
Volume=(4/3)pir^3
(area of base)*height
S=180(n-2)

46. Same Rate
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
(1/3)LW*H
2 equal sides - 2 equal angles

47. Direct Variation
0 - -2 - -4 - ...
x1/y1 = x2/y2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

48. Percentage Change
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
(area of base)*height
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
([old-new]/old)*100%

49. Special Right Triangles
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Order doesn't matter - nCr=n! / r!(n-r)!
A=(3root3/2)r^2

50. Area of a Sector
Part/whole = %/100
Volume=(4/3)pir^3
= (x degree / 360) pi*r^2
(area of base)*height