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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. Same Distance
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A=S^2 - P=4S - Diagonal is root2 times side

2. Direct Variation
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
x1y1 = x2y2
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
x1/y1 = x2/y2

3. Similar Triangles
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
1 - 3 - 5 - ...
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

4. Triangle Inequality
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
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
x1y1 = x2y2
D=R*T - W=R*T

5. Real Wheel Formula
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Positive and negative whole numbers
(1/3)pir^2*h
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

6. Square
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
A=[(B1+B2)*H]/2
D=R*T - W=R*T
A=S^2 - P=4S - Diagonal is root2 times side

7. Rational Number
1 - 3 - 5 - ...
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
0 - -2 - -4 - ...

8. Length on an Arc
= (x degree / 360) C
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
A=L*W - P=2L+2W - Diagonals equal length
An=A1+(n-1)d

9. Congruent Triangles
S-S-S - S-A-S - A-S-A
#successful events / total# possible outcomes
= (x degree / 360) pi*r^2
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

10. Rectangles
D/W=R1T1 + R2T2
0 - -2 - -4 - ...
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

11. Exponent Rules
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
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
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

12. Area Trapezoid
S=180(n-2)
A=[(B1+B2)*H]/2
2 equal sides - 2 equal angles
A=S^2 - P=4S - Diagonal is root2 times side

13. Permutations
([old-new]/old)*100%
Order matters - nPr=n! / (n-r)!
0 - -2 - -4 - ...
D/W=R1T1 + R2T2

14. Fundamental Counting Principle
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
1 - 3 - 5 - ...
S-S-S - S-A-S - A-S-A
Multiply number of choices available in each option to get total number of options

15. Odd Numbers
The most frequently occurring number in a set
D/W= (R1+R2)*T
1 - 3 - 5 - ...
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

16. Combined Rates
D/W=R1T1 + R2T2
A=1/2bh
The most frequently occurring number in a set
Multiply number of choices available in each option to get total number of options

17. Average Rate
(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
A=1/2bh
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

18. Indirect Variation
Consists of all of the elements that appear in either set without repeating elements
x1y1 = x2y2
Square root[(x2-x1)^2 + (y2-y1)^2]
Multiply number of choices available in each option to get total number of options

19. Geometric Sequences
Multiply number of choices available in each option to get total number of options
Positive and negative whole numbers
An=A1(r)^n-1
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

20. Mode
The most frequently occurring number in a set
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=L*W - P=2L+2W - Diagonals equal length
A=1/2bh

21. Same Work
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
An=A1(r)^n-1

22. Combinations

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23. Even/Odd Results
Positive and negative whole numbers
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
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

24. Volume of Cone
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
(1/3)pir^2*h
(area of base)*height

25. Median
Middle number (or average of 2) of set from smallest to largest
(1/3)LW*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
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

26. Isosceles Triangle
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
D/W=R1T1 + R2T2
(1/3)pir^2*h
2 equal sides - 2 equal angles

27. Right Triangle
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
Positive and negative whole numbers

28. Intersection
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
An=A1(r)^n-1
Consists of all the elements that appear in both sets
Part/whole = %/100

29. Volume of Prism
(1/3)pir^2*h
(area of base)*height
x1/y1 = x2/y2
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

30. Same Rate
Multiply number of choices available in each option to get total number of options
([old-new]/old)*100%
(1/3)LW*H
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

31. Union
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
Consists of all of the elements that appear in either set without repeating elements
Part/whole = %/100
360

32. Volume of Sphere
Volume=(4/3)pir^3
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
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

33. Volume of Pyramid
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
(1/3)LW*H
Volume=(4/3)pir^3
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

34. Adding/Subtracting Exponents
Order matters - nPr=n! / (n-r)!
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
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=1/2bh

35. Area Hexagon
A=(3root3/2)r^2
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
2 equal sides - 2 equal angles
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

36. Equilateral Triangle
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
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
(area of base)*height
1 - 3 - 5 - ...

37. Sum of Exterior Angles
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
360

38. Sum of Interior Angles
S=180(n-2)
A=L*W - P=2L+2W - Diagonals equal length
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

39. Percentage Change
A=1/2bh
A=S^2 - P=4S - Diagonal is root2 times side
([old-new]/old)*100%
x1y1 = x2y2

40. Extension of the Pythagorean Theorem
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
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
(distance between opposite vertices) - square root(L^2+W^2+H^2)
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

41. Distance/Work Formula
D=R*T - W=R*T
A=(3root3/2)r^2
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 number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

42. Integer
T(up)=D/R1 T(down)=D/R2 - Add and solve for 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
The most frequently occurring number in a set
Positive and negative whole numbers

43. Percents
Part/whole = %/100
A=1/2bh
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

44. Distance Formula
Square root[(x2-x1)^2 + (y2-y1)^2]
An=A1+(n-1)d
360
(area of base)*height

45. Weighted Averages
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Order matters - nPr=n! / (n-r)!
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

46. Parallelograms
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
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
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

47. Special Right Triangles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Middle number (or average of 2) of set from smallest to largest
([old-new]/old)*100%
Order doesn't matter - nCr=n! / r!(n-r)!

48. Even Numbers
#successful events / total# possible outcomes
Positive and negative whole numbers
0 - -2 - -4 - ...
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

49. Area of a Sector
= (x degree / 360) C
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
= (x degree / 360) pi*r^2
An=A1(r)^n-1

50. Weighted Average
Part/whole = %/100
Positive and negative whole numbers
Order matters - nPr=n! / (n-r)!
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

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SAT Math Formulas

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