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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.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Even/Odd Results
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
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
Volume=(4/3)pir^3
0 - -2 - -4 - ...

2. Sum of Exterior Angles
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
(area of base)*height
360
x1/y1 = x2/y2

3. Adding/Subtracting Exponents
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
(1/3)pir^2*h
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
(area of base)*height

4. Combined Rates
Consists of all the elements that appear in both sets
D/W=R1T1 + R2T2
2 equal sides - 2 equal angles
Consists of all of the elements that appear in either set without repeating elements

5. Volume of Pyramid
(1/3)LW*H
Consists of all the elements that appear in both sets
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

6. Volume of Sphere
Volume=(4/3)pir^3
x1y1 = x2y2
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
Positive and negative whole numbers

7. 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
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
An=A1+(n-1)d

8. Indirect Variation
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
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=L*W - P=2L+2W - Diagonals equal length

9. Length on an Arc
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Positive and negative whole numbers
x1/y1 = x2/y2
= (x degree / 360) C

10. Parallelograms
x1/y1 = x2/y2
S=180(n-2)
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

11. Odd Numbers
D/W=R1T1 + R2T2
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Volume=(4/3)pir^3
1 - 3 - 5 - ...

12. Rectangles
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
1 - 3 - 5 - ...
A=L*W - P=2L+2W - Diagonals equal length
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

13. Direct Variation
x1/y1 = x2/y2
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
S-S-S - S-A-S - A-S-A
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

14. Right Triangle
A=(3root3/2)r^2
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
1 - 3 - 5 - ...
(distance between opposite vertices) - square root(L^2+W^2+H^2)

15. Distance/Work Formula
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)
D=R*T - W=R*T
Consists of all the elements that appear in both sets

16. Weighted Averages
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
S=180(n-2)
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
(area of base)*height

17. Area of a Triangle
S=180(n-2)
A=1/2bh
360
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

18. Percentage Change
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
([old-new]/old)*100%
Order doesn't matter - nCr=n! / r!(n-r)!
A=1/2bh

19. Mode
D=R*T - W=R*T
Part/whole = %/100
The most frequently occurring number in a set
(1/3)pir^2*h

20. Percents
Part/whole = %/100
Positive and negative whole numbers
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

21. Fundamental Counting Principle
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
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
2 equal sides - 2 equal angles

22. Real Wheel Formula
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Multiply number of choices available in each option to get total number of options
0 - -2 - -4 - ...
S-S-S - S-A-S - A-S-A

23. Area of a Sector
360
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
Part/whole = %/100
= (x degree / 360) pi*r^2

24. Probability
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
#successful events / total# possible outcomes
Order doesn't matter - nCr=n! / r!(n-r)!

25. Square
x1y1 = x2y2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A=S^2 - P=4S - Diagonal is root2 times side
(distance between opposite vertices) - square root(L^2+W^2+H^2)

26. Union
= (x degree / 360) pi*r^2
Consists of all of the elements that appear in either set without repeating elements
([old-new]/old)*100%
S-S-S - S-A-S - A-S-A

27. Integer
Positive and negative whole numbers
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
360

28. Geometric Sequences
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
A=L*W - P=2L+2W - Diagonals equal length
An=A1(r)^n-1

29. Similar 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
x1y1 = x2y2
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

30. Volume of Prism
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=(4/3)pir^3
Consists of all the elements that appear in both sets
(area of base)*height

31. Cylinders
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
D/W=R1T1 + R2T2
S-S-S - S-A-S - A-S-A
A=L*W - P=2L+2W - Diagonals equal length

32. Average Rate
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Multiply number of choices available in each option to get total number of options
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
D/W=R1T1 + R2T2

33. Combinations

34. Area Trapezoid
A=[(B1+B2)*H]/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
D/W= (R1+R2)*T
D=R*T - W=R*T

35. Same Distance
Volume=(4/3)pir^3
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
A=(3root3/2)r^2
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

36. Sum of Interior Angles
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Middle number (or average of 2) of set from smallest to largest
S=180(n-2)
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

37. Distance Formula
Consists of all of the elements that appear in either set without repeating elements
S-S-S - S-A-S - A-S-A
Square root[(x2-x1)^2 + (y2-y1)^2]
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

38. Weighted Average
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
D/W=R1T1 + R2T2
= (x degree / 360) C
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

39. Area Hexagon
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
A=(3root3/2)r^2
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
1 - 3 - 5 - ...

40. Arithmetic Sequence
1 - 3 - 5 - ...
(1/3)pir^2*h
D=R*T - W=R*T
An=A1+(n-1)d

41. Extension of the Pythagorean Theorem
(distance between opposite vertices) - square root(L^2+W^2+H^2)
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
= (x degree / 360) C
#successful events / total# possible outcomes

42. Isosceles Triangle
2 equal sides - 2 equal angles
360
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
(1/3)LW*H

43. Intersection
x1/y1 = x2/y2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Consists of all the elements that appear in both sets
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

44. Rational Number
#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
= (x degree / 360) pi*r^2
An=A1+(n-1)d

45. Same Work
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
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Order doesn't matter - nCr=n! / r!(n-r)!

46. Same Time
D/W= (R1+R2)*T
= (x degree / 360) C
A=S^2 - P=4S - Diagonal is root2 times side
0 - -2 - -4 - ...

47. Equilateral Triangle
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
D/W=R1T1 + R2T2
A=[(B1+B2)*H]/2

48. Congruent Triangles
S-S-S - S-A-S - A-S-A
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Order matters - nPr=n! / (n-r)!
An=A1(r)^n-1

49. Mixture Formula
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
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
A=[(B1+B2)*H]/2
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

50. Exponent Rules
A=S^2 - P=4S - Diagonal is root2 times side
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Consists of all of the elements that appear in either set without repeating elements
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