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SAT Math Formulas

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. Permutations
#successful events / total# possible outcomes
Consists of all of the elements that appear in either set without repeating elements
D=R*T - W=R*T
Order matters - nPr=n! / (n-r)!

2. Same Distance
Consists of all the elements that appear in both sets
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Consists of all of the elements that appear in either set without repeating elements
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

3. Area Trapezoid
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A=[(B1+B2)*H]/2
D/W=R1T1 + R2T2
An=A1+(n-1)d

4. Volume of Cone
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)pir^2*h
A=L*W - P=2L+2W - Diagonals equal length
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

5. Even/Odd Results
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
([old-new]/old)*100%
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
x1y1 = x2y2

6. Even Numbers
1 - 3 - 5 - ...
0 - -2 - -4 - ...
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

7. Arithmetic Sequence
(distance between opposite vertices) - square root(L^2+W^2+H^2)
An=A1+(n-1)d
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(area of base)*height

8. Weighted Averages
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
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)(number1) + (avg2)(number2) = (avgT)(numberT)
S-S-S - S-A-S - A-S-A

9. Geometric Sequences
An=A1(r)^n-1
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
D/W=R1T1 + R2T2

10. Direct Variation
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
D/W= (R1+R2)*T
Order doesn't matter - nCr=n! / r!(n-r)!
x1/y1 = x2/y2

11. Exponent Rules
= (x degree / 360) C
D/W= (R1+R2)*T
(area of base)*height
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

12. 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
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
A=[(B1+B2)*H]/2

13. Mixture Formula
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
(1/3)pir^2*h
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
A=1/2bh

14. Mode
([old-new]/old)*100%
The most frequently occurring number in a set
(1/3)LW*H
S=180(n-2)

15. Length on an Arc
The most frequently occurring number in a set
= (x degree / 360) C
Positive and negative whole numbers
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

16. Average Rate
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Part/whole = %/100
([old-new]/old)*100%
360

17. Odd Numbers
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
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

18. Volume of Pyramid
(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
Order doesn't matter - nCr=n! / r!(n-r)!
360

19. Weighted Average
A=L*W - P=2L+2W - Diagonals equal length
S=180(n-2)
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

20. Real Wheel Formula
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
(area of base)*height
D/W= (R1+R2)*T

21. Volume of Sphere
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Volume=(4/3)pir^3
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
2 equal sides - 2 equal angles

22. Isosceles Triangle
= (x degree / 360) pi*r^2
Square root[(x2-x1)^2 + (y2-y1)^2]
2 equal sides - 2 equal angles
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

23. Probability
2 equal sides - 2 equal angles
Order matters - nPr=n! / (n-r)!
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
#successful events / total# possible outcomes

24. Special Right Triangles
A=[(B1+B2)*H]/2
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
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. Rectangles
A=L*W - P=2L+2W - Diagonals equal length
A=1/2bh
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
(distance between opposite vertices) - square root(L^2+W^2+H^2)

26. Combined Rates
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
2 equal sides - 2 equal angles
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
D/W=R1T1 + R2T2

27. Similar Triangles
([old-new]/old)*100%
#successful events / total# possible outcomes
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

28. Union
Consists of all the elements that appear in both sets
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
0 - -2 - -4 - ...
Consists of all of the elements that appear in either set without repeating elements

29. Distance Formula
(1/3)pir^2*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
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Square root[(x2-x1)^2 + (y2-y1)^2]

30. Combinations

31. Same Time
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
D/W= (R1+R2)*T
= (x degree / 360) pi*r^2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

32. Square
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=S^2 - P=4S - Diagonal is root2 times side
An=A1+(n-1)d
D/W= (R1+R2)*T

33. Equilateral Triangle
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
An=A1(r)^n-1
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
0 - -2 - -4 - ...

34. Sum of Exterior Angles
Consists of all the elements that appear in both sets
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
360
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

35. Area of a Triangle
= (x degree / 360) pi*r^2
Multiply number of choices available in each option to get total number of options
A=1/2bh
Consists of all the elements that appear in both sets

36. Right Triangle
#successful events / total# possible outcomes
Positive and negative whole numbers
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

37. Volume of Prism
(area of base)*height
= (x degree / 360) pi*r^2
S-S-S - S-A-S - A-S-A
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

38. Congruent Triangles
(1/3)pir^2*h
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
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

39. Median
Order matters - nPr=n! / (n-r)!
D=R*T - W=R*T
Order doesn't matter - nCr=n! / r!(n-r)!
Middle number (or average of 2) of set from smallest to largest

40. Parallelograms
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
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
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

41. Fundamental Counting Principle
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 number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
Multiply number of choices available in each option to get total number of options

42. Distance/Work Formula
Square root[(x2-x1)^2 + (y2-y1)^2]
A=[(B1+B2)*H]/2
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

43. Indirect Variation
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Volume=(4/3)pir^3
(area of base)*height
x1y1 = x2y2

44. Rational Number
Consists of all the elements that appear in both sets
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
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) C

45. Cylinders
360
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
= (x degree / 360) C

46. Area of a Sector
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Order matters - nPr=n! / (n-r)!
= (x degree / 360) pi*r^2
A=L*W - P=2L+2W - Diagonals equal length

47. Percentage Change
S=180(n-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
The most frequently occurring number in a set
([old-new]/old)*100%

48. Intersection
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Consists of all the elements that appear in both sets
The most frequently occurring number in a set
D=R*T - W=R*T

49. Sum of Interior Angles
S=180(n-2)
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Square root[(x2-x1)^2 + (y2-y1)^2]
0 - -2 - -4 - ...

50. Extension of the Pythagorean Theorem
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
x1/y1 = x2/y2
(distance between opposite vertices) - square root(L^2+W^2+H^2)
(N1T1)/W1 = (N2T2)/W2 - N=number of workers