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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. Integer
Consists of all the elements that appear in both sets
= (x degree / 360) C
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Positive and negative whole numbers

2. Even Numbers
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
0 - -2 - -4 - ...
S=180(n-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

3. Arithmetic Sequence
An=A1+(n-1)d
(1/3)pir^2*h
1 - 3 - 5 - ...
Order doesn't matter - nCr=n! / r!(n-r)!

4. Fundamental Counting Principle
Multiply number of choices available in each option to get total number of options
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
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Middle number (or average of 2) of set from smallest to largest

5. Odd Numbers
0 - -2 - -4 - ...
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
The most frequently occurring number in a set
1 - 3 - 5 - ...

6. Similar Triangles
Square root[(x2-x1)^2 + (y2-y1)^2]
0 - -2 - -4 - ...
([old-new]/old)*100%
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

7. Mode
(1/3)pir^2*h
The most frequently occurring number in a set
2 equal sides - 2 equal angles
1 - 3 - 5 - ...

8. Distance Formula
Volume=(4/3)pir^3
([old-new]/old)*100%
D=R*T - W=R*T
Square root[(x2-x1)^2 + (y2-y1)^2]

9. Median
([old-new]/old)*100%
Multiply number of choices available in each option to get total number of options
Square root[(x2-x1)^2 + (y2-y1)^2]
Middle number (or average of 2) of set from smallest to largest

10. Right Triangle
Part/whole = %/100
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
D=R*T - W=R*T
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

11. Square
x1y1 = x2y2
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
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

12. Adding/Subtracting Exponents
1 - 3 - 5 - ...
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
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

13. Combinations

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14. Distance/Work Formula
= (x degree / 360) C
(distance between opposite vertices) - square root(L^2+W^2+H^2)
D=R*T - W=R*T
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

15. 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
360
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

16. Area of a Triangle
A=(3root3/2)r^2
A=1/2bh
S-S-S - S-A-S - A-S-A
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

17. Area Trapezoid
(distance between opposite vertices) - square root(L^2+W^2+H^2)
A=[(B1+B2)*H]/2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

18. Same Time
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
D/W= (R1+R2)*T
Middle number (or average of 2) of set from smallest to largest
Square root[(x2-x1)^2 + (y2-y1)^2]

19. Rectangles
D/W= (R1+R2)*T
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
A=L*W - P=2L+2W - Diagonals equal length
Volume=(4/3)pir^3

20. Weighted Averages
A=L*W - P=2L+2W - Diagonals equal length
1 - 3 - 5 - ...
(1/3)LW*H
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

21. Exponent Rules
Square root[(x2-x1)^2 + (y2-y1)^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
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

22. Even/Odd Results
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Consists of all of the elements that appear in either set without repeating elements
= (x degree / 360) C
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

23. Rational Number
An=A1+(n-1)d
A=1/2bh
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
([old-new]/old)*100%

24. Length on an Arc
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
= (x degree / 360) C
D=R*T - W=R*T
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

25. Average Rate
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
(1/3)LW*H
360
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

26. Same Rate
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
= (x degree / 360) pi*r^2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Part/whole = %/100

27. Real Wheel Formula
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
D=R*T - W=R*T
A=[(B1+B2)*H]/2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

28. Volume of Pyramid
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
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
(area of base)*height
(1/3)LW*H

29. Same Distance
#successful events / total# possible outcomes
(area of base)*height
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

30. Percentage Change
(distance between opposite vertices) - square root(L^2+W^2+H^2)
([old-new]/old)*100%
x1/y1 = x2/y2
A=(3root3/2)r^2

31. Sum of Exterior Angles
360
S-S-S - S-A-S - A-S-A
A=[(B1+B2)*H]/2
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

32. Direct Variation
x1/y1 = x2/y2
Positive and negative whole numbers
A=1/2bh
(area of base)*height

33. Area of a Sector
([old-new]/old)*100%
= (x degree / 360) pi*r^2
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

34. Percents
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
S=180(n-2)
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Part/whole = %/100

35. Area Hexagon
A=(3root3/2)r^2
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)
(1/3)LW*H

36. Same Work
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
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
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

37. Geometric Sequences
An=A1(r)^n-1
Consists of all of the elements that appear in either set without repeating elements
(area of base)*height
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

38. Volume of Sphere
Volume=(4/3)pir^3
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
(1/3)pir^2*h
x1y1 = x2y2

39. Combined Rates
= (x degree / 360) C
x1y1 = x2y2
D/W=R1T1 + R2T2
Consists of all of the elements that appear in either set without repeating elements

40. Extension of the Pythagorean Theorem
(distance between opposite vertices) - square root(L^2+W^2+H^2)
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
The most frequently occurring number in a set
D/W=R1T1 + R2T2

41. Congruent Triangles
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
S-S-S - S-A-S - A-S-A
A=(3root3/2)r^2
2 equal sides - 2 equal angles

42. Volume of Cone
The most frequently occurring number in a set
(1/3)pir^2*h
Consists of all the elements that appear in both sets
#successful events / total# possible outcomes

43. Special Right Triangles
An=A1+(n-1)d
([old-new]/old)*100%
A=S^2 - P=4S - Diagonal is root2 times side
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

44. Union
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
An=A1(r)^n-1
Consists of all of the elements that appear in either set without repeating elements

45. Sum of Interior Angles
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
A=(3root3/2)r^2
S=180(n-2)
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

46. Weighted Average
A=L*W - P=2L+2W - Diagonals equal length
D=R*T - W=R*T
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
S=180(n-2)

47. Volume of Prism
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
(area of base)*height
S=180(n-2)
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

48. Intersection
Consists of all the elements that appear in both sets
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-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

49. Parallelograms
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
360
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Consists of all of the elements that appear in either set without repeating elements

50. Probability
Volume=(4/3)pir^3
An=A1(r)^n-1
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
#successful events / total# possible outcomes