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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. Direct Variation
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
x1/y1 = x2/y2
D/W=R1T1 + R2T2
Order matters - nPr=n! / (n-r)!

2. Arithmetic Sequence
An=A1+(n-1)d
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
S=180(n-2)
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

3. Indirect Variation
x1y1 = x2y2
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)
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

4. Square
A=S^2 - P=4S - Diagonal is root2 times side
D/W= (R1+R2)*T
S=180(n-2)
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

5. 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
D/W=R1T1 + R2T2
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Volume=(4/3)pir^3

6. Volume of Cone
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
([old-new]/old)*100%
D/W=R1T1 + R2T2
(1/3)pir^2*h

7. Even/Odd Results
Positive and negative whole numbers
S-S-S - S-A-S - A-S-A
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
S=180(n-2)

8. Union
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)
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 of the elements that appear in either set without repeating elements

9. Volume of Prism
A=[(B1+B2)*H]/2
(area of base)*height
A=1/2bh
1 - 3 - 5 - ...

10. Distance Formula
Order matters - nPr=n! / (n-r)!
Square root[(x2-x1)^2 + (y2-y1)^2]
The most frequently occurring number in a set
A=(3root3/2)r^2

11. Volume of Pyramid
An=A1(r)^n-1
(1/3)LW*H
D/W= (R1+R2)*T
(distance between opposite vertices) - square root(L^2+W^2+H^2)

12. Even Numbers
0 - -2 - -4 - ...
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
The most frequently occurring number in a set

13. Geometric Sequences
(area of base)*height
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
An=A1(r)^n-1
#successful events / total# possible outcomes

14. Congruent Triangles
Square root[(x2-x1)^2 + (y2-y1)^2]
S=180(n-2)
D/W=R1T1 + R2T2
S-S-S - S-A-S - A-S-A

15. Sum of Exterior Angles
360
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
An=A1(r)^n-1

16. Same Time
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
1 - 3 - 5 - ...
D/W= (R1+R2)*T

17. Combinations

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18. Isosceles Triangle
(area of base)*height
A=S^2 - P=4S - Diagonal is root2 times side
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
2 equal sides - 2 equal angles

19. Special Right Triangles
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
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
(1/3)LW*H

20. Combined Rates
D/W=R1T1 + R2T2
Multiply number of choices available in each option to get total number of options
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
S-S-S - S-A-S - A-S-A

21. Percentage Change
D/W=R1T1 + R2T2
([old-new]/old)*100%
D/W= (R1+R2)*T
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

22. Area of a Triangle
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
An=A1(r)^n-1
A=1/2bh
(1/3)pir^2*h

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

24. Probability
D/W=R1T1 + R2T2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Middle number (or average of 2) of set from smallest to largest
#successful events / total# possible outcomes

25. Equilateral Triangle
(distance between opposite vertices) - square root(L^2+W^2+H^2)
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)

26. Real Wheel Formula
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
A=L*W - P=2L+2W - Diagonals equal length
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

27. Cylinders
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
An=A1(r)^n-1
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

28. Rational Number
A=L*W - P=2L+2W - Diagonals equal length
Positive and negative whole numbers
Multiply number of choices available in each option to get total number of options
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

29. Fundamental Counting Principle
A=[(B1+B2)*H]/2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
A=S^2 - P=4S - Diagonal is root2 times side
Multiply number of choices available in each option to get total number of options

30. Parallelograms
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Positive and negative whole numbers
Volume=(4/3)pir^3
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

31. Percents
(1/3)LW*H
Part/whole = %/100
A=L*W - P=2L+2W - Diagonals equal length
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

32. Right Triangle
360
A=L*W - P=2L+2W - Diagonals equal length
= (x degree / 360) pi*r^2
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

33. Similar Triangles
A=L*W - P=2L+2W - Diagonals equal length
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Consists of all the elements that appear in both sets

34. Median
1 - 3 - 5 - ...
S-S-S - S-A-S - A-S-A
Middle number (or average of 2) of set from smallest to largest
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

35. Volume of Sphere
(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
= (x degree / 360) C
Volume=(4/3)pir^3

36. Integer
An=A1+(n-1)d
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Positive and negative whole numbers

37. Permutations
([old-new]/old)*100%
Order matters - nPr=n! / (n-r)!
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

38. Mode
= (x degree / 360) C
(area of base)*height
The most frequently occurring number in a set
= (x degree / 360) pi*r^2

39. Same Distance
D=R*T - W=R*T
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
A=L*W - P=2L+2W - Diagonals equal length
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

40. Area Hexagon
Square root[(x2-x1)^2 + (y2-y1)^2]
Consists of all the elements that appear in both sets
D/W= (R1+R2)*T
A=(3root3/2)r^2

41. Weighted Average
Consists of all the elements that appear in both sets
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A=[(B1+B2)*H]/2
x1/y1 = x2/y2

42. Area of a Sector
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
= (x degree / 360) pi*r^2
Volume=(4/3)pir^3
1 - 3 - 5 - ...

43. Sum of Interior Angles
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
D/W=R1T1 + R2T2
Middle number (or average of 2) of set from smallest to largest
S=180(n-2)

44. Average Rate
([old-new]/old)*100%
An=A1(r)^n-1
Middle number (or average of 2) of set from smallest to largest
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

45. Exponent Rules
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
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
Multiply number of choices available in each option to get total number of options
A=[(B1+B2)*H]/2

46. Odd Numbers
1 - 3 - 5 - ...
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=[(B1+B2)*H]/2
D/W=R1T1 + R2T2

47. Area Trapezoid
= (x degree / 360) C
Order matters - nPr=n! / (n-r)!
A=[(B1+B2)*H]/2
A=L*W - P=2L+2W - Diagonals equal length

48. Distance/Work Formula
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
S=180(n-2)
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
D=R*T - W=R*T

49. Extension of the Pythagorean Theorem
The most frequently occurring number in a set
(distance between opposite vertices) - square root(L^2+W^2+H^2)
S-S-S - S-A-S - A-S-A
A=(3root3/2)r^2

50. Rectangles
Middle number (or average of 2) of set from smallest to largest
A=L*W - P=2L+2W - Diagonals equal length
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
= (x degree / 360) pi*r^2