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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. Volume of Cone
(1/3)pir^2*h
A=[(B1+B2)*H]/2
D/W=R1T1 + R2T2
S=180(n-2)

2. Length on an Arc
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
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
= (x degree / 360) C

3. Same Distance
1 - 3 - 5 - ...
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
S-S-S - S-A-S - A-S-A
= (x degree / 360) pi*r^2

4. Arithmetic Sequence
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
An=A1+(n-1)d
An=A1(r)^n-1

5. Distance Formula
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Square root[(x2-x1)^2 + (y2-y1)^2]
#successful events / total# possible outcomes

6. Sum of Interior Angles
([old-new]/old)*100%
A=(3root3/2)r^2
S=180(n-2)
D=R*T - W=R*T

7. Intersection
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A=[(B1+B2)*H]/2
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Consists of all the elements that appear in both sets

8. Mixture Formula
(area of base)*height
= (x degree / 360) pi*r^2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
An=A1+(n-1)d

9. Isosceles Triangle
2 equal sides - 2 equal angles
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
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

10. Even Numbers
0 - -2 - -4 - ...
([old-new]/old)*100%
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
x1/y1 = x2/y2

11. Probability
D=R*T - W=R*T
#successful events / total# possible outcomes
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Multiply number of choices available in each option to get total number of options

12. Permutations
An=A1+(n-1)d
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
Order matters - nPr=n! / (n-r)!
A=1/2bh

13. Integer
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Positive and negative whole numbers
= (x degree / 360) C
A=S^2 - P=4S - Diagonal is root2 times side

14. Odd Numbers
Order matters - nPr=n! / (n-r)!
D/W= (R1+R2)*T
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
1 - 3 - 5 - ...

15. Congruent Triangles
S-S-S - S-A-S - A-S-A
(1/3)pir^2*h
Consists of all the elements that appear in both sets
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

16. Real Wheel Formula
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
D=R*T - W=R*T
S-S-S - S-A-S - A-S-A

17. Extension of the Pythagorean Theorem
A=[(B1+B2)*H]/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
(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

18. Average Rate
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
A=1/2bh
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

19. Sum of Exterior Angles
D=R*T - W=R*T
360
2 equal sides - 2 equal angles
A=1/2bh

20. Right Triangle
= (x degree / 360) C
A=1/2bh
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

21. Weighted Averages
A=1/2bh
S=180(n-2)
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Order matters - nPr=n! / (n-r)!

22. Mode
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
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

23. Volume of Sphere
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Volume=(4/3)pir^3
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
D=R*T - W=R*T

24. Indirect Variation
D/W= (R1+R2)*T
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
Consists of all the elements that appear in both sets

25. Combinations

26. Special Right Triangles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
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
The most frequently occurring number in a set

27. Fundamental Counting Principle
A=[(B1+B2)*H]/2
= (x degree / 360) pi*r^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
Multiply number of choices available in each option to get total number of options

28. Rectangles
A=L*W - P=2L+2W - Diagonals equal length
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
Positive and negative whole numbers

29. Same Time
Order doesn't matter - nCr=n! / r!(n-r)!
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=(3root3/2)r^2
D/W= (R1+R2)*T

30. Adding/Subtracting Exponents
Consists of all the elements that appear in both sets
S-S-S - S-A-S - A-S-A
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)LW*H

31. Exponent Rules
Part/whole = %/100
= (x degree / 360) pi*r^2
Consists of all the elements that appear in both sets
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

32. Median
0 - -2 - -4 - ...
#successful events / total# possible outcomes
A=L*W - P=2L+2W - Diagonals equal length
Middle number (or average of 2) of set from smallest to largest

33. Geometric Sequences
An=A1(r)^n-1
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
D/W=R1T1 + R2T2
= (x degree / 360) C

34. Same Work
= (x degree / 360) pi*r^2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
The most frequently occurring number in a set
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

35. Distance/Work Formula
Order doesn't matter - nCr=n! / r!(n-r)!
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=R*T - W=R*T
A=(3root3/2)r^2

36. Rational Number
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Middle number (or average of 2) of set from smallest to largest
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

37. Triangle Inequality
S=180(n-2)
Square root[(x2-x1)^2 + (y2-y1)^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
(1/3)LW*H

38. Square
A=1/2bh
Square root[(x2-x1)^2 + (y2-y1)^2]
A=S^2 - P=4S - Diagonal is root2 times side
Order matters - nPr=n! / (n-r)!

39. Even/Odd Results
Square root[(x2-x1)^2 + (y2-y1)^2]
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=[(B1+B2)*H]/2

40. Area of a Sector
(area of base)*height
= (x degree / 360) pi*r^2
Part/whole = %/100
0 - -2 - -4 - ...

41. Volume of Pyramid
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
(1/3)LW*H
A=S^2 - P=4S - Diagonal is root2 times side

42. Cylinders
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A=(3root3/2)r^2
360
A=S^2 - P=4S - Diagonal is root2 times side

43. Volume of Prism
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
A=L*W - P=2L+2W - Diagonals equal length
(distance between opposite vertices) - square root(L^2+W^2+H^2)
(area of base)*height

44. Similar Triangles
A=[(B1+B2)*H]/2
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
D/W=R1T1 + R2T2
Order matters - nPr=n! / (n-r)!

45. Area of a Triangle
#successful events / total# possible outcomes
A=1/2bh
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

46. Weighted Average
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
= (x degree / 360) pi*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

47. Union
#successful events / total# possible outcomes
Consists of all of the elements that appear in either set without repeating elements
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

48. Area Trapezoid
x1/y1 = x2/y2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
A=[(B1+B2)*H]/2
0 - -2 - -4 - ...

49. Direct Variation
x1/y1 = x2/y2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
360
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

50. Equilateral Triangle
Order doesn't matter - nCr=n! / r!(n-r)!
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
#successful events / total# possible outcomes
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)