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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. Isosceles Triangle
Square root[(x2-x1)^2 + (y2-y1)^2]
2 equal sides - 2 equal angles
Part/whole = %/100
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

2. Median
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
Middle number (or average of 2) of set from smallest to largest
x1/y1 = x2/y2

3. Odd Numbers
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A=[(B1+B2)*H]/2
2 equal sides - 2 equal angles
1 - 3 - 5 - ...

4. Union
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Consists of all of the elements that appear in either set without repeating elements
0 - -2 - -4 - ...

5. Length on an Arc
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
= (x degree / 360) C
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

6. Sum of Exterior Angles
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
0 - -2 - -4 - ...
360
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

7. Exponent Rules
Positive and negative whole numbers
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 - 5 - ...
Volume=(4/3)pir^3

8. Combined Rates
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
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
D/W=R1T1 + R2T2
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

9. Weighted Averages
A=L*W - P=2L+2W - Diagonals equal length
Middle number (or average of 2) of set from smallest to largest
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

10. Distance Formula
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Consists of all of the elements that appear in either set without repeating elements
0 - -2 - -4 - ...
Square root[(x2-x1)^2 + (y2-y1)^2]

11. 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
A=[(B1+B2)*H]/2
#successful events / total# possible outcomes
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

12. Similar Triangles
The most frequently occurring number in a set
= (x degree / 360) C
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
(distance between opposite vertices) - square root(L^2+W^2+H^2)

13. Congruent Triangles
S-S-S - S-A-S - A-S-A
= (x degree / 360) pi*r^2
360
x1/y1 = x2/y2

14. Same Distance
D/W= (R1+R2)*T
S=180(n-2)
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

15. Integer
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
2 equal sides - 2 equal angles
Positive and negative whole numbers

16. Permutations
Order doesn't matter - nCr=n! / r!(n-r)!
D/W= (R1+R2)*T
1 - 3 - 5 - ...
Order matters - nPr=n! / (n-r)!

17. Volume of Pyramid
(area of base)*height
S-S-S - S-A-S - A-S-A
(1/3)LW*H
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

18. Area of a Sector
= (x degree / 360) pi*r^2
Volume=(4/3)pir^3
A=(3root3/2)r^2
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

19. Right Triangle
Volume=(4/3)pir^3
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^2 + b^2 = c^2 - 3-4-5 - 5-12-13

20. Extension of the Pythagorean Theorem
(distance between opposite vertices) - square root(L^2+W^2+H^2)
= (x degree / 360) pi*r^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

21. 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
(area of base)*height
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

22. Rectangles
A=L*W - P=2L+2W - Diagonals equal length
A=[(B1+B2)*H]/2
A=1/2bh
D/W=R1T1 + R2T2

23. Parallelograms
Order doesn't matter - nCr=n! / r!(n-r)!
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
Middle number (or average of 2) of set from smallest to largest

24. Average Rate
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Part/whole = %/100
Volume=(4/3)pir^3
An=A1(r)^n-1

25. Direct Variation
(1/3)LW*H
x1/y1 = x2/y2
S=180(n-2)
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

26. Volume of Cone
Multiply number of choices available in each option to get total number of options
(1/3)pir^2*h
Consists of all the elements that appear in both sets
D/W=R1T1 + R2T2

27. Same Rate
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
2 equal sides - 2 equal angles
Middle number (or average of 2) of set from smallest to largest

28. Real Wheel Formula
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
([old-new]/old)*100%
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

29. Fundamental Counting Principle
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
D=R*T - W=R*T
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Multiply number of choices available in each option to get total number of options

30. Rational Number
Positive and negative whole numbers
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
2 equal sides - 2 equal angles

31. Weighted Average
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
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)
(1/3)LW*H

32. Even/Odd Results
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
= (x degree / 360) pi*r^2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
S=180(n-2)

33. Same Time
Order doesn't matter - nCr=n! / r!(n-r)!
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
D/W= (R1+R2)*T

34. Geometric Sequences
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
([old-new]/old)*100%
(distance between opposite vertices) - square root(L^2+W^2+H^2)
An=A1(r)^n-1

35. Even Numbers
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
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
0 - -2 - -4 - ...
(1/3)pir^2*h

36. Intersection
#successful events / total# possible outcomes
D=R*T - W=R*T
Consists of all the elements that appear in both sets
(1/3)pir^2*h

37. Same Work
Positive and negative whole numbers
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
A=1/2bh
Order matters - nPr=n! / (n-r)!

38. Special Right Triangles
S=180(n-2)
Order matters - nPr=n! / (n-r)!
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
A=L*W - P=2L+2W - Diagonals equal length

39. Area Hexagon
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
A=(3root3/2)r^2
0 - -2 - -4 - ...
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

40. Indirect Variation
= (x degree / 360) pi*r^2
x1y1 = x2y2
0 - -2 - -4 - ...
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

41. Area of a Triangle
A=1/2bh
A=(3root3/2)r^2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
#successful events / total# possible outcomes

42. Adding/Subtracting Exponents
D=R*T - W=R*T
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
A=[(B1+B2)*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

43. Percents
Part/whole = %/100
1 - 3 - 5 - ...
S=180(n-2)
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

44. Mode
360
(1/3)pir^2*h
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
The most frequently occurring number in a set

45. Distance/Work Formula
D=R*T - W=R*T
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
0 - -2 - -4 - ...
(1/3)pir^2*h

46. Mixture Formula
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
A=(3root3/2)r^2
D=R*T - W=R*T

47. Percentage Change
2 equal sides - 2 equal angles
A=(3root3/2)r^2
([old-new]/old)*100%
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. Square
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
An=A1(r)^n-1
0 - -2 - -4 - ...
A=S^2 - P=4S - Diagonal is root2 times side

49. Area Trapezoid
A=[(B1+B2)*H]/2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Consists of all of the elements that appear in either set without repeating elements
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

50. Cylinders
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
(distance between opposite vertices) - square root(L^2+W^2+H^2)
x1/y1 = x2/y2