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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. Exponent Rules
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
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
D/W= (R1+R2)*T

2. Distance Formula
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Square root[(x2-x1)^2 + (y2-y1)^2]
= (x degree / 360) pi*r^2

3. Area Hexagon
A=(3root3/2)r^2
x1y1 = x2y2
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
(area of base)*height

4. Even Numbers
2 equal sides - 2 equal angles
0 - -2 - -4 - ...
A=[(B1+B2)*H]/2
(area of base)*height

5. Intersection
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
Consists of all the elements that appear in both sets
The most frequently occurring number in a set
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

6. Combined Rates
(distance between opposite vertices) - square root(L^2+W^2+H^2)
= (x degree / 360) C
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
D/W=R1T1 + R2T2

7. Special Right Triangles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
0 - -2 - -4 - ...
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
1 - 3 - 5 - ...

8. Mode
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
The most frequently occurring number in a set
Square root[(x2-x1)^2 + (y2-y1)^2]
Multiply number of choices available in each option to get total number of options

9. Fundamental Counting Principle
Middle number (or average of 2) of set from smallest to largest
0 - -2 - -4 - ...
Multiply number of choices available in each option to get total number of options
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

10. Rational Number
= (x degree / 360) pi*r^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)pir^2*h
Consists of all the elements that appear in both sets

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^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
A=S^2 - P=4S - Diagonal is root2 times side

12. Area of a Triangle
A=1/2bh
A=(3root3/2)r^2
Positive and negative whole numbers
An=A1(r)^n-1

13. Distance/Work Formula
D=R*T - W=R*T
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
A=1/2bh
A=(3root3/2)r^2

14. Mixture Formula
#successful events / total# possible outcomes
The most frequently occurring number in a set
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

15. Cylinders
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
(1/3)pir^2*h
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

16. Equilateral Triangle
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
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

17. Sum of Exterior Angles
360
A=1/2bh
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
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

18. Rectangles
(area of base)*height
A=L*W - P=2L+2W - Diagonals equal length
(distance between opposite vertices) - square root(L^2+W^2+H^2)
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

19. Right Triangle
D/W= (R1+R2)*T
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
x1y1 = x2y2
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

20. Volume of Cone
S=180(n-2)
Multiply number of choices available in each option to get total number of options
(1/3)pir^2*h
D/W= (R1+R2)*T

21. Permutations
Order matters - nPr=n! / (n-r)!
(distance between opposite vertices) - square root(L^2+W^2+H^2)
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
x1/y1 = x2/y2

22. Extension of the Pythagorean Theorem
= (x degree / 360) C
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
(distance between opposite vertices) - square root(L^2+W^2+H^2)

23. Square
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A=S^2 - P=4S - Diagonal is root2 times side
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

24. Direct Variation
x1/y1 = x2/y2
Order matters - nPr=n! / (n-r)!
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

25. Area Trapezoid
A=[(B1+B2)*H]/2
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
([old-new]/old)*100%

26. Union
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Consists of all of the elements that appear in either set without repeating elements
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

27. Combinations

28. Arithmetic Sequence
An=A1+(n-1)d
Order doesn't matter - nCr=n! / r!(n-r)!
Part/whole = %/100
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

29. Adding/Subtracting Exponents
Order matters - nPr=n! / (n-r)!
= (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
An=A1+(n-1)d

30. Congruent Triangles
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
2 equal sides - 2 equal angles
S-S-S - S-A-S - A-S-A

31. Volume of Sphere
Volume=(4/3)pir^3
A=L*W - P=2L+2W - Diagonals equal length
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

32. Length on an Arc
= (x degree / 360) C
(1/3)pir^2*h
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)

33. Same Distance
D/W= (R1+R2)*T
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
D=R*T - W=R*T
S=180(n-2)

34. Even/Odd Results
S=180(n-2)
1 - 3 - 5 - ...
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Positive and negative whole numbers

35. Parallelograms
x1/y1 = x2/y2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
(1/3)LW*H
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

36. Probability
([old-new]/old)*100%
An=A1+(n-1)d
Order doesn't matter - nCr=n! / r!(n-r)!
#successful events / total# possible outcomes

37. Weighted Average
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Consists of all of the elements that appear in either set without repeating elements
A=(3root3/2)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

38. Similar Triangles
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
x1y1 = x2y2
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

39. Real Wheel Formula
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
1 - 3 - 5 - ...
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

40. Area of a Sector
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
= (x degree / 360) pi*r^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
x1/y1 = x2/y2

41. Odd Numbers
(area of base)*height
(1/3)pir^2*h
1 - 3 - 5 - ...
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

42. Sum of Interior Angles
Order matters - nPr=n! / (n-r)!
S=180(n-2)
D/W=R1T1 + R2T2
S-S-S - S-A-S - A-S-A

43. Integer
0 - -2 - -4 - ...
D=R*T - W=R*T
360
Positive and negative whole numbers

44. Same Time
= (x degree / 360) pi*r^2
D/W= (R1+R2)*T
Consists of all of the elements that appear in either set without repeating elements
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

45. Volume of Pyramid
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
A=(3root3/2)r^2
(1/3)LW*H

46. Median
D/W=R1T1 + R2T2
An=A1+(n-1)d
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Middle number (or average of 2) of set from smallest to largest

47. Percents
= (x degree / 360) C
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
D=R*T - W=R*T
Part/whole = %/100

48. Indirect Variation
D=R*T - W=R*T
x1y1 = x2y2
Volume=(4/3)pir^3
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

49. Average Rate
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Consists of all of the elements that appear in either set without repeating elements

50. Percentage Change
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
([old-new]/old)*100%
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
Middle number (or average of 2) of set from smallest to largest