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Test your basic knowledge |

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. Geometric Sequences
= (x degree / 360) pi*r^2
An=A1(r)^n-1
1 - 3 - 5 - ...
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

2. Same Rate
= (x degree / 360) pi*r^2
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
S=180(n-2)
0 - -2 - -4 - ...

3. Volume of Prism
Order matters - nPr=n! / (n-r)!
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
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

4. Mixture Formula
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
S-S-S - S-A-S - A-S-A
(1/3)pir^2*h
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

5. Sum of Interior Angles
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
A=L*W - P=2L+2W - Diagonals equal length
S=180(n-2)

6. Volume of Pyramid
(1/3)LW*H
#successful events / total# possible outcomes
S=180(n-2)
D/W= (R1+R2)*T

7. Combinations

8. Direct Variation
x1/y1 = x2/y2
An=A1+(n-1)d
The most frequently occurring number in a set
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

9. Parallelograms
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
0 - -2 - -4 - ...
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

10. Area Hexagon
A=(3root3/2)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
Order matters - nPr=n! / (n-r)!
(distance between opposite vertices) - square root(L^2+W^2+H^2)

11. Square
Middle number (or average of 2) of set from smallest to largest
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A=S^2 - P=4S - Diagonal is root2 times side
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

12. Permutations
A=1/2bh
= (x degree / 360) pi*r^2
Square root[(x2-x1)^2 + (y2-y1)^2]
Order matters - nPr=n! / (n-r)!

13. Mode
The most frequently occurring number in a set
Positive and negative whole numbers
= (x degree / 360) C
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

14. Odd Numbers
Consists of all of the elements that appear in either set without repeating elements
D/W= (R1+R2)*T
1 - 3 - 5 - ...
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

15. Extension of the Pythagorean Theorem
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Order matters - nPr=n! / (n-r)!
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Square root[(x2-x1)^2 + (y2-y1)^2]

16. Volume of Cone
(1/3)pir^2*h
1 - 3 - 5 - ...
(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

17. Cylinders
0 - -2 - -4 - ...
#successful events / total# possible outcomes
S-S-S - S-A-S - A-S-A
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

18. Union
D/W=R1T1 + R2T2
Consists of all of the elements that appear in either set without repeating elements
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

19. Equilateral Triangle
Order matters - nPr=n! / (n-r)!
A=L*W - P=2L+2W - Diagonals equal length
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Order doesn't matter - nCr=n! / r!(n-r)!

20. Distance Formula
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A=(3root3/2)r^2
Square root[(x2-x1)^2 + (y2-y1)^2]
x1/y1 = x2/y2

21. Area Trapezoid
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
A=[(B1+B2)*H]/2
1 - 3 - 5 - ...
Multiply number of choices available in each option to get total number of options

22. Combined Rates
D/W=R1T1 + R2T2
Volume=(4/3)pir^3
A=L*W - P=2L+2W - Diagonals equal length
Order matters - nPr=n! / (n-r)!

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

24. Same Time
0 - -2 - -4 - ...
A=S^2 - P=4S - Diagonal is root2 times 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
D/W= (R1+R2)*T

25. Average Rate
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
x1/y1 = x2/y2
S-S-S - S-A-S - A-S-A
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

26. Indirect Variation
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
x1y1 = x2y2
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

27. Real Wheel Formula
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Middle number (or average of 2) of set from smallest to largest
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

28. Volume of Sphere
D/W=R1T1 + R2T2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Volume=(4/3)pir^3
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

29. Area of a Triangle
The most frequently occurring number in a set
Positive and negative whole numbers
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
A=1/2bh

30. Intersection
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
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
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

31. Probability
A=L*W - P=2L+2W - Diagonals equal length
#successful events / total# possible outcomes
The most frequently occurring number in a set
Part/whole = %/100

32. Distance/Work Formula
D=R*T - W=R*T
Square root[(x2-x1)^2 + (y2-y1)^2]
([old-new]/old)*100%
An=A1(r)^n-1

33. Percentage Change
= (x degree / 360) C
(area of base)*height
An=A1+(n-1)d
([old-new]/old)*100%

34. Even Numbers
360
0 - -2 - -4 - ...
A=L*W - P=2L+2W - Diagonals equal length
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

35. Rectangles
Consists of all of the elements that appear in either set without repeating elements
([old-new]/old)*100%
(area of base)*height
A=L*W - P=2L+2W - Diagonals equal length

36. Length on an Arc
= (x degree / 360) C
Order matters - nPr=n! / (n-r)!
Middle number (or average of 2) of set from smallest to largest
An=A1+(n-1)d

37. Rational Number
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
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=1/2bh
(1/3)pir^2*h

38. Area of a Sector
= (x degree / 360) pi*r^2
(1/3)LW*H
2 equal sides - 2 equal angles
An=A1+(n-1)d

39. Special Right Triangles
An=A1+(n-1)d
A=L*W - P=2L+2W - Diagonals equal length
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
(1/3)pir^2*h

40. 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
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-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

41. Isosceles Triangle
2 equal sides - 2 equal angles
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
An=A1(r)^n-1
= (x degree / 360) C

42. Median
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Order doesn't matter - nCr=n! / r!(n-r)!
Volume=(4/3)pir^3
Middle number (or average of 2) of set from smallest to largest

43. Sum of Exterior Angles
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
360
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

44. Right Triangle
x1/y1 = x2/y2
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
(area of base)*height
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

45. Adding/Subtracting Exponents
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
0 - -2 - -4 - ...
x1y1 = x2y2
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

46. Same Distance
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
A=S^2 - P=4S - Diagonal is root2 times side

47. Similar Triangles
(1/3)LW*H
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
([old-new]/old)*100%
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

48. Integer
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Positive and negative whole numbers
0 - -2 - -4 - ...

49. Weighted Averages
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
x1/y1 = x2/y2
A=1/2bh

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