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. Even Numbers
S-S-S - S-A-S - A-S-A
0 - -2 - -4 - ...
([old-new]/old)*100%
D/W= (R1+R2)*T

2. Percentage Change
([old-new]/old)*100%
An=A1(r)^n-1
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

3. Volume of Cone
Consists of all of the elements that appear in either set without repeating elements
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
Part/whole = %/100
(1/3)pir^2*h

4. Real Wheel Formula
2 equal sides - 2 equal angles
A=(3root3/2)r^2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

5. Sum of Exterior Angles
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
#successful events / total# possible outcomes
360

6. Rectangles
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
Order doesn't matter - nCr=n! / r!(n-r)!
A=L*W - P=2L+2W - Diagonals equal length
#successful events / total# possible outcomes

7. Same Work
(area of base)*height
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
(1/3)pir^2*h
A=1/2bh

8. Triangle Inequality
(area of base)*height
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
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

9. Similar Triangles
= (x degree / 360) C
Multiply number of choices available in each option to get total number of options
Square root[(x2-x1)^2 + (y2-y1)^2]
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

10. Area of a Sector
= (x degree / 360) pi*r^2
1 - 3 - 5 - ...
([old-new]/old)*100%
Consists of all of the elements that appear in either set without repeating elements

11. Geometric Sequences
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
An=A1(r)^n-1
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

12. Exponent Rules
An=A1(r)^n-1
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 - ...
D=R*T - W=R*T

13. Equilateral Triangle
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
= (x degree / 360) C
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
(1/3)pir^2*h

14. Median
([old-new]/old)*100%
x1/y1 = x2/y2
Middle number (or average of 2) of set from smallest to largest
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

15. Same Time
An=A1+(n-1)d
A=[(B1+B2)*H]/2
Order matters - nPr=n! / (n-r)!
D/W= (R1+R2)*T

16. Combined Rates
360
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
S-S-S - S-A-S - A-S-A
D/W=R1T1 + R2T2

17. Sum of Interior Angles
Square root[(x2-x1)^2 + (y2-y1)^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
360
S=180(n-2)

18. Parallelograms
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
A=L*W - P=2L+2W - Diagonals equal length
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)

19. Integer
Consists of all the elements that appear in both sets
Positive and negative whole numbers
An=A1(r)^n-1
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

20. Indirect Variation
2 equal sides - 2 equal angles
x1y1 = x2y2
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Consists of all of the elements that appear in either set without repeating elements

21. Distance/Work Formula
Part/whole = %/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
D=R*T - W=R*T
A=(3root3/2)r^2

22. Weighted Average
x1y1 = x2y2
A=1/2bh
2 equal sides - 2 equal angles
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

23. Even/Odd Results
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
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Square root[(x2-x1)^2 + (y2-y1)^2]
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

24. Area Trapezoid
360
D/W=R1T1 + R2T2
A=[(B1+B2)*H]/2
x1y1 = x2y2

25. Area of a Triangle
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
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
A=1/2bh

26. Intersection
x1y1 = x2y2
(1/3)LW*H
Consists of all the elements that appear in both sets
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

27. Rational Number
(1/3)pir^2*h
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
Part/whole = %/100

28. Square
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
A=L*W - P=2L+2W - Diagonals equal length
Volume=(4/3)pir^3

29. Congruent Triangles
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)(number1) + (avg2)(number2) = (avgT)(numberT)
S-S-S - S-A-S - A-S-A
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

30. Mixture Formula
A=1/2bh
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
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
Order matters - nPr=n! / (n-r)!

31. Same Distance
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Consists of all the elements that appear in both sets
D/W= (R1+R2)*T

32. Extension of the Pythagorean Theorem
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Middle number (or average of 2) of set from smallest to largest
x1/y1 = x2/y2

33. Union
Consists of all of the elements that appear in either set without repeating elements
Middle number (or average of 2) of set from smallest to largest
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
An=A1(r)^n-1

34. Area Hexagon
A=(3root3/2)r^2
= (x degree / 360) C
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
D/W=R1T1 + R2T2

35. Length on an Arc
Consists of all the elements that appear in both sets
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
= (x degree / 360) C

36. Fundamental Counting Principle
A=L*W - P=2L+2W - Diagonals equal length
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Multiply number of choices available in each option to get total number of options
S-S-S - S-A-S - A-S-A

37. Percents
= (x degree / 360) pi*r^2
Part/whole = %/100
An=A1+(n-1)d
Order doesn't matter - nCr=n! / r!(n-r)!

38. Adding/Subtracting Exponents
A=1/2bh
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
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
2 equal sides - 2 equal angles

39. Volume of Sphere
A=L*W - P=2L+2W - Diagonals equal length
Volume=(4/3)pir^3
0 - -2 - -4 - ...
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

40. Direct Variation
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
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
x1/y1 = x2/y2
An=A1(r)^n-1

41. Permutations
D=R*T - W=R*T
A=L*W - P=2L+2W - Diagonals equal length
S-S-S - S-A-S - A-S-A
Order matters - nPr=n! / (n-r)!

42. Average Rate
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Part/whole = %/100
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
1 - 3 - 5 - ...

43. Combinations

44. Arithmetic Sequence
An=A1+(n-1)d
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
0 - -2 - -4 - ...
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

45. Same Rate
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Positive and negative whole numbers
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
An=A1(r)^n-1

46. Weighted Averages
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Part/whole = %/100
x1y1 = x2y2
Consists of all the elements that appear in both sets

47. Volume of Pyramid
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
Consists of all the elements that appear in both sets
(1/3)LW*H

48. Special Right Triangles
Middle number (or average of 2) of set from smallest to largest
0 - -2 - -4 - ...
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
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

49. Odd Numbers
1 - 3 - 5 - ...
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

50. Mode
The most frequently occurring number in a set
A=1/2bh
(area of base)*height
0 - -2 - -4 - ...