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Test your basic knowledge |
SAT Math Formulas
Start Test
Study First
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. Same Rate
An=A1(r)^n-1
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
1 - 3 - 5 - ...
2. Cylinders
Consists of all the elements that appear in both sets
The most frequently occurring number in a set
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A=[(B1+B2)*H]/2
3. Rectangles
A=[(B1+B2)*H]/2
A=L*W - P=2L+2W - Diagonals equal length
x1y1 = x2y2
(distance between opposite vertices) - square root(L^2+W^2+H^2)
4. Adding/Subtracting Exponents
Positive and negative whole numbers
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
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
Middle number (or average of 2) of set from smallest to largest
5. Rational Number
1 - 3 - 5 - ...
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
6. Volume of Cone
x1y1 = x2y2
(1/3)pir^2*h
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
7. Congruent Triangles
Positive and negative whole numbers
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
S-S-S - S-A-S - A-S-A
Multiply number of choices available in each option to get total number of options
8. Same Work
(area of base)*height
Order matters - nPr=n! / (n-r)!
Positive and negative whole numbers
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
9. Similar Triangles
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
A=S^2 - P=4S - Diagonal is root2 times side
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
10. Special Right Triangles
The most frequently occurring number in a set
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Middle number (or average of 2) of set from smallest to largest
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
11. Sum of Exterior Angles
Square root[(x2-x1)^2 + (y2-y1)^2]
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A=1/2bh
360
12. Odd 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 - ...
A=S^2 - P=4S - Diagonal is root2 times side
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
13. Arithmetic Sequence
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
= (x degree / 360) pi*r^2
An=A1+(n-1)d
Positive and negative whole numbers
14. Area of a Triangle
Part/whole = %/100
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
(distance between opposite vertices) - square root(L^2+W^2+H^2)
A=1/2bh
15. Equilateral Triangle
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
#successful events / total# possible outcomes
A=S^2 - P=4S - Diagonal is root2 times side
16. Sum of Interior Angles
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
= (x degree / 360) pi*r^2
Volume=(4/3)pir^3
S=180(n-2)
17. Same Distance
2 equal sides - 2 equal angles
A=L*W - P=2L+2W - Diagonals equal length
(1/3)pir^2*h
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
18. Real Wheel Formula
A=L*W - P=2L+2W - Diagonals equal length
Consists of all of the elements that appear in either set without repeating elements
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
19. Mixture Formula
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
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=[(B1+B2)*H]/2
20. Percents
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
Part/whole = %/100
(distance between opposite vertices) - square root(L^2+W^2+H^2)
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
21. Weighted Average
D/W=R1T1 + R2T2
1 - 3 - 5 - ...
x1y1 = x2y2
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
22. Volume of Sphere
Order matters - nPr=n! / (n-r)!
Volume=(4/3)pir^3
A=S^2 - P=4S - Diagonal is root2 times side
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 Pyramid
An=A1+(n-1)d
(1/3)LW*H
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
24. Average Rate
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
D=R*T - W=R*T
25. Probability
x1/y1 = x2/y2
#successful events / total# possible outcomes
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
A=L*W - P=2L+2W - Diagonals equal length
26. Intersection
Consists of all the elements that appear in both sets
(area of base)*height
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
D/W=R1T1 + R2T2
27. Fundamental Counting Principle
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
D/W= (R1+R2)*T
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Multiply number of choices available in each option to get total number of options
28. Parallelograms
2 equal sides - 2 equal angles
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Volume=(4/3)pir^3
(1/3)LW*H
29. Percentage Change
An=A1(r)^n-1
A=[(B1+B2)*H]/2
x1y1 = x2y2
([old-new]/old)*100%
30. Volume of Prism
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
An=A1(r)^n-1
(area of base)*height
The most frequently occurring number in a set
31. Square
Part/whole = %/100
Multiply number of choices available in each option to get total number of options
A=S^2 - P=4S - Diagonal is root2 times side
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
32. Length on an Arc
= (x degree / 360) C
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
= (x degree / 360) pi*r^2
33. Mode
D=R*T - W=R*T
The most frequently occurring number in a set
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
34. Area of a Sector
= (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
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
2 equal sides - 2 equal angles
35. Triangle Inequality
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
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
2 equal sides - 2 equal angles
36. Distance Formula
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
Square root[(x2-x1)^2 + (y2-y1)^2]
(area of base)*height
Volume=(4/3)pir^3
37. Combinations
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38. Right Triangle
([old-new]/old)*100%
Order matters - nPr=n! / (n-r)!
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
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
39. Geometric Sequences
(area of base)*height
D=R*T - W=R*T
Middle number (or average of 2) of set from smallest to largest
An=A1(r)^n-1
40. Area Trapezoid
Square root[(x2-x1)^2 + (y2-y1)^2]
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
= (x degree / 360) C
A=[(B1+B2)*H]/2
41. Union
360
(1/3)LW*H
Consists of all of the elements that appear in either set without repeating elements
Part/whole = %/100
42. Isosceles Triangle
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
A=L*W - P=2L+2W - Diagonals equal length
2 equal sides - 2 equal angles
Volume=(4/3)pir^3
43. Direct Variation
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
x1/y1 = x2/y2
#successful events / total# possible outcomes
44. Indirect Variation
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
x1y1 = x2y2
D=R*T - W=R*T
Consists of all of the elements that appear in either set without repeating elements
45. Even/Odd Results
The most frequently occurring number in a set
2 equal sides - 2 equal angles
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
46. Same Time
D/W= (R1+R2)*T
#successful events / total# possible outcomes
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
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
47. Even Numbers
0 - -2 - -4 - ...
Consists of all of the elements that appear in either set without repeating elements
x1y1 = x2y2
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
48. Median
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Middle number (or average of 2) of set from smallest to largest
A=1/2bh
49. Permutations
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
S-S-S - S-A-S - A-S-A
Multiply number of choices available in each option to get total number of options
Order matters - nPr=n! / (n-r)!
50. Weighted Averages
= (x degree / 360) pi*r^2
Consists of all of the elements that appear in either set without repeating elements
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Positive and negative whole numbers