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SAT Math 2

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. Law of Cosines
Two sides and two angle are equal
C = a + b - 2abcos(C)
An = a1 + (n-1)d
(n/2)(a1 + an)

2. If the general parabola equation is y = ax+bx+c - what is the vertex of the parabola
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Hypotenuse is xv2 - and the sides are x.
x = -b/2a y= c - (b/4a)
SA = 4pr

3. Formula for the diagonal length of a cube
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(n/2)(a1 + an)
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
D= sv3

4. Surface area of a cone
F(x) = f(-x)
An = a1 + (n-1)d
V= (1/3)(prh)
SA = pr +prl

5. Standard form for a hyperbola that opens to the sides
A = (degree of the arc / 360)(area of a circle)
(x-h)/a - (y-k)/b = 1
Adding or subtracting 180 to ? and reversing the sign of r.
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx

6. Formula for arc length
(x-h) + (y-k) = r - where (h -k) is the center of the circle
Arc length equals = (degree of the arc / 360)(circumference)
y = a(x-h) + k - where the vertex is (h -k)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

7. How to find the distance between two points in 3d plane?
Square the differences between each coordinate - then square root the sum
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
Between the vertex and the minor axis on the major axis
y = a(x-h) + k - where the vertex is (h -k)

8. Formula for the diagonal length of a rectangular prism
y = a(x-h) + k - where the vertex is (h -k)
D = v(l+w+h)
V= (1/3)(prh)
A = ((s1 + s2)h) / 2

9. Difference between 2 Angles formulas
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
No equal sides and no equal angles
Sin(a-b) = sin(a)cos(b) - sin(b)cos(a) cos(a-b) = cos(a)cos(b) + sin(a)sin(b) tan(a-b) = [tan(a) - tan(b)] / [1+tan(a)tan(b)]
N-1

10. Pythagorean Identities
The greatest common factor is 1 - but the numbers are not necessarily prime.
(n-2)180
y = a(x-h) + k - where the vertex is (h -k)
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx

11. What is the triangle inequality rule?
Hypotenuse is 2x - short side is x - long side is xv3
SA = 4pr
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
x=rcos?(theta) y=rsin? (theta)

12. 45-45-90 triangle
90
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
SA = 4pr
Hypotenuse is xv2 - and the sides are x.

13. Formula for the area of a sector
A = (degree of the arc / 360)(area of a circle)
The greatest common factor is 1 - but the numbers are not necessarily prime.
N-1
Arc length equals = (degree of the arc / 360)(circumference)

14. Volume of a pyramid
V = (1/3)bh
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
A = (degree of the arc / 360)(area of a circle)
(n-2)180

15. Permutation formula (ordering)
F(x) = f(-x)
SA = 4pr
NPr = n! / (n-r)!
90

16. What are the conversion equations for polar coordinates to normal coordinates?
x=rcos?(theta) y=rsin? (theta)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
F(x) = -f(-x)
NPr = n! / (n-r)!

17. Sum of finite geometric series
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(1-r/1-r)
Two sides and two angle are equal

18. Define an odd function.
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
A = (degree of the arc / 360)(area of a circle)
F(x) = f(-x)
F(x) = -f(-x)

19. Two vectors are perpendicular if
Hypotenuse is 2x - short side is x - long side is xv3
N-1
Their dot product = 0
V= (1/3)(prh)

20. Volume of a sphere
Two sides and two angle are equal
The greatest common factor is 1 - but the numbers are not necessarily prime.
F(x) = f(-x)
V = (4/3)pr

21. In an ellipse - where are the foci?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Between the vertex and the minor axis on the major axis
D= sv3
y-y1 = m(x-x1)

22. What is the form of a polar coordinate?
An = a1rn?
(x-h)/a - (y-k)/b = 1
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
All whole numbers except for 0

23. Where is tangent positive/negative?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
(x-h)/a + (y-k)/b = 1 - where (h -k) is the center of the ellipse - the length of the horizontal axis is 2a - the length of the vertical axis is 2b - if a>b - the horizontal axis is the major axis.
C = a + b - 2abcos(C)
(x-h) + (y-k) = r - where (h -k) is the center of the circle

24. Standard form equation for an ellipse
A = ((s1 + s2)h) / 2
No equal sides and no equal angles
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
(x-h)/a + (y-k)/b = 1 - where (h -k) is the center of the ellipse - the length of the horizontal axis is 2a - the length of the vertical axis is 2b - if a>b - the horizontal axis is the major axis.

25. Formula for the area of a trapezoid
x = -b/2a y= c - (b/4a)
F(x) = f(-x)
D = v(l+w+h)
A = ((s1 + s2)h) / 2

26. Standard form equation for circle
Their dot product = 0
(x-h) + (y-k) = r - where (h -k) is the center of the circle
C = a + b - 2abcos(C)
SA = 4pr

27. What is the order of operations?
N-1
V = (4/3)pr
An = a1rn?
Parentheses - exponents - multiplication - division - addition - subtraction

28. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
V = (4/3)pr
SA = pr +prl
(x-h) + (y-k) = r - where (h -k) is the center of the circle

29. Formula for calculation exponential growth
F(x) = -f(-x)
Final amount = original amount x (1+growth rate)^number of changes
D= sv3
180

30. Define an even function.
F(x) = f(-x)
V = (1/3)bh
NCr = nPr / r! = n! / (n-r)!r!
Arc length equals = (degree of the arc / 360)(circumference)

31. Formula for geometric sequence
A = ((s1 + s2)h) / 2
An = a1rn?
Arc length equals = (degree of the arc / 360)(circumference)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

32. Sum of 2 Angles Formulas
Their dot product = 0
Sin(a+b) = sin(a)cos(b) + sin(b)cos(a) cos(a+b) = cos(a)cos(b) - sin(a)sin(b) tan(a+b) = [tan(a) + tan(b)] / [1-tan(a)tan(b)]
180
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

33. Formula for the volume of a cone
C = a + b - 2abcos(C)
y = a(x-h) + k - where the vertex is (h -k)
NCr = nPr / r! = n! / (n-r)!r!
V= (1/3)(prh)

34. Double Angle Formulas
(1-r/1-r)
Between the vertex and the minor axis on the major axis
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
V = (4/3)pr

35. How can you determine the arc degree or central angle of an inscribed angle?
Multiply the inscribed angle by 2
x = -b/2a y= c - (b/4a)
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
Sin(a-b) = sin(a)cos(b) - sin(b)cos(a) cos(a-b) = cos(a)cos(b) + sin(a)sin(b) tan(a-b) = [tan(a) - tan(b)] / [1+tan(a)tan(b)]

36. How to determine if a number is prime
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
(x-h) + (y-k) = r - where (h -k) is the center of the circle
A = (degree of the arc / 360)(area of a circle)
D= sv3

37. How can multiple polar coordinates be made?
Adding or subtracting 180 to ? and reversing the sign of r.
F(x) = f(-x)
y = a(x-h) + k - where the vertex is (h -k)
Final amount = original amount x (1+growth rate)^number of changes

38. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
90
No equal sides and no equal angles
y-y1 = m(x-x1)
A = ((s1 + s2)h) / 2

39. Sum of n terms of an arithmetic sequence
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
Adding or subtracting 180 to ? and reversing the sign of r.
No equal sides and no equal angles
(n/2)(a1 + an)

40. Complimentary angles add up to
90
(n-2)180
NCr = nPr / r! = n! / (n-r)!r!
F(x) = f(-x)

41. 30-60-90 triangle
NPr = n! / (n-r)!
(x-h)/a - (y-k)/b = 1
Square the differences between each coordinate - then square root the sum
Hypotenuse is 2x - short side is x - long side is xv3

42. What are natural numbers?
90
D= sv3
(x-h)/a - (y-k)/b = 1
All whole numbers except for 0

43. What is the sum of the interior angles for a polygon with n sides?
D = v(l+w+h)
Their dot product = 0
(n-2)180
Between the vertex and the minor axis on the major axis

44. How many ways can n elements be ordered?
Adding or subtracting 180 to ? and reversing the sign of r.
SA = 4pr
Final amount = original amount x (1+growth rate)^number of changes
N!

45. Standard form of the equation of a parabola.
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
Multiply the inscribed angle by 2
NPr = n! / (n-r)!
y = a(x-h) + k - where the vertex is (h -k)

46. Sum of infinite geometric series
Sin(a-b) = sin(a)cos(b) - sin(b)cos(a) cos(a-b) = cos(a)cos(b) + sin(a)sin(b) tan(a-b) = [tan(a) - tan(b)] / [1+tan(a)tan(b)]
Two sides and two angle are equal
a1 / 1-r
V = (4/3)pr

47. Supplementary angles add up to
180
(y-k)/a - (x-h)/b = 1
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

48. Standard form for a hyperbola that opens vertically
(y-k)/a - (x-h)/b = 1
x = -b/2a y= c - (b/4a)
NPr = n! / (n-r)!
A = (degree of the arc / 360)(area of a circle)

49. Formula for arithmetic sequence
(y-k)/a - (x-h)/b = 1
x=rcos?(theta) y=rsin? (theta)
y = a(x-h) + k - where the vertex is (h -k)
An = a1 + (n-1)d

50. What are relatively prime numbers?
N-1
90
The greatest common factor is 1 - but the numbers are not necessarily prime.
(n-2)180

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SAT Math 2

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