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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. Formula for arc length
Adding or subtracting 180 to ? and reversing the sign of r.
NCr = nPr / r! = n! / (n-r)!r!
Square the differences between each coordinate - then square root the sum
Arc length equals = (degree of the arc / 360)(circumference)

2. How to find the distance between two points in 3d plane?
(1-r/1-r)
Square the differences between each coordinate - then square root the sum
A = ((s1 + s2)h) / 2
V= (1/3)(prh)

3. 45-45-90 triangle
D= sv3
(x-h)/a - (y-k)/b = 1
Hypotenuse is xv2 - and the sides are x.
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

4. Formula for the area of a sector
All whole numbers except for 0
A = (degree of the arc / 360)(area of a circle)
C = a + b - 2abcos(C)
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx

5. Formula for the diagonal length of a rectangular prism
(n/2)(a1 + an)
V= (1/3)(prh)
(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.
D = v(l+w+h)

6. Standard form equation for an ellipse
a1 / 1-r
Arc length equals = (degree of the arc / 360)(circumference)
An = a1rn?
(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.

7. 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
F(x) = -f(-x)
NPr = n! / (n-r)!
C = a + b - 2abcos(C)

8. What is the form of a polar coordinate?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
F(x) = f(-x)
No equal sides and no equal angles
x=rcos?(theta) y=rsin? (theta)

9. What is the order of operations?
Parentheses - exponents - multiplication - division - addition - subtraction
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)]
Hypotenuse is 2x - short side is x - long side is xv3

10. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
Their dot product = 0
x = -b/2a y= c - (b/4a)
y-y1 = m(x-x1)
(n-2)180

11. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
SA = pr +prl

12. Formula for arithmetic sequence
Multiply the inscribed angle by 2
An = a1 + (n-1)d
180
(x-h)/a - (y-k)/b = 1

13. Scalene triangle
y-y1 = m(x-x1)
A = (degree of the arc / 360)(area of a circle)
a1 / 1-r
No equal sides and no equal angles

14. Formula for the diagonal length of a cube
(x-h) + (y-k) = r - where (h -k) is the center of the circle
N!
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
D= sv3

15. 30-60-90 triangle
C = a + b - 2abcos(C)
Hypotenuse is 2x - short side is x - long side is xv3
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
180

16. Standard form of the equation of a parabola.
SA = pr +prl
(1-r/1-r)
y = a(x-h) + k - where the vertex is (h -k)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

17. Sum of infinite geometric series
180
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
A = ((s1 + s2)h) / 2
a1 / 1-r

18. What are the conversion equations for polar coordinates to normal coordinates?
NCr = nPr / r! = n! / (n-r)!r!
Multiply the inscribed angle by 2
x=rcos?(theta) y=rsin? (theta)
(y-k)/a - (x-h)/b = 1

19. Where is tangent positive/negative?
Adding or subtracting 180 to ? and reversing the sign of r.
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)]
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
C = a + b - 2abcos(C)

20. How can you determine the arc degree or central angle of an inscribed angle?
D = v(l+w+h)
Adding or subtracting 180 to ? and reversing the sign of r.
Multiply the inscribed angle by 2
N-1

21. Isosceles Triangles
(x-h)/a - (y-k)/b = 1
Two sides and two angle are equal
NPr = n! / (n-r)!
180

22. What is the sum of the interior angles for a polygon with n sides?
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
Adding or subtracting 180 to ? and reversing the sign of r.
(n-2)180
(y-k)/a - (x-h)/b = 1

23. Standard form equation for circle
a1 / 1-r
(x-h) + (y-k) = r - where (h -k) is the center of the circle
Arc length equals = (degree of the arc / 360)(circumference)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

24. Law of Cosines
Their dot product = 0
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
N-1
C = a + b - 2abcos(C)

25. In an ellipse - where are the foci?
(x-h)/a - (y-k)/b = 1
NCr = nPr / r! = n! / (n-r)!r!
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Between the vertex and the minor axis on the major axis

26. Formula for geometric sequence
An = a1rn?
SA = pr +prl
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
SA = 4pr

27. Combination formula
NCr = nPr / r! = n! / (n-r)!r!
Square the differences between each coordinate - then square root the sum
Their dot product = 0
(y-k)/a - (x-h)/b = 1

28. What are natural numbers?
180
(x-h)/a - (y-k)/b = 1
F(x) = f(-x)
All whole numbers except for 0

29. Sum of n terms of an arithmetic sequence
SA = pr +prl
NPr = n! / (n-r)!
(n/2)(a1 + an)
Hypotenuse is xv2 - and the sides are x.

30. What is the triangle inequality rule?
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
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-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.
NPr = n! / (n-r)!

31. Formula for calculation exponential growth
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Final amount = original amount x (1+growth rate)^number of changes
F(x) = -f(-x)
(n/2)(a1 + an)

32. Double Angle Formulas
An = a1rn?
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
Arc length equals = (degree of the arc / 360)(circumference)
Hypotenuse is xv2 - and the sides are x.

33. Difference between 2 Angles formulas
x = -b/2a y= c - (b/4a)
Hypotenuse is 2x - short side is x - long side is xv3
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)]
The greatest common factor is 1 - but the numbers are not necessarily prime.

34. Two vectors are perpendicular if
A = ((s1 + s2)h) / 2
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
Their dot product = 0
An = a1 + (n-1)d

35. Define an even function.
Hypotenuse is 2x - short side is x - long side is xv3
F(x) = f(-x)
Between the vertex and the minor axis on the major axis
y-y1 = m(x-x1)

36. Volume of a sphere
Final amount = original amount x (1+growth rate)^number of changes
V = (4/3)pr
A = ((s1 + s2)h) / 2
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

37. Standard form for a hyperbola that opens vertically
N!
(1-r/1-r)
(y-k)/a - (x-h)/b = 1
N-1

38. Pythagorean Identities
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)]
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
(1-r/1-r)

39. Define an odd function.
Between the vertex and the minor axis on the major axis
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Their dot product = 0
F(x) = -f(-x)

40. How can multiple polar coordinates be made?
a1 / 1-r
All whole numbers except for 0
Adding or subtracting 180 to ? and reversing the sign of r.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

41. Permutation formula (ordering)
NPr = n! / (n-r)!
(n/2)(a1 + an)
Parentheses - exponents - multiplication - division - addition - subtraction
x = -b/2a y= c - (b/4a)

42. Sum of finite geometric series
A = (degree of the arc / 360)(area of a circle)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Two sides and two angle are equal
(1-r/1-r)

43. How many ways can n elements be ordered?
(x-h)/a - (y-k)/b = 1
Hypotenuse is 2x - short side is x - long side is xv3
N!
NCr = nPr / r! = n! / (n-r)!r!

44. If the general parabola equation is y = ax+bx+c - what is the vertex of the parabola
x = -b/2a y= c - (b/4a)
Hypotenuse is 2x - short side is x - long side is xv3
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
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)]

45. Complimentary angles add up to
Between the vertex and the minor axis on the major axis
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.
V = (4/3)pr

46. Surface area of a sphere
F(x) = f(-x)
N-1
SA = 4pr
V = (4/3)pr

47. Sum of 2 Angles Formulas
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
NPr = n! / (n-r)!
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)]

48. Volume of a pyramid
(n/2)(a1 + an)
V = (1/3)bh
Between the vertex and the minor axis on the major axis
Final amount = original amount x (1+growth rate)^number of changes

49. Formula for the area of a trapezoid
(1-r/1-r)
Their dot product = 0
A = ((s1 + s2)h) / 2
y-y1 = m(x-x1)

50. Supplementary angles add up to
V = (4/3)pr
D= sv3
180
(x-h)/a - (y-k)/b = 1

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SAT Math 2

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