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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.
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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. Surface area of a cone
SA = pr +prl
y = a(x-h) + k - where the vertex is (h -k)
Hypotenuse is xv2 - and the sides are x.
The greatest common factor is 1 - but the numbers are not necessarily prime.

2. Permutation formula (ordering)
An = a1rn?
NPr = n! / (n-r)!
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.

3. Scalene triangle
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
C = a + b - 2abcos(C)
Their dot product = 0
No equal sides and no equal angles

4. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
Between the vertex and the minor axis on the major axis
y = a(x-h) + k - where the vertex is (h -k)
N-1
(n/2)(a1 + an)

5. How can you determine the arc degree or central angle of an inscribed angle?
Hypotenuse is xv2 - and the sides are x.
No equal sides and no equal angles
Multiply the inscribed angle by 2
90

6. Sum of 2 Angles Formulas
(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.
V= (1/3)(prh)
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)]
a1 / 1-r

7. What are relatively prime numbers?
SA = 4pr
SA = pr +prl
The greatest common factor is 1 - but the numbers are not necessarily prime.
(x-h) + (y-k) = r - where (h -k) is the center of the circle

8. Formula for calculation exponential growth
F(x) = -f(-x)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Final amount = original amount x (1+growth rate)^number of changes
D = v(l+w+h)

9. Standard form for a hyperbola that opens vertically
D= sv3
y-y1 = m(x-x1)
(y-k)/a - (x-h)/b = 1
(x-h) + (y-k) = r - where (h -k) is the center of the circle

10. Two vectors are perpendicular if
Hypotenuse is xv2 - and the sides are x.
NPr = n! / (n-r)!
Their dot product = 0
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx

11. Law of Cosines
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Final amount = original amount x (1+growth rate)^number of changes
D= sv3
C = a + b - 2abcos(C)

12. Formula for the diagonal length of a cube
V = (4/3)pr
D= sv3
Multiply the inscribed angle by 2
y-y1 = m(x-x1)

13. Volume of a pyramid
No equal sides and no equal angles
V = (1/3)bh
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)]
(y-k)/a - (x-h)/b = 1

14. Formula for the area of a sector
a1 / 1-r
A = (degree of the arc / 360)(area of a circle)
(y-k)/a - (x-h)/b = 1
Parentheses - exponents - multiplication - division - addition - subtraction

15. Volume of a sphere
V = (4/3)pr
Square the differences between each coordinate - then square root the sum
V = (1/3)bh
Multiply the inscribed angle by 2

16. Define an odd function.
F(x) = -f(-x)
All whole numbers except for 0
(x-h)/a - (y-k)/b = 1
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx

17. Formula for arc length
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
Arc length equals = (degree of the arc / 360)(circumference)
V = (4/3)pr
Multiply the inscribed angle by 2

18. Difference between 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)]
y-y1 = m(x-x1)
NPr = n! / (n-r)!

19. Formula for geometric sequence
An = a1rn?
Square the differences between each coordinate - then square root the sum
A = (degree of the arc / 360)(area of a circle)
C = a + b - 2abcos(C)

20. 45-45-90 triangle
x=rcos?(theta) y=rsin? (theta)
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
V = (4/3)pr
Hypotenuse is xv2 - and the sides are x.

21. Supplementary angles add up to
(x-h)/a - (y-k)/b = 1
Arc length equals = (degree of the arc / 360)(circumference)
180
Hypotenuse is xv2 - and the sides are x.

22. Complimentary angles add up to
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)]
90
V= (1/3)(prh)
(x-h) + (y-k) = r - where (h -k) is the center of the circle

23. Formula for the diagonal length of a rectangular prism
F(x) = -f(-x)
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
D= sv3
D = v(l+w+h)

24. Formula for arithmetic sequence
Adding or subtracting 180 to ? and reversing the sign of r.
(1-r/1-r)
A = ((s1 + s2)h) / 2
An = a1 + (n-1)d

25. What are the conversion equations for polar coordinates to normal coordinates?
Parentheses - exponents - multiplication - division - addition - subtraction
90
x=rcos?(theta) y=rsin? (theta)
x = -b/2a y= c - (b/4a)

26. 30-60-90 triangle
A = (degree of the arc / 360)(area of a circle)
y-y1 = m(x-x1)
Hypotenuse is 2x - short side is x - long side is xv3
D= sv3

27. What are natural numbers?
All whole numbers except for 0
An = a1rn?
V= (1/3)(prh)
(x-h)/a - (y-k)/b = 1

28. What is the order of operations?
Parentheses - exponents - multiplication - division - addition - subtraction
D = v(l+w+h)
Final amount = original amount x (1+growth rate)^number of changes
V= (1/3)(prh)

29. How to find the distance between two points in 3d plane?
x=rcos?(theta) y=rsin? (theta)
Square the differences between each coordinate - then square root the sum
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
An = a1rn?

30. Double Angle Formulas
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
90
x=rcos?(theta) y=rsin? (theta)
(n/2)(a1 + an)

31. Standard form equation for an ellipse
(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
C = a + b - 2abcos(C)
(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.

32. What is the sum of the interior angles for a polygon with n sides?
V= (1/3)(prh)
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)]
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
(n-2)180

33. Standard form for a hyperbola that opens to the sides
(x-h)/a - (y-k)/b = 1
Hypotenuse is xv2 - and the sides are x.
Between the vertex and the minor axis on the major axis
F(x) = f(-x)

34. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
D = v(l+w+h)
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
y-y1 = m(x-x1)

35. Sum of finite geometric series
Hypotenuse is 2x - short side is x - long side is xv3
N!
(1-r/1-r)
F(x) = f(-x)

36. If the general parabola equation is y = ax+bx+c - what is the vertex of the parabola
NCr = nPr / r! = n! / (n-r)!r!
D = v(l+w+h)
x = -b/2a y= c - (b/4a)
(x-h) + (y-k) = r - where (h -k) is the center of the circle

37. Surface area of a sphere
The greatest common factor is 1 - but the numbers are not necessarily prime.
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
Adding or subtracting 180 to ? and reversing the sign of r.
SA = 4pr

38. Standard form equation for circle
Hypotenuse is xv2 - and the sides are x.
A = (degree of the arc / 360)(area of a circle)
D = v(l+w+h)
(x-h) + (y-k) = r - where (h -k) is the center of the circle

39. In an ellipse - where are the foci?
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)]
(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
An = a1 + (n-1)d

40. Formula for the area of a trapezoid
Hypotenuse is xv2 - and the sides are x.
A = ((s1 + s2)h) / 2
(x-h) + (y-k) = r - where (h -k) is the center of the circle
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

41. Pythagorean Identities
a1 / 1-r
A = ((s1 + s2)h) / 2
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
V= (1/3)(prh)

42. How can multiple polar coordinates be made?
A = (degree of the arc / 360)(area of a circle)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Two sides and two angle are equal
Adding or subtracting 180 to ? and reversing the sign of r.

43. How many ways can n elements be ordered?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
a1 / 1-r
N!

44. Where is tangent positive/negative?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Between the vertex and the minor axis on the major axis
N!
NCr = nPr / r! = n! / (n-r)!r!

45. What is the form of a polar coordinate?
N-1
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
y = a(x-h) + k - where the vertex is (h -k)
SA = pr +prl

46. What is the triangle inequality rule?
All whole numbers except for 0
Square the differences between each coordinate - then square root the sum
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
NPr = n! / (n-r)!

47. Standard form of the equation of a parabola.
(x-h) + (y-k) = r - where (h -k) is the center of the circle
y = a(x-h) + k - where the vertex is (h -k)
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)]

48. How to determine if a number is prime
Adding or subtracting 180 to ? and reversing the sign of r.
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
NPr = n! / (n-r)!
C = a + b - 2abcos(C)

49. Combination formula
Parentheses - exponents - multiplication - division - addition - subtraction
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
C = a + b - 2abcos(C)
NCr = nPr / r! = n! / (n-r)!r!

50. Define an even function.
F(x) = f(-x)
No equal sides and no equal angles
Their dot product = 0
(x-h)/a - (y-k)/b = 1

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