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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. What is the triangle inequality rule?
No equal sides and no equal angles
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.
A = ((s1 + s2)h) / 2

2. Surface area of a sphere
(n-2)180
SA = 4pr
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)]
Adding or subtracting 180 to ? and reversing the sign of r.

3. In an ellipse - where are the foci?
Adding or subtracting 180 to ? and reversing the sign of r.
Between the vertex and the minor axis on the major axis
NPr = n! / (n-r)!
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

4. Law of Cosines
a1 / 1-r
The greatest common factor is 1 - but the numbers are not necessarily prime.
No equal sides and no equal angles
C = a + b - 2abcos(C)

5. Standard form for a hyperbola that opens vertically
Adding or subtracting 180 to ? and reversing the sign of r.
(y-k)/a - (x-h)/b = 1
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)]
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx

6. Permutation formula (ordering)
NPr = n! / (n-r)!
SA = 4pr
N!
Adding or subtracting 180 to ? and reversing the sign of r.

7. Standard form equation for circle
N-1
(x-h) + (y-k) = r - where (h -k) is the center of the circle
A = ((s1 + s2)h) / 2
F(x) = -f(-x)

8. Standard form for a hyperbola that opens to the sides
Two sides and two angle are equal
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
(x-h)/a - (y-k)/b = 1

9. Formula for the volume of a cone
V= (1/3)(prh)
180
SA = 4pr
Between the vertex and the minor axis on the major axis

10. Difference between 2 Angles formulas
All whole numbers except for 0
N!
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)]
A = ((s1 + s2)h) / 2

11. Formula for calculation exponential growth
D = v(l+w+h)
Final amount = original amount x (1+growth rate)^number of changes
V= (1/3)(prh)
No equal sides and no equal angles

12. Volume of a sphere
V = (4/3)pr
(x-h)/a - (y-k)/b = 1
Hypotenuse is xv2 - and the sides are x.
V = (1/3)bh

13. If the general parabola equation is y = ax+bx+c - what is the vertex of the parabola
D= sv3
Adding or subtracting 180 to ? and reversing the sign of r.
SA = pr +prl
x = -b/2a y= c - (b/4a)

14. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
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)]
Between the vertex and the minor axis on the major axis
y-y1 = m(x-x1)
180

15. Sum of n terms of an arithmetic sequence
Final amount = original amount x (1+growth rate)^number of changes
(n/2)(a1 + an)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
A = (degree of the arc / 360)(area of a circle)

16. What is the order of operations?
SA = 4pr
Parentheses - exponents - multiplication - division - addition - subtraction
y-y1 = m(x-x1)
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx

17. Where is tangent positive/negative?
V = (4/3)pr
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
x = -b/2a y= c - (b/4a)
V = (1/3)bh

18. What are natural numbers?
All whole numbers except for 0
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
Hypotenuse is xv2 - and the sides are x.
Multiply the inscribed angle by 2

19. Sum of finite geometric series
(1-r/1-r)
C = a + b - 2abcos(C)
N-1
D = v(l+w+h)

20. Formula for the area of a trapezoid
(y-k)/a - (x-h)/b = 1
Two sides and two angle are equal
Multiply the inscribed angle by 2
A = ((s1 + s2)h) / 2

21. Standard form of the equation of a parabola.
Final amount = original amount x (1+growth rate)^number of changes
Multiply the inscribed angle by 2
D = v(l+w+h)
y = a(x-h) + k - where the vertex is (h -k)

22. Sum of 2 Angles Formulas
y-y1 = m(x-x1)
Two sides and two angle are equal
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)]
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)]

23. Supplementary angles add up to
Two sides and two angle are equal
(y-k)/a - (x-h)/b = 1
180
A = ((s1 + s2)h) / 2

24. Isosceles Triangles
(n/2)(a1 + an)
Two sides and two angle are equal
(x-h) + (y-k) = r - where (h -k) is the center of the circle
Between the vertex and the minor axis on the major axis

25. Sum of infinite geometric series
SA = pr +prl
F(x) = f(-x)
Two sides and two angle are equal
a1 / 1-r

26. Formula for geometric sequence
Their dot product = 0
V= (1/3)(prh)
NCr = nPr / r! = n! / (n-r)!r!
An = a1rn?

27. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
Between the vertex and the minor axis on the major axis
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
Arc length equals = (degree of the arc / 360)(circumference)

28. Define an odd function.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
F(x) = -f(-x)
180
Parentheses - exponents - multiplication - division - addition - subtraction

29. What is the form of a polar coordinate?
(n/2)(a1 + an)
(n-2)180
(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

30. What are relatively prime numbers?
The greatest common factor is 1 - but the numbers are not necessarily prime.
Arc length equals = (degree of the arc / 360)(circumference)
(x-h)/a - (y-k)/b = 1
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)]

31. How can you determine the arc degree or central angle of an inscribed angle?
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
Multiply the inscribed angle by 2
y = a(x-h) + k - where the vertex is (h -k)
(1-r/1-r)

32. Define an even function.
Between the vertex and the minor axis on the major axis
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
SA = pr +prl
F(x) = f(-x)

33. Standard form equation for an ellipse
180
x = -b/2a y= c - (b/4a)
(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.
a1 / 1-r

34. Complimentary angles add up to
90
Adding or subtracting 180 to ? and reversing the sign of r.
All whole numbers except for 0
y = a(x-h) + k - where the vertex is (h -k)

35. What are the conversion equations for polar coordinates to normal coordinates?
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)]
V= (1/3)(prh)
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)

36. How can multiple polar coordinates be made?
Adding or subtracting 180 to ? and reversing the sign of r.
Square the differences between each coordinate - then square root the sum
NPr = n! / (n-r)!
An = a1 + (n-1)d

37. Volume of a pyramid
C = a + b - 2abcos(C)
V = (1/3)bh
Multiply the inscribed angle by 2
An = a1rn?

38. How to find the distance between two points in 3d plane?
(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
Square the differences between each coordinate - then square root the sum
An = a1rn?

39. Two vectors are perpendicular if
An = a1 + (n-1)d
Their dot product = 0
Two sides and two angle are equal
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

40. What is the sum of the interior angles for a polygon with n sides?
All whole numbers except for 0
F(x) = -f(-x)
y = a(x-h) + k - where the vertex is (h -k)
(n-2)180

41. Formula for the diagonal length of a cube
(x-h) + (y-k) = r - where (h -k) is the center of the circle
D= sv3
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Multiply the inscribed angle by 2

42. Pythagorean Identities
(y-k)/a - (x-h)/b = 1
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
y-y1 = m(x-x1)
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx

43. Formula for arithmetic sequence
An = a1 + (n-1)d
D = v(l+w+h)
Multiply the inscribed angle by 2
SA = pr +prl

44. Combination formula
(n/2)(a1 + an)
90
An = a1rn?
NCr = nPr / r! = n! / (n-r)!r!

45. 30-60-90 triangle
180
D = v(l+w+h)
Multiply the inscribed angle by 2
Hypotenuse is 2x - short side is x - long side is xv3

46. 45-45-90 triangle
SA = 4pr
90
Hypotenuse is xv2 - and the sides are x.
y-y1 = m(x-x1)

47. Scalene triangle
No equal sides and no equal angles
a1 / 1-r
An = a1rn?
A = (degree of the arc / 360)(area of a circle)

48. Surface area of a cone
Two sides and two angle are equal
SA = pr +prl
A = ((s1 + s2)h) / 2
No equal sides and no equal angles

49. Formula for the diagonal length of a rectangular prism
V = (4/3)pr
D = v(l+w+h)
x = -b/2a y= c - (b/4a)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

50. 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
y-y1 = m(x-x1)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Their dot product = 0

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SAT Math 2

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