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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. Sum of n terms of an arithmetic sequence
V = (1/3)bh
(n/2)(a1 + an)
No equal sides and no equal angles
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

2. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
y-y1 = m(x-x1)
(n/2)(a1 + an)
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!

3. Volume of a pyramid
NPr = n! / (n-r)!
V = (1/3)bh
180
(x-h) + (y-k) = r - where (h -k) is the center of the circle

4. 30-60-90 triangle
Adding or subtracting 180 to ? and reversing the sign of r.
F(x) = -f(-x)
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
Hypotenuse is 2x - short side is x - long side is xv3

5. If the general parabola equation is y = ax+bx+c - what is the vertex of the parabola
(x-h)/a - (y-k)/b = 1
(y-k)/a - (x-h)/b = 1
x = -b/2a y= c - (b/4a)
F(x) = -f(-x)

6. What are natural numbers?
V= (1/3)(prh)
All whole numbers except for 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

7. What is the order of operations?
NPr = n! / (n-r)!
Parentheses - exponents - multiplication - division - addition - subtraction
SA = pr +prl
a1 / 1-r

8. Where is tangent positive/negative?
D= sv3
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Their dot product = 0

9. Supplementary angles add up to
x = -b/2a y= c - (b/4a)
V= (1/3)(prh)
No equal sides and no equal angles
180

10. Pythagorean Identities
Square the differences between each coordinate - then square root the sum
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
180
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

11. Complimentary angles add up to
90
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
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)]
Arc length equals = (degree of the arc / 360)(circumference)

12. Combination formula
NCr = nPr / r! = n! / (n-r)!r!
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
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)]

13. How to find the distance between two points in 3d plane?
(x-h)/a - (y-k)/b = 1
Square the differences between each coordinate - then square root the sum
Parentheses - exponents - multiplication - division - addition - subtraction
(n-2)180

14. 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
x=rcos?(theta) y=rsin? (theta)
An = a1 + (n-1)d
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx

15. Formula for the volume of a cone
NPr = n! / (n-r)!
V= (1/3)(prh)
V = (4/3)pr
(x-h)/a - (y-k)/b = 1

16. Scalene triangle
D= sv3
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
No equal sides and no equal angles
Hypotenuse is 2x - short side is x - long side is xv3

17. How can you determine the arc degree or central angle of an inscribed angle?
Multiply the inscribed angle by 2
The greatest common factor is 1 - but the numbers are not necessarily prime.
(n/2)(a1 + an)
Arc length equals = (degree of the arc / 360)(circumference)

18. What is the sum of the interior angles for a polygon with n sides?
a1 / 1-r
Adding or subtracting 180 to ? and reversing the sign of r.
(n-2)180
Arc length equals = (degree of the arc / 360)(circumference)

19. Formula for the diagonal length of a rectangular prism
N-1
y-y1 = m(x-x1)
V = (1/3)bh
D = v(l+w+h)

20. 45-45-90 triangle
An = a1 + (n-1)d
x = -b/2a y= c - (b/4a)
Hypotenuse is xv2 - and the sides are x.
Hypotenuse is 2x - short side is x - long side is xv3

21. Sum of 2 Angles Formulas
Final amount = original amount x (1+growth rate)^number of changes
y-y1 = m(x-x1)
Parentheses - exponents - multiplication - division - addition - subtraction
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)]

22. Formula for calculation exponential growth
F(x) = f(-x)
(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.
Final amount = original amount x (1+growth rate)^number of changes
SA = pr +prl

23. Define an even function.
90
(n/2)(a1 + an)
C = a + b - 2abcos(C)
F(x) = f(-x)

24. Two vectors are perpendicular if
Parentheses - exponents - multiplication - division - addition - subtraction
Their dot product = 0
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
A = ((s1 + s2)h) / 2

25. Surface area of a sphere
SA = 4pr
Multiply the inscribed angle by 2
D= sv3
Square the differences between each coordinate - then square root the sum

26. Standard form equation for circle
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)]
F(x) = -f(-x)
a1 / 1-r
(x-h) + (y-k) = r - where (h -k) is the center of the circle

27. How to determine if a number is prime
(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)
Between the vertex and the minor axis on the major axis

28. How many ways can n elements be ordered?
N!
y-y1 = m(x-x1)
F(x) = -f(-x)
Hypotenuse is xv2 - and the sides are x.

29. Standard form of the equation of a parabola.
V= (1/3)(prh)
y = a(x-h) + k - where the vertex is (h -k)
The greatest common factor is 1 - but the numbers are not necessarily prime.
90

30. Permutation formula (ordering)
NPr = n! / (n-r)!
Their dot product = 0
(x-h)/a - (y-k)/b = 1
D = v(l+w+h)

31. What are relatively prime numbers?
Arc length equals = (degree of the arc / 360)(circumference)
The greatest common factor is 1 - but the numbers are not necessarily prime.
An = a1rn?
F(x) = -f(-x)

32. Sum of finite geometric series
All whole numbers except for 0
(1-r/1-r)
D= sv3
Arc length equals = (degree of the arc / 360)(circumference)

33. Surface area of a cone
SA = pr +prl
180
C = a + b - 2abcos(C)
N!

34. Double Angle Formulas
Multiply the inscribed angle by 2
(n/2)(a1 + an)
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx

35. What is the triangle inequality rule?
All whole numbers except for 0
NPr = n! / (n-r)!
a1 / 1-r
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

36. In an ellipse - where are the foci?
NCr = nPr / r! = n! / (n-r)!r!
Their dot product = 0
Between the vertex and the minor axis on the major axis
F(x) = f(-x)

37. Formula for geometric sequence
V = (1/3)bh
D= sv3
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
An = a1rn?

38. Formula for the area of a trapezoid
Hypotenuse is xv2 - and the sides are x.
V= (1/3)(prh)
x=rcos?(theta) y=rsin? (theta)
A = ((s1 + s2)h) / 2

39. Formula for the diagonal length of a cube
Multiply the inscribed angle by 2
D = v(l+w+h)
An = a1rn?
D= sv3

40. What are the conversion equations for polar coordinates to normal coordinates?
x=rcos?(theta) y=rsin? (theta)
D= sv3
Between the vertex and the minor axis on the major axis
The greatest common factor is 1 - but the numbers are not necessarily prime.

41. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
The greatest common factor is 1 - but the numbers are not necessarily prime.
Two sides and two angle are equal
Square the differences between each coordinate - then square root the sum
N-1

42. Law of Cosines
F(x) = f(-x)
C = a + b - 2abcos(C)
(n/2)(a1 + an)
Adding or subtracting 180 to ? and reversing the sign of r.

43. Formula for the area of a sector
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
NPr = n! / (n-r)!
A = (degree of the arc / 360)(area of a circle)
D= sv3

44. How can multiple polar coordinates be made?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
All whole numbers except for 0
Adding or subtracting 180 to ? and reversing the sign of r.
90

45. Standard form for a hyperbola that opens to the sides
y-y1 = m(x-x1)
(x-h)/a - (y-k)/b = 1
A = ((s1 + s2)h) / 2
(n-2)180

46. Formula for arc length
Their dot product = 0
Arc length equals = (degree of the arc / 360)(circumference)
N!
(y-k)/a - (x-h)/b = 1

47. Isosceles Triangles
F(x) = -f(-x)
(x-h)/a - (y-k)/b = 1
Two sides and two angle are equal
F(x) = f(-x)

48. Sum of infinite 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.
N!
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
a1 / 1-r

49. Formula for arithmetic sequence
An = a1 + (n-1)d
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.
Adding or subtracting 180 to ? and reversing the sign of r.

50. Standard form for a hyperbola that opens vertically
Arc length equals = (degree of the arc / 360)(circumference)
A = (degree of the arc / 360)(area of a circle)
y = a(x-h) + k - where the vertex is (h -k)
(y-k)/a - (x-h)/b = 1

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SAT Math 2

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