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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. Law of Cosines
C² = a² + b² - 2abcos(C)
a1 / 1-r
An = a1 + (n-1)d
NCr = nPr / r! = n! / (n-r)!r!

2. How many ways can n elements be ordered?
N!
SA = pr² +prl
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)]
x = -b/2a y= c - (b²/4a)

3. Combination formula
NCr = nPr / r! = n! / (n-r)!r!
y-y1 = m(x-x1)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Between the vertex and the minor axis on the major axis

4. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
V = (4/3)pr³
A = (degree of the arc / 360)(area of a circle)
C² = a² + b² - 2abcos(C)

5. Complimentary angles add up to
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
90°
180°

6. Formula for the volume of a cone
V= (1/3)(pr²h)
(1-r/1-r)
x = -b/2a y= c - (b²/4a)
A = ((s1 + s2)h) / 2

7. How can multiple polar coordinates be made?
(1-r/1-r)
A = (degree of the arc / 360)(area of a circle)
Adding or subtracting 180 to ? and reversing the sign of r.
F(x) = f(-x)

8. Standard form of the equation of a parabola.
y = a(x-h)² + k - where the vertex is (h -k)
No equal sides and no equal angles
90°
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

9. Define an odd function.
F(x) = -f(-x)
The greatest common factor is 1 - but the numbers are not necessarily prime.
An = a1 + (n-1)d
(x-h)²/a² + (y-k)²/b² = 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.

10. What are natural numbers?
a1 / 1-r
All whole numbers except for 0
N-1
(y-k)²/a² - (x-h)²/b² = 1

11. Where is tangent positive/negative?
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
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Square the differences between each coordinate - then square root the sum

12. How to determine if a number is prime
y-y1 = m(x-x1)
An = a1rn?¹
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
No equal sides and no equal angles

13. Sum of n terms of an arithmetic sequence
(1-r/1-r)
N-1
Multiply the inscribed angle by 2
(n/2)(a1 + an)

14. Standard form for a hyperbola that opens to the sides
D= sv3
A = (degree of the arc / 360)(area of a circle)
(x-h)²/a² - (y-k)²/b² = 1
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

15. Supplementary angles add up to
Arc length equals = (degree of the arc / 360)(circumference)
(1-r/1-r)
a1 / 1-r
180°

16. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
SA = 4pr²
x = -b/2a y= c - (b²/4a)
(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

17. 45-45-90 triangle
A = ((s1 + s2)h) / 2
x = -b/2a y= c - (b²/4a)
(x-h)²/a² - (y-k)²/b² = 1
Hypotenuse is xv2 - and the sides are x.

18. Define an even function.
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
A = (degree of the arc / 360)(area of a circle)
F(x) = f(-x)
NCr = nPr / r! = n! / (n-r)!r!

19. Scalene triangle
N!
a1 / 1-r
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
No equal sides and no equal angles

20. Isosceles Triangles
180°
An = a1 + (n-1)d
Two sides and two angle are equal
x=rcos?(theta) y=rsin? (theta)

21. How to find the distance between two points in 3d plane?
Square the differences between each coordinate - then square root the sum
An = a1rn?¹
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Parentheses - exponents - multiplication - division - addition - subtraction

22. Formula for arithmetic sequence
D= sv3
An = a1 + (n-1)d
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Parentheses - exponents - multiplication - division - addition - subtraction

23. Difference between 2 Angles formulas
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)]
An = a1rn?¹
Hypotenuse is xv2 - and the sides are x.
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

24. Formula for the area of a trapezoid
V= (1/3)(pr²h)
A = ((s1 + s2)h) / 2
N-1
Two sides and two angle are equal

25. Formula for arc length
Arc length equals = (degree of the arc / 360)(circumference)
SA = pr² +prl
Their dot product = 0
(n-2)180

26. Formula for the area of a sector
y-y1 = m(x-x1)
C² = a² + b² - 2abcos(C)
An = a1rn?¹
A = (degree of the arc / 360)(area of a circle)

27. Sum of infinite geometric series
All whole numbers except for 0
a1 / 1-r
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
180°

28. What is the sum of the interior angles for a polygon with n sides?
(n-2)180
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Arc length equals = (degree of the arc / 360)(circumference)
SA = pr² +prl

29. Volume of a sphere
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)]
Their dot product = 0
V = (4/3)pr³
Parentheses - exponents - multiplication - division - addition - subtraction

30. What are relatively prime numbers?
Square the differences between each coordinate - then square root the sum
The greatest common factor is 1 - but the numbers are not necessarily prime.
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)]
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

31. How can you determine the arc degree or central angle of an inscribed angle?
x = -b/2a y= c - (b²/4a)
SA = pr² +prl
Multiply the inscribed angle by 2
Between the vertex and the minor axis on the major axis

32. Formula for geometric sequence
Hypotenuse is xv2 - and the sides are x.
An = a1rn?¹
Hypotenuse is 2x - short side is x - long side is xv3
C² = a² + b² - 2abcos(C)

33. Standard form for a hyperbola that opens vertically
Hypotenuse is xv2 - and the sides are x.
a1 / 1-r
(y-k)²/a² - (x-h)²/b² = 1
F(x) = -f(-x)

34. Sum of finite geometric series
Hypotenuse is xv2 - and the sides are x.
(1-r/1-r)
All whole numbers except for 0
V = (1/3)bh

35. What is the order of operations?
Hypotenuse is xv2 - and the sides are x.
y = a(x-h)² + k - where the vertex is (h -k)
Parentheses - exponents - multiplication - division - addition - subtraction
SA = pr² +prl

36. Volume of a pyramid
(n/2)(a1 + an)
(x-h)²/a² + (y-k)²/b² = 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.
Multiply the inscribed angle by 2
V = (1/3)bh

37. 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
a1 / 1-r
An = a1 + (n-1)d

38. Permutation formula (ordering)
An = a1 + (n-1)d
NPr = n! / (n-r)!
NCr = nPr / r! = n! / (n-r)!r!
(n/2)(a1 + an)

39. 30-60-90 triangle
Hypotenuse is 2x - short side is x - long side is xv3
Arc length equals = (degree of the arc / 360)(circumference)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
SA = 4pr²

40. Surface area of a sphere
y-y1 = m(x-x1)
SA = 4pr²
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.

41. Double Angle Formulas
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
All whole numbers except for 0
x = -b/2a y= c - (b²/4a)
F(x) = f(-x)

42. What are the conversion equations for polar coordinates to normal coordinates?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
x=rcos?(theta) y=rsin? (theta)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
No equal sides and no equal angles

43. In an ellipse - where are the foci?
C² = a² + b² - 2abcos(C)
(x-h)²/a² + (y-k)²/b² = 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)bh
Between the vertex and the minor axis on the major axis

44. What is the triangle inequality rule?
C² = a² + b² - 2abcos(C)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Parentheses - exponents - multiplication - division - addition - subtraction
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

45. Formula for calculation exponential growth
No equal sides and no equal angles
(y-k)²/a² - (x-h)²/b² = 1
N!
Final amount = original amount x (1+growth rate)^number of changes

46. Surface area of a cone
Final amount = original amount x (1+growth rate)^number of changes
Arc length equals = (degree of the arc / 360)(circumference)
D= sv3
SA = pr² +prl

47. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
V = (1/3)bh
y-y1 = m(x-x1)
V = (4/3)pr³
No equal sides and no equal angles

48. Formula for the diagonal length of a rectangular prism
Between the vertex and the minor axis on the major axis
D = v(l²+w²+h²)
Arc length equals = (degree of the arc / 360)(circumference)
SA = 4pr²

49. Pythagorean Identities
An = a1 + (n-1)d
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
(x-h)²/a² - (y-k)²/b² = 1
(n/2)(a1 + an)

50. Standard form equation for an ellipse
NCr = nPr / r! = n! / (n-r)!r!
y-y1 = m(x-x1)
(n/2)(a1 + an)
(x-h)²/a² + (y-k)²/b² = 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.