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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. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
N-1
180°
A = ((s1 + s2)h) / 2
y-y1 = m(x-x1)

2. What is the triangle inequality rule?
V= (1/3)(pr²h)
V = (4/3)pr³
(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.
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. What are natural numbers?
All whole numbers except for 0
(x-h)² + (y-k)² = r² - where (h -k) is the center of the 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)]
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
x = -b/2a y= c - (b²/4a)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
y = a(x-h)² + k - where the vertex is (h -k)

5. Pythagorean Identities
Hypotenuse is xv2 - and the sides are x.
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
(1-r/1-r)

6. Sum of n terms of an arithmetic sequence
(n/2)(a1 + an)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
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

7. Define an even function.
F(x) = f(-x)
Between the vertex and the minor axis on the major axis
SA = pr² +prl
a1 / 1-r

8. Standard form equation for circle
a1 / 1-r
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
F(x) = -f(-x)

9. Formula for calculation exponential growth
Final amount = original amount x (1+growth rate)^number of changes
Between the vertex and the minor axis on the major axis
(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.
An = a1 + (n-1)d

10. What are relatively prime numbers?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
x=rcos?(theta) y=rsin? (theta)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
The greatest common factor is 1 - but the numbers are not necessarily prime.

11. Sum of finite geometric series
(1-r/1-r)
Adding or subtracting 180 to ? and reversing the sign of r.
SA = pr² +prl
A = (degree of the arc / 360)(area of a circle)

12. Complimentary angles add up to
Hypotenuse is 2x - short side is x - long side is xv3
y = a(x-h)² + k - where the vertex is (h -k)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
90°

13. Isosceles Triangles
F(x) = f(-x)
Two sides and two angle are equal
y-y1 = m(x-x1)
D= sv3

14. 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
A = (degree of the arc / 360)(area of a circle)
Parentheses - exponents - multiplication - division - addition - subtraction
All whole numbers except for 0

15. Formula for the diagonal length of a cube
D= sv3
SA = pr² +prl
Arc length equals = (degree of the arc / 360)(circumference)
The greatest common factor is 1 - but the numbers are not necessarily prime.

16. Formula for arc length
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)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
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)]

17. Two vectors are perpendicular if
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)]
Their dot product = 0
F(x) = -f(-x)

18. Supplementary angles add up to
N!
SA = pr² +prl
Two sides and two angle are equal
180°

19. Formula for the volume of a cone
D= sv3
No equal sides and no equal angles
N-1
V= (1/3)(pr²h)

20. Define an odd function.
a1 / 1-r
F(x) = -f(-x)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
V = (1/3)bh

21. Surface area of a sphere
Their dot product = 0
SA = pr² +prl
(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.
SA = 4pr²

22. How can multiple polar coordinates be made?
An = a1rn?¹
Adding or subtracting 180 to ? and reversing the sign of r.
(y-k)²/a² - (x-h)²/b² = 1
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

23. Permutation formula (ordering)
NPr = n! / (n-r)!
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
(n-2)180
An = a1 + (n-1)d

24. Scalene triangle
Final amount = original amount x (1+growth rate)^number of changes
No equal sides and no equal angles
Their dot product = 0
Square the differences between each coordinate - then square root the sum

25. Sum of 2 Angles Formulas
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
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)]
Final amount = original amount x (1+growth rate)^number of changes

26. Double Angle Formulas
x = -b/2a y= c - (b²/4a)
180°
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
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)]

27. Formula for the area of a trapezoid
Arc length equals = (degree of the arc / 360)(circumference)
NPr = n! / (n-r)!
A = ((s1 + s2)h) / 2
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)]

28. How can you determine the arc degree or central angle of an inscribed angle?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Square the differences between each coordinate - then square root the sum
N-1
Multiply the inscribed angle by 2

29. Formula for arithmetic sequence
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
D= sv3
NCr = nPr / r! = n! / (n-r)!r!
An = a1 + (n-1)d

30. Where is tangent positive/negative?
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
180°
x = -b/2a y= c - (b²/4a)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

31. Standard form for a hyperbola that opens vertically
V = (1/3)bh
(y-k)²/a² - (x-h)²/b² = 1
Between the vertex and the minor axis on the major axis
(n/2)(a1 + an)

32. What is the order of operations?
Parentheses - exponents - multiplication - division - addition - subtraction
NPr = n! / (n-r)!
N!
Adding or subtracting 180 to ? and reversing the sign of r.

33. 45-45-90 triangle
The greatest common factor is 1 - but the numbers are not necessarily prime.
An = a1 + (n-1)d
Hypotenuse is xv2 - and the sides are x.
(n-2)180

34. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
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)
N!

35. Formula for the diagonal length of a rectangular prism
No equal sides and no equal angles
D = v(l²+w²+h²)
Hypotenuse is 2x - short side is x - long side is xv3
SA = 4pr²

36. Standard form equation for an ellipse
y-y1 = m(x-x1)
SA = pr² +prl
(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.
Hypotenuse is 2x - short side is x - long side is xv3

37. Law of Cosines
x = -b/2a y= c - (b²/4a)
Final amount = original amount x (1+growth rate)^number of changes
C² = a² + b² - 2abcos(C)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

38. Formula for the area of a sector
A = (degree of the arc / 360)(area of a circle)
(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)(pr²h)
C² = a² + b² - 2abcos(C)

39. What is the sum of the interior angles for a polygon with n sides?
(1-r/1-r)
The greatest common factor is 1 - but the numbers are not necessarily prime.
(n-2)180
NPr = n! / (n-r)!

40. Volume of a sphere
(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.
180°
(n-2)180
V = (4/3)pr³

41. Volume of a pyramid
F(x) = f(-x)
V = (1/3)bh
Final amount = original amount x (1+growth rate)^number of changes
90°

42. What is the form of a polar coordinate?
90°
F(x) = f(-x)
(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

43. How many ways can n elements be ordered?
N!
Hypotenuse is xv2 - and the sides are x.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
A = ((s1 + s2)h) / 2

44. Standard form of the equation of a parabola.
(n/2)(a1 + an)
NCr = nPr / r! = n! / (n-r)!r!
(n-2)180
y = a(x-h)² + k - where the vertex is (h -k)

45. How to find the distance between two points in 3d plane?
Hypotenuse is 2x - short side is x - long side is xv3
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Square the differences between each coordinate - then square root the sum

46. Sum of infinite geometric series
F(x) = f(-x)
V = (1/3)bh
180°
a1 / 1-r

47. 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)]
x = -b/2a y= c - (b²/4a)
(y-k)²/a² - (x-h)²/b² = 1
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

48. In an ellipse - where are the foci?
Between the vertex and the minor axis on the major axis
Their dot product = 0
90°
a1 / 1-r

49. 30-60-90 triangle
Hypotenuse is 2x - short side is x - long side is xv3
SA = 4pr²
(1-r/1-r)
180°

50. Standard form for a hyperbola that opens to the sides
Hypotenuse is 2x - short side is x - long side is xv3
NCr = nPr / r! = n! / (n-r)!r!
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
(x-h)²/a² - (y-k)²/b² = 1

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SAT Math 2

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