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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. Supplementary angles add up to
180°
(y-k)²/a² - (x-h)²/b² = 1
Hypotenuse is 2x - short side is x - long side is xv3
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

2. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
180°
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(n-2)180
x = -b/2a y= c - (b²/4a)

3. Volume of a pyramid
V = (1/3)bh
An = a1rn?¹
y-y1 = m(x-x1)
N!

4. Double Angle Formulas
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Adding or subtracting 180 to ? and reversing the sign of r.
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)]

5. Isosceles Triangles
All whole numbers except for 0
Two sides and two angle are equal
90°
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)]

6. Sum of finite geometric series
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)]
(1-r/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.

7. Complimentary angles add up to
Final amount = original amount x (1+growth rate)^number of changes
90°
Their dot product = 0
Square the differences between each coordinate - then square root the sum

8. How can you determine the arc degree or central angle of an inscribed angle?
Multiply the inscribed angle by 2
a1 / 1-r
90°
D= sv3

9. What are the conversion equations for polar coordinates to normal coordinates?
(x-h)²/a² - (y-k)²/b² = 1
90°
x=rcos?(theta) y=rsin? (theta)
SA = pr² +prl

10. How many ways can n elements be ordered?
N!
No equal sides and no equal angles
180°
An = a1rn?¹

11. What is the sum of the interior angles for a polygon with n sides?
(y-k)²/a² - (x-h)²/b² = 1
An = a1rn?¹
(x-h)²/a² - (y-k)²/b² = 1
(n-2)180

12. Standard form equation for circle
C² = a² + b² - 2abcos(C)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
180°
Their dot product = 0

13. Surface area of a sphere
y = a(x-h)² + k - where the vertex is (h -k)
An = a1rn?¹
No equal sides and no equal angles
SA = 4pr²

14. Permutation formula (ordering)
NPr = n! / (n-r)!
All whole numbers except for 0
Arc length equals = (degree of the arc / 360)(circumference)
SA = pr² +prl

15. Standard form equation for an ellipse
180°
Adding or subtracting 180 to ? and reversing the sign of r.
(x-h)²/a² - (y-k)²/b² = 1
(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.

16. Define an even function.
NPr = n! / (n-r)!
90°
F(x) = f(-x)
D= sv3

17. 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)
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.
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

18. What is the order of operations?
Parentheses - exponents - multiplication - division - addition - subtraction
y-y1 = m(x-x1)
A = ((s1 + s2)h) / 2
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

19. 30-60-90 triangle
SA = pr² +prl
Between the vertex and the minor axis on the major axis
90°
Hypotenuse is 2x - short side is x - long side is xv3

20. Two vectors are perpendicular if
Their dot product = 0
(x-h)² + (y-k)² = r² - where (h -k) is the center of the 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.
(1-r/1-r)

21. How can multiple polar coordinates be made?
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
y-y1 = m(x-x1)
(n/2)(a1 + an)
Adding or subtracting 180 to ? and reversing the sign of r.

22. What is the triangle inequality rule?
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.
The greatest common factor is 1 - but the numbers are not necessarily prime.
NPr = n! / (n-r)!

23. Formula for arc length
(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.
(n-2)180
Arc length equals = (degree of the arc / 360)(circumference)
The greatest common factor is 1 - but the numbers are not necessarily prime.

24. Formula for the volume of a cone
Hypotenuse is 2x - short side is x - long side is xv3
y = a(x-h)² + k - where the vertex is (h -k)
V= (1/3)(pr²h)
(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.

25. How to find the distance between two points in 3d plane?
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Square the differences between each coordinate - then square root the sum
(y-k)²/a² - (x-h)²/b² = 1
a1 / 1-r

26. Where is tangent positive/negative?
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
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)]
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

27. Surface area of a cone
y = a(x-h)² + k - where the vertex is (h -k)
SA = pr² +prl
D= sv3
90°

28. Formula for arithmetic sequence
Parentheses - exponents - multiplication - division - addition - subtraction
An = a1 + (n-1)d
N-1
(n-2)180

29. Formula for geometric sequence
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
The greatest common factor is 1 - but the numbers are not necessarily prime.
SA = pr² +prl
An = a1rn?¹

30. Combination formula
F(x) = -f(-x)
(n/2)(a1 + an)
NCr = nPr / r! = n! / (n-r)!r!
N-1

31. Sum of 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)
Adding or subtracting 180 to ? and reversing the sign of r.
N!

32. Formula for the area of a sector
90°
A = (degree of the arc / 360)(area of a circle)
Multiply the inscribed angle by 2
An = a1 + (n-1)d

33. Scalene triangle
No equal sides and no equal angles
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
F(x) = f(-x)
(y-k)²/a² - (x-h)²/b² = 1

34. 45-45-90 triangle
Hypotenuse is xv2 - and the sides are x.
(y-k)²/a² - (x-h)²/b² = 1
(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)]

35. Formula for calculation exponential growth
C² = a² + b² - 2abcos(C)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Final amount = original amount x (1+growth rate)^number of changes
D = v(l²+w²+h²)

36. Formula for the area of a trapezoid
x = -b/2a y= c - (b²/4a)
Between the vertex and the minor axis on the major axis
A = ((s1 + s2)h) / 2
(n/2)(a1 + an)

37. 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
N-1
F(x) = f(-x)
SA = 4pr²

38. Law of Cosines
NPr = n! / (n-r)!
(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.
C² = a² + b² - 2abcos(C)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

39. In an ellipse - where are the foci?
Hypotenuse is 2x - short side is x - long side is xv3
Between the vertex and the minor axis on the major axis
A = (degree of the arc / 360)(area of a circle)
V = (1/3)bh

40. What are relatively prime numbers?
All whole numbers except for 0
F(x) = f(-x)
180°
The greatest common factor is 1 - but the numbers are not necessarily prime.

41. Define an odd function.
V = (1/3)bh
V = (4/3)pr³
F(x) = -f(-x)
SA = 4pr²

42. Standard form for a hyperbola that opens vertically
N-1
The greatest common factor is 1 - but the numbers are not necessarily prime.
(y-k)²/a² - (x-h)²/b² = 1
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

43. Sum of n terms of an arithmetic sequence
An = a1rn?¹
Two sides and two angle are equal
(n/2)(a1 + an)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

44. Formula for the diagonal length of a cube
a1 / 1-r
D= sv3
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
F(x) = f(-x)

45. Volume of a sphere
(y-k)²/a² - (x-h)²/b² = 1
N-1
V = (4/3)pr³
An = a1rn?¹

46. Pythagorean Identities
x = -b/2a y= c - (b²/4a)
The greatest common factor is 1 - but the numbers are not necessarily prime.
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
D= sv3

47. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
An = a1 + (n-1)d
V= (1/3)(pr²h)
(y-k)²/a² - (x-h)²/b² = 1

48. Standard form for a hyperbola that opens to the sides
F(x) = -f(-x)
Two sides and two angle are equal
(x-h)²/a² - (y-k)²/b² = 1
F(x) = f(-x)

49. Difference between 2 Angles formulas
180°
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-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)]

50. 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
NPr = n! / (n-r)!
Square the differences between each coordinate - then square root the sum
(y-k)²/a² - (x-h)²/b² = 1