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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.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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 infinite geometric series
x=rcos?(theta) y=rsin? (theta)
An = a1rn?¹
a1 / 1-r
Between the vertex and the minor axis on the major axis

2. How can multiple polar coordinates be made?
Adding or subtracting 180 to ? and reversing the sign of r.
Their dot product = 0
F(x) = -f(-x)
SA = pr² +prl

3. What are relatively prime numbers?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
The greatest common factor is 1 - but the numbers are not necessarily prime.
SA = 4pr²
An = a1 + (n-1)d

4. Volume of a pyramid
V = (1/3)bh
F(x) = -f(-x)
Hypotenuse is 2x - short side is x - long side is xv3
N!

5. Define an odd function.
F(x) = -f(-x)
N!
(y-k)²/a² - (x-h)²/b² = 1
(n-2)180

6. How can you determine the arc degree or central angle of an inscribed angle?
NCr = nPr / r! = n! / (n-r)!r!
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)]
Parentheses - exponents - multiplication - division - addition - subtraction
Multiply the inscribed angle by 2

7. Define an even function.
F(x) = f(-x)
All whole numbers except for 0
SA = pr² +prl
x = -b/2a y= c - (b²/4a)

8. 45-45-90 triangle
A = ((s1 + s2)h) / 2
Hypotenuse is xv2 - and the sides are x.
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 = a1 + (n-1)d

9. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
Square the differences between each coordinate - then square root the sum
a1 / 1-r
C² = a² + b² - 2abcos(C)
N-1

10. How many ways can n elements be ordered?
(n/2)(a1 + an)
a1 / 1-r
N!
(1-r/1-r)

11. How to find the distance between two points in 3d plane?
(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.
Adding or subtracting 180 to ? and reversing the sign of r.
Square the differences between each coordinate - then square root the sum
Parentheses - exponents - multiplication - division - addition - subtraction

12. Volume of a sphere
a1 / 1-r
Between the vertex and the minor axis on the major axis
V = (4/3)pr³
An = a1 + (n-1)d

13. 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/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)]
NCr = nPr / r! = n! / (n-r)!r!

14. Standard form of the equation of a parabola.
y = a(x-h)² + k - where the vertex is (h -k)
(y-k)²/a² - (x-h)²/b² = 1
a1 / 1-r
Square the differences between each coordinate - then square root the sum

15. Standard form equation for circle
C² = a² + b² - 2abcos(C)
A = ((s1 + s2)h) / 2
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

16. 30-60-90 triangle
Hypotenuse is 2x - short side is x - long side is xv3
The greatest common factor is 1 - but the numbers are not necessarily prime.
V = (4/3)pr³
NCr = nPr / r! = n! / (n-r)!r!

17. Formula for arithmetic sequence
V = (4/3)pr³
Between the vertex and the minor axis on the major axis
An = a1 + (n-1)d
V= (1/3)(pr²h)

18. Formula for the volume of a cone
V= (1/3)(pr²h)
Adding or subtracting 180 to ? and reversing the sign of r.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
The greatest common factor is 1 - but the numbers are not necessarily prime.

19. Double Angle Formulas
(1-r/1-r)
NCr = nPr / r! = n! / (n-r)!r!
No equal sides and no equal angles
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

20. Formula for arc length
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Arc length equals = (degree of the arc / 360)(circumference)
(y-k)²/a² - (x-h)²/b² = 1
F(x) = f(-x)

21. Isosceles Triangles
180°
A = (degree of the arc / 360)(area of a circle)
Two sides and two angle are equal
(y-k)²/a² - (x-h)²/b² = 1

22. Standard form equation for an ellipse
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)]
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.

23. What is the order of operations?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
An = a1rn?¹
Parentheses - exponents - multiplication - division - addition - subtraction
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

24. Formula for the area of a sector
180°
Multiply the inscribed angle by 2
A = (degree of the arc / 360)(area of a circle)
SA = pr² +prl

25. Formula for the area of a trapezoid
V= (1/3)(pr²h)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
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)]

26. Where is tangent positive/negative?
(1-r/1-r)
(n/2)(a1 + an)
Their dot product = 0
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

27. In an ellipse - where are the foci?
No equal sides and no equal angles
Between the vertex and the minor axis on the major axis
NPr = n! / (n-r)!
F(x) = -f(-x)

28. Formula for the diagonal length of a cube
D= sv3
SA = 4pr²
The greatest common factor is 1 - but the numbers are not necessarily prime.
N-1

29. Surface area of a cone
SA = pr² +prl
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-h)² + (y-k)² = r² - where (h -k) is the center of the circle
A = ((s1 + s2)h) / 2

30. Permutation formula (ordering)
V = (1/3)bh
Square the differences between each coordinate - then square root the sum
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
NPr = n! / (n-r)!

31. Scalene triangle
No equal sides and no equal angles
a1 / 1-r
SA = pr² +prl
x=rcos?(theta) y=rsin? (theta)

32. Sum of n terms of an arithmetic sequence
180°
Hypotenuse is xv2 - and the sides are x.
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
(n/2)(a1 + an)

33. Sum of finite geometric series
(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)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

34. 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-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
Square the differences between each coordinate - then square root the sum

35. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
The greatest common factor is 1 - but the numbers are not necessarily prime.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
x = -b/2a y= c - (b²/4a)

36. Supplementary angles add up to
D= sv3
(n/2)(a1 + an)
180°
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

37. Standard form for a hyperbola that opens to the sides
An = a1 + (n-1)d
Between the vertex and the minor axis on the major axis
SA = 4pr²
(x-h)²/a² - (y-k)²/b² = 1

38. What are natural numbers?
SA = 4pr²
All whole numbers except for 0
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
C² = a² + b² - 2abcos(C)

39. Surface area of a sphere
SA = 4pr²
C² = a² + b² - 2abcos(C)
V = (4/3)pr³
(y-k)²/a² - (x-h)²/b² = 1

40. Formula for geometric sequence
A = (degree of the arc / 360)(area of a circle)
V= (1/3)(pr²h)
An = a1rn?¹
V = (1/3)bh

41. Complimentary angles add up to
C² = a² + b² - 2abcos(C)
90°
F(x) = f(-x)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

42. What are the conversion equations for polar coordinates to normal coordinates?
x=rcos?(theta) y=rsin? (theta)
Adding or subtracting 180 to ? and reversing the sign of r.
Their dot product = 0
x = -b/2a y= c - (b²/4a)

43. What is the triangle inequality rule?
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)]
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
D = v(l²+w²+h²)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

44. Difference between 2 Angles formulas
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)]
Square the differences between each coordinate - then square root the sum

45. Formula for calculation exponential growth
Final amount = original amount x (1+growth rate)^number of changes
A = (degree of the arc / 360)(area of a 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)]
NCr = nPr / r! = n! / (n-r)!r!

46. Two vectors are perpendicular if
No equal sides and no equal angles
Their dot product = 0
(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.
Parentheses - exponents - multiplication - division - addition - subtraction

47. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
F(x) = -f(-x)
y-y1 = m(x-x1)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
x=rcos?(theta) y=rsin? (theta)

48. Law of Cosines
C² = a² + b² - 2abcos(C)
(y-k)²/a² - (x-h)²/b² = 1
Parentheses - exponents - multiplication - division - addition - subtraction
NPr = n! / (n-r)!

49. Pythagorean Identities
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
90°
N-1
(n/2)(a1 + an)

50. Formula for the diagonal length of a rectangular prism
D = v(l²+w²+h²)
NPr = n! / (n-r)!
An = a1rn?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)]