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SAT Math 2

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. Formula for the diagonal length of a cube
Adding or subtracting 180 to ? and reversing the sign of r.
N!
D= sv3
Hypotenuse is xv2 - and the sides are x.

2. What are natural numbers?
(x-h)²/a² - (y-k)²/b² = 1
Parentheses - exponents - multiplication - division - addition - subtraction
(n-2)180
All whole numbers except for 0

3. What is the triangle inequality rule?
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-k)²/a² - (x-h)²/b² = 1
(1-r/1-r)
Their dot product = 0

4. What are the conversion equations for polar coordinates to normal coordinates?
A = ((s1 + s2)h) / 2
Two sides and two angle are equal
SA = 4pr²
x=rcos?(theta) y=rsin? (theta)

5. 30-60-90 triangle
Hypotenuse is 2x - short side is x - long side is xv3
A = ((s1 + s2)h) / 2
NCr = nPr / r! = n! / (n-r)!r!
SA = 4pr²

6. Combination formula
V = (4/3)pr³
Their dot product = 0
NCr = nPr / r! = n! / (n-r)!r!
A = ((s1 + s2)h) / 2

7. 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)]
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=rcos?(theta) y=rsin? (theta)
V = (4/3)pr³

8. What is the order of operations?
Parentheses - exponents - multiplication - division - addition - subtraction
a1 / 1-r
x = -b/2a y= c - (b²/4a)
(n-2)180

9. Difference between 2 Angles formulas
No equal sides and no equal angles
(x-h)²/a² - (y-k)²/b² = 1
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)]

10. What are relatively prime numbers?
(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.
(y-k)²/a² - (x-h)²/b² = 1
(x-h)²/a² - (y-k)²/b² = 1
The greatest common factor is 1 - but the numbers are not necessarily prime.

11. Define an even function.
F(x) = f(-x)
Adding or subtracting 180 to ? and reversing the sign of r.
Hypotenuse is xv2 - and the sides are x.
D= sv3

12. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
(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-1
C² = a² + b² - 2abcos(C)
90°

13. How many ways can n elements be ordered?
Between the vertex and the minor axis on the major axis
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Adding or subtracting 180 to ? and reversing the sign of r.
N!

14. Two vectors are perpendicular if
A = (degree of the arc / 360)(area of a circle)
Their dot product = 0
y = a(x-h)² + k - where the vertex is (h -k)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

15. Pythagorean Identities
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
(y-k)²/a² - (x-h)²/b² = 1
V = (1/3)bh
Between the vertex and the minor axis on the major axis

16. Volume of a pyramid
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)]
V = (1/3)bh
F(x) = -f(-x)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

17. What is the sum of the interior angles for a polygon with n sides?
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)]
90°
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
(n-2)180

18. Formula for geometric sequence
An = a1rn?¹
SA = pr² +prl
NPr = n! / (n-r)!
90°

19. Define an odd function.
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
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)]
90°
F(x) = -f(-x)

20. Supplementary angles add up to
180°
V = (1/3)bh
D= sv3
(n/2)(a1 + an)

21. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
y-y1 = m(x-x1)
All whole numbers except for 0
a1 / 1-r

22. Surface area of a cone
An = a1 + (n-1)d
SA = pr² +prl
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(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. Formula for the diagonal length of a rectangular prism
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
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)]
A = (degree of the arc / 360)(area of a circle)
D = v(l²+w²+h²)

24. Standard form for a hyperbola that opens vertically
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-k)²/a² - (x-h)²/b² = 1
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
N!

25. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
V = (4/3)pr³
x = -b/2a y= c - (b²/4a)
(1-r/1-r)
(x-h)²/a² - (y-k)²/b² = 1

26. Double Angle Formulas
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
N!
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(n/2)(a1 + an)

27. Formula for the area of a trapezoid
y = a(x-h)² + k - where the vertex is (h -k)
A = ((s1 + s2)h) / 2
180°
SA = 4pr²

28. Sum of finite geometric series
(1-r/1-r)
Multiply the inscribed angle by 2
SA = 4pr²
V= (1/3)(pr²h)

29. 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
90°
N-1
The greatest common factor is 1 - but the numbers are not necessarily prime.

30. Formula for the area of a sector
A = (degree of the arc / 360)(area of a circle)
Hypotenuse is xv2 - and the sides are x.
180°
V= (1/3)(pr²h)

31. Standard form equation for circle
(n/2)(a1 + an)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
A = ((s1 + s2)h) / 2
90°

32. What is the form of a polar coordinate?
y = a(x-h)² + k - where the vertex is (h -k)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-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.
Adding or subtracting 180 to ? and reversing the sign of r.

33. Sum of n terms of an arithmetic sequence
An = a1 + (n-1)d
(n/2)(a1 + an)
Hypotenuse is xv2 - and the sides are x.
V = (1/3)bh

34. 45-45-90 triangle
N-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.
D = v(l²+w²+h²)
Hypotenuse is xv2 - and the sides are x.

35. How can you determine the arc degree or central angle of an inscribed angle?
y-y1 = m(x-x1)
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.
Multiply the inscribed angle by 2

36. Formula for arithmetic sequence
No equal sides and no equal angles
Square the differences between each coordinate - then square root the sum
F(x) = f(-x)
An = a1 + (n-1)d

37. Standard form equation for an ellipse
(n/2)(a1 + an)
x = -b/2a y= c - (b²/4a)
(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 = (4/3)pr³

38. Scalene triangle
No equal sides and no equal angles
F(x) = f(-x)
C² = a² + b² - 2abcos(C)
(n-2)180

39. Complimentary angles add up to
F(x) = -f(-x)
Square the differences between each coordinate - then square root the sum
An = a1 + (n-1)d
90°

40. How can multiple polar coordinates be made?
Hypotenuse is 2x - short side is x - long side is xv3
SA = pr² +prl
An = a1rn?¹
Adding or subtracting 180 to ? and reversing the sign of r.

41. How to find the distance between two points in 3d plane?
An = a1rn?¹
V = (1/3)bh
Multiply the inscribed angle by 2
Square the differences between each coordinate - then square root the sum

42. Formula for the volume of a cone
V= (1/3)(pr²h)
V = (1/3)bh
A = (degree of the arc / 360)(area of a circle)
90°

43. Where is tangent positive/negative?
All whole numbers except for 0
(1-r/1-r)
N!
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

44. Sum of infinite geometric series
a1 / 1-r
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Hypotenuse is 2x - short side is x - long side is xv3
NCr = nPr / r! = n! / (n-r)!r!

45. Isosceles Triangles
Two sides and two angle are equal
N-1
Final amount = original amount x (1+growth rate)^number of changes
Adding or subtracting 180 to ? and reversing the sign of r.

46. Standard form of the equation of a parabola.
C² = a² + b² - 2abcos(C)
y = a(x-h)² + k - where the vertex is (h -k)
y-y1 = m(x-x1)
x=rcos?(theta) y=rsin? (theta)

47. Law of Cosines
(n/2)(a1 + an)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
C² = a² + b² - 2abcos(C)
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)]

48. Standard form for a hyperbola that opens to the sides
A = ((s1 + s2)h) / 2
y = a(x-h)² + k - where the vertex is (h -k)
(x-h)²/a² - (y-k)²/b² = 1
F(x) = f(-x)

49. Permutation formula (ordering)
y-y1 = m(x-x1)
x = -b/2a y= c - (b²/4a)
A = (degree of the arc / 360)(area of a circle)
NPr = n! / (n-r)!

50. 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)]
A = (degree of the arc / 360)(area of a circle)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
x = -b/2a y= c - (b²/4a)