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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. What is the order of operations?
Parentheses - exponents - multiplication - division - addition - subtraction
180°
(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.
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)]

2. Difference between 2 Angles formulas
C² = a² + b² - 2abcos(C)
(y-k)²/a² - (x-h)²/b² = 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)]
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. Law of Cosines
C² = a² + b² - 2abcos(C)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
D = v(l²+w²+h²)
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)]

4. What is the sum of the interior angles for a polygon with n sides?
Arc length equals = (degree of the arc / 360)(circumference)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
D = v(l²+w²+h²)
(n-2)180

5. Surface area of a cone
The greatest common factor is 1 - but the numbers are not necessarily prime.
90°
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
SA = pr² +prl

6. Sum of n terms of an arithmetic sequence
Between the vertex and the minor axis on the major axis
(n/2)(a1 + an)
y-y1 = m(x-x1)
x=rcos?(theta) y=rsin? (theta)

7. What is the form of a polar coordinate?
Adding or subtracting 180 to ? and reversing the sign of r.
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
y-y1 = m(x-x1)

8. What is the triangle inequality rule?
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
F(x) = -f(-x)
90°
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

9. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
90°
Their dot product = 0
N-1
All whole numbers except for 0

10. What are relatively prime numbers?
The greatest common factor is 1 - but the numbers are not necessarily prime.
Arc length equals = (degree of the arc / 360)(circumference)
C² = a² + b² - 2abcos(C)
Two sides and two angle are equal

11. Volume of a sphere
All whole numbers except for 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.
V = (4/3)pr³
Hypotenuse is 2x - short side is x - long side is xv3

12. Surface area of a sphere
C² = a² + b² - 2abcos(C)
SA = 4pr²
180°
90°

13. Sum of finite geometric series
Two sides and two angle are equal
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)]
(1-r/1-r)

14. Standard form equation for an ellipse
y = a(x-h)² + k - where the vertex is (h -k)
(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 xv2 - and the sides are x.
Their dot product = 0

15. Define an odd function.
Hypotenuse is xv2 - and the sides are x.
C² = a² + b² - 2abcos(C)
F(x) = -f(-x)
(x-h)²/a² - (y-k)²/b² = 1

16. 45-45-90 triangle
(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.
Their dot product = 0
(1-r/1-r)
Hypotenuse is xv2 - and the sides are x.

17. Standard form for a hyperbola that opens vertically
An = a1 + (n-1)d
(y-k)²/a² - (x-h)²/b² = 1
y = a(x-h)² + k - where the vertex is (h -k)
(n-2)180

18. Formula for the diagonal length of a rectangular prism
(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
D = v(l²+w²+h²)
V = (4/3)pr³

19. Supplementary angles add up to
180°
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)]
Hypotenuse is xv2 - and the sides are x.

20. Formula for geometric sequence
Parentheses - exponents - multiplication - division - addition - subtraction
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
NPr = n! / (n-r)!
An = a1rn?¹

21. How to find the distance between two points in 3d plane?
N-1
Square the differences between each coordinate - then square root the sum
No equal sides and no equal angles
(y-k)²/a² - (x-h)²/b² = 1

22. 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)]
NCr = nPr / r! = n! / (n-r)!r!
V= (1/3)(pr²h)
Two sides and two angle are equal

23. How many ways can n elements be ordered?
NPr = n! / (n-r)!
y-y1 = m(x-x1)
N!
x = -b/2a y= c - (b²/4a)

24. Permutation formula (ordering)
y-y1 = m(x-x1)
NPr = n! / (n-r)!
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
N-1

25. Pythagorean Identities
(x-h)²/a² - (y-k)²/b² = 1
F(x) = f(-x)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
C² = a² + b² - 2abcos(C)

26. Formula for the diagonal length of a cube
SA = 4pr²
V = (4/3)pr³
V = (1/3)bh
D= sv3

27. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
SA = 4pr²
y-y1 = m(x-x1)
A = ((s1 + s2)h) / 2
SA = pr² +prl

28. Formula for the volume of a cone
SA = 4pr²
V= (1/3)(pr²h)
(n-2)180
All whole numbers except for 0

29. Standard form equation for circle
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
D= sv3
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
The greatest common factor is 1 - but the numbers are not necessarily prime.

30. Define an even function.
All whole numbers except for 0
F(x) = f(-x)
An = a1rn?¹
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

31. Scalene triangle
The greatest common factor is 1 - but the numbers are not necessarily prime.
No equal sides and no equal angles
(x-h)²/a² - (y-k)²/b² = 1
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

32. How can multiple polar coordinates be made?
Two sides and two angle are equal
Adding or subtracting 180 to ? and reversing the sign of r.
180°
SA = 4pr²

33. Formula for the area of a trapezoid
A = ((s1 + s2)h) / 2
(n-2)180
(x-h)²/a² - (y-k)²/b² = 1
y-y1 = m(x-x1)

34. What are natural numbers?
Their dot product = 0
F(x) = -f(-x)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
All whole numbers except for 0

35. Standard form of the equation of a parabola.
y = a(x-h)² + k - where the vertex is (h -k)
180°
x = -b/2a y= c - (b²/4a)
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)]

36. 30-60-90 triangle
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
An = a1 + (n-1)d
Hypotenuse is 2x - short side is x - long side is xv3
Between the vertex and the minor axis on the major axis

37. Isosceles Triangles
Two sides and two angle are equal
Final amount = original amount x (1+growth rate)^number of changes
N-1
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

38. What are the conversion equations for polar coordinates to normal coordinates?
y-y1 = m(x-x1)
SA = 4pr²
x=rcos?(theta) y=rsin? (theta)
C² = a² + b² - 2abcos(C)

39. Where is tangent positive/negative?
F(x) = -f(-x)
Two sides and two angle are equal
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
V = (1/3)bh

40. In an ellipse - where are the foci?
Between the vertex and the minor axis on the major axis
Square the differences between each coordinate - then square root the sum
NPr = n! / (n-r)!
x = -b/2a y= c - (b²/4a)

41. Formula for arc length
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
SA = pr² +prl
Adding or subtracting 180 to ? and reversing the sign of r.
Arc length equals = (degree of the arc / 360)(circumference)

42. Formula for arithmetic sequence
(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.
x=rcos?(theta) y=rsin? (theta)
An = a1 + (n-1)d
Arc length equals = (degree of the arc / 360)(circumference)

43. Formula for calculation exponential growth
Square the differences between each coordinate - then square root the sum
(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.
Final amount = original amount x (1+growth rate)^number of changes
SA = pr² +prl

44. Standard form for a hyperbola that opens to the sides
(x-h)²/a² - (y-k)²/b² = 1
90°
An = a1 + (n-1)d
A = ((s1 + s2)h) / 2

45. Combination formula
NPr = n! / (n-r)!
N!
NCr = nPr / r! = n! / (n-r)!r!
No equal sides and no equal angles

46. Two vectors are perpendicular if
Their dot product = 0
Adding or subtracting 180 to ? and reversing the sign of r.
(n/2)(a1 + an)
Two sides and two angle are equal

47. Volume of a pyramid
(1-r/1-r)
V = (1/3)bh
SA = pr² +prl
x=rcos?(theta) y=rsin? (theta)

48. Formula for the area of a sector
Adding or subtracting 180 to ? and reversing the sign of r.
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
C² = a² + b² - 2abcos(C)
A = (degree of the arc / 360)(area of a circle)

49. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
V= (1/3)(pr²h)
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
Square the differences between each coordinate - then square root the sum

50. Sum of infinite geometric series
A = ((s1 + s2)h) / 2
a1 / 1-r
Arc length equals = (degree of the arc / 360)(circumference)
Adding or subtracting 180 to ? and reversing the sign of r.