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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. How many ways can n elements be ordered?
N!
(n/2)(a1 + an)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Arc length equals = (degree of the arc / 360)(circumference)

2. How to find the distance between two points in 3d plane?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
A = ((s1 + s2)h) / 2
Square the differences between each coordinate - then square root the sum
C² = a² + b² - 2abcos(C)

3. Supplementary angles add up to
180°
V= (1/3)(pr²h)
D= sv3
All whole numbers except for 0

4. Formula for arc length
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
(1-r/1-r)
V = (1/3)bh
Arc length equals = (degree of the arc / 360)(circumference)

5. Standard form for a hyperbola that opens vertically
Hypotenuse is 2x - short side is x - long side is xv3
(y-k)²/a² - (x-h)²/b² = 1
N!
V = (1/3)bh

6. Sum of finite geometric series
A = (degree of the arc / 360)(area of a circle)
F(x) = f(-x)
y = a(x-h)² + k - where the vertex is (h -k)
(1-r/1-r)

7. What are relatively prime numbers?
A = (degree of the arc / 360)(area of a circle)
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.
y-y1 = m(x-x1)

8. 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
All whole numbers except for 0
(n-2)180
Hypotenuse is xv2 - and the sides are x.

9. Sum of n terms of an arithmetic sequence
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Arc length equals = (degree of the arc / 360)(circumference)
(n/2)(a1 + an)
SA = pr² +prl

10. Volume of a pyramid
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
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)]
V = (1/3)bh

11. Surface area 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.
(n/2)(a1 + an)
SA = 4pr²
Square the differences between each coordinate - then square root the sum

12. Combination formula
A = (degree of the arc / 360)(area of a circle)
F(x) = -f(-x)
NCr = nPr / r! = n! / (n-r)!r!
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

13. Formula for the diagonal length of a cube
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
x = -b/2a y= c - (b²/4a)
SA = 4pr²
D= sv3

14. In an ellipse - where are the foci?
N!
An = a1rn?¹
Between the vertex and the minor axis on the major axis
Parentheses - exponents - multiplication - division - addition - subtraction

15. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
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 2x - short side is x - long side is xv3
(n-2)180
y-y1 = m(x-x1)

16. Double Angle Formulas
D = v(l²+w²+h²)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Hypotenuse is 2x - short side is x - long side is xv3
The greatest common factor is 1 - but the numbers are not necessarily prime.

17. Formula for arithmetic sequence
D= sv3
(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
90°

18. Formula for calculation exponential growth
SA = pr² +prl
Final amount = original amount x (1+growth rate)^number of changes
(1-r/1-r)
Arc length equals = (degree of the arc / 360)(circumference)

19. What is the sum of the interior angles for a polygon with n sides?
90°
(n-2)180
F(x) = -f(-x)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

20. 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)]
No equal sides and no equal angles
N-1
Adding or subtracting 180 to ? and reversing the sign of r.

21. Pythagorean Identities
N-1
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Final amount = original amount x (1+growth rate)^number of changes
F(x) = f(-x)

22. How can you determine the arc degree or central angle of an inscribed angle?
90°
y = a(x-h)² + k - where the vertex is (h -k)
Multiply the inscribed angle by 2
Adding or subtracting 180 to ? and reversing the sign of r.

23. 30-60-90 triangle
(n/2)(a1 + an)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Hypotenuse is 2x - short side is x - long side is xv3
The greatest common factor is 1 - but the numbers are not necessarily prime.

24. Define an even function.
The greatest common factor is 1 - but the numbers are not necessarily prime.
F(x) = f(-x)
(x-h)²/a² - (y-k)²/b² = 1
F(x) = -f(-x)

25. Formula for the area of a sector
A = (degree of the arc / 360)(area of a circle)
F(x) = -f(-x)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
N-1

26. Complimentary angles add up to
Between the vertex and the minor axis on the major axis
Hypotenuse is xv2 - and the sides are x.
Square the differences between each coordinate - then square root the sum
90°

27. Define an odd function.
An = a1rn?¹
y-y1 = m(x-x1)
N!
F(x) = -f(-x)

28. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
(n-2)180
(x-h)²/a² - (y-k)²/b² = 1
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

29. Sum of infinite geometric series
x=rcos?(theta) y=rsin? (theta)
An = a1rn?¹
a1 / 1-r
Final amount = original amount x (1+growth rate)^number of changes

30. Standard form of the equation of a parabola.
(n-2)180
SA = pr² +prl
Two sides and two angle are equal
y = a(x-h)² + k - where the vertex is (h -k)

31. What are the conversion equations for polar coordinates to normal coordinates?
x=rcos?(theta) y=rsin? (theta)
V = (1/3)bh
SA = pr² +prl
Square the differences between each coordinate - then square root the sum

32. Volume of a sphere
V = (4/3)pr³
All whole numbers except for 0
(x-h)²/a² - (y-k)²/b² = 1
Hypotenuse is xv2 - and the sides are x.

33. Scalene triangle
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
No equal sides and no equal angles
SA = 4pr²
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. How can multiple polar coordinates be made?
NCr = nPr / r! = n! / (n-r)!r!
Adding or subtracting 180 to ? and reversing the sign of r.
D= sv3
V= (1/3)(pr²h)

35. Standard form for a hyperbola that opens to the sides
x=rcos?(theta) y=rsin? (theta)
180°
(x-h)²/a² - (y-k)²/b² = 1
SA = pr² +prl

36. Isosceles Triangles
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)]
Two sides and two angle are equal
NPr = n! / (n-r)!
N-1

37. Standard form equation for an ellipse
A = ((s1 + s2)h) / 2
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
(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.

38. Formula for the diagonal length of a rectangular prism
An = a1rn?¹
D = v(l²+w²+h²)
V = (4/3)pr³
A = ((s1 + s2)h) / 2

39. Two vectors are perpendicular if
Their dot product = 0
y = a(x-h)² + k - where the vertex is (h -k)
D = v(l²+w²+h²)
(1-r/1-r)

40. 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
(y-k)²/a² - (x-h)²/b² = 1
Hypotenuse is xv2 - and the sides are x.

41. Surface area of a cone
N-1
y = a(x-h)² + k - where the vertex is (h -k)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
SA = pr² +prl

42. 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.
V = (1/3)bh
Multiply the inscribed angle by 2
y-y1 = m(x-x1)

43. Where is tangent positive/negative?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Between the vertex and the minor axis on the major axis
An = a1rn?¹
NCr = nPr / r! = n! / (n-r)!r!

44. How to determine if a number is prime
V= (1/3)(pr²h)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
NCr = nPr / r! = n! / (n-r)!r!

45. Formula for geometric sequence
An = a1rn?¹
(1-r/1-r)
Multiply the inscribed angle by 2
C² = a² + b² - 2abcos(C)

46. 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)]
The greatest common factor is 1 - but the numbers are not necessarily prime.
Their dot product = 0
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

47. Formula for the area of a trapezoid
The greatest common factor is 1 - but the numbers are not necessarily prime.
NCr = nPr / r! = n! / (n-r)!r!
No equal sides and no equal angles
A = ((s1 + s2)h) / 2

48. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
(n/2)(a1 + an)
An = a1rn?¹
x = -b/2a y= c - (b²/4a)
D = v(l²+w²+h²)

49. Permutation formula (ordering)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
NPr = n! / (n-r)!
N-1

50. Formula for the volume of a cone
V= (1/3)(pr²h)
Arc length equals = (degree of the arc / 360)(circumference)
Hypotenuse is 2x - short side is x - long side is xv3
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x