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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. 45-45-90 triangle
NPr = n! / (n-r)!
SA = pr² +prl
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Hypotenuse is xv2 - and the sides are x.

2. Where is tangent positive/negative?
(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.
SA = pr² +prl
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

3. How many ways can n elements be ordered?
N!
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)]
Parentheses - exponents - multiplication - division - addition - subtraction

4. Formula for arc length
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)!
SA = 4pr²
Arc length equals = (degree of the arc / 360)(circumference)

5. Permutation formula (ordering)
NPr = n! / (n-r)!
Hypotenuse is xv2 - and the sides are x.
(n/2)(a1 + an)
D= sv3

6. Standard form equation for circle
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Two sides and two angle are equal
(n-2)180
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

7. 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
Their dot product = 0
(x-h)²/a² - (y-k)²/b² = 1

8. Sum of finite geometric series
a1 / 1-r
(1-r/1-r)
x=rcos?(theta) y=rsin? (theta)
V = (4/3)pr³

9. Combination formula
NCr = nPr / r! = n! / (n-r)!r!
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
NPr = n! / (n-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)]

10. Formula for the diagonal length of a cube
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
NCr = nPr / r! = n! / (n-r)!r!
D= sv3
y = a(x-h)² + k - where the vertex is (h -k)

11. Formula for the volume of a cone
Parentheses - exponents - multiplication - division - addition - subtraction
V= (1/3)(pr²h)
180°
D = v(l²+w²+h²)

12. Volume of a pyramid
SA = pr² +prl
Square the differences between each coordinate - then square root the sum
V = (1/3)bh
(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.

13. In an ellipse - where are the foci?
An = a1rn?¹
C² = a² + b² - 2abcos(C)
(n/2)(a1 + an)
Between the vertex and the minor axis on the major axis

14. What is the sum of the interior angles for a polygon with n sides?
(n-2)180
NCr = nPr / r! = n! / (n-r)!r!
C² = a² + b² - 2abcos(C)
The greatest common factor is 1 - but the numbers are not necessarily prime.

15. Standard form of the equation of a parabola.
Hypotenuse is xv2 - and the sides are x.
y = a(x-h)² + k - where the vertex is (h -k)
SA = pr² +prl
F(x) = f(-x)

16. How can multiple polar coordinates be made?
180°
The greatest common factor is 1 - but the numbers are not necessarily prime.
Adding or subtracting 180 to ? and reversing the sign of r.
N-1

17. What are natural numbers?
All whole numbers except for 0
180°
Hypotenuse is xv2 - and the sides are x.
Hypotenuse is 2x - short side is x - long side is xv3

18. 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)]
Square the differences between each coordinate - then square root the sum
F(x) = f(-x)
An = a1rn?¹

19. What is the triangle inequality rule?
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
All whole numbers except for 0
A = (degree of the arc / 360)(area of a circle)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

20. Pythagorean Identities
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Two sides and two angle are equal
D= sv3

21. Sum of infinite geometric series
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
C² = a² + b² - 2abcos(C)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
a1 / 1-r

22. Formula for calculation exponential growth
Multiply the inscribed angle by 2
Square the differences between each coordinate - then square root the sum
Final amount = original amount x (1+growth rate)^number of changes
A = (degree of the arc / 360)(area of a circle)

23. Surface area of a cone
N-1
SA = pr² +prl
Hypotenuse is 2x - short side is x - long side is xv3
Two sides and two angle are equal

24. Double Angle Formulas
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
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)]
A = (degree of the arc / 360)(area of a circle)

25. Formula for geometric sequence
A = (degree of the arc / 360)(area of a circle)
Final amount = original amount x (1+growth rate)^number of changes
An = a1rn?¹
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

26. Define an odd function.
180°
V = (1/3)bh
D= sv3
F(x) = -f(-x)

27. Formula for the area of a sector
A = (degree of the arc / 360)(area of a circle)
y = a(x-h)² + k - where the vertex is (h -k)
No equal sides and no equal angles
(1-r/1-r)

28. How to determine if a number is prime
(n-2)180
D = v(l²+w²+h²)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
F(x) = f(-x)

29. Sum of n terms of an arithmetic sequence
V = (4/3)pr³
No equal sides and no equal angles
(n/2)(a1 + an)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

30. What are relatively prime numbers?
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
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 = a(x-h)² + k - where the vertex is (h -k)
The greatest common factor is 1 - but the numbers are not necessarily prime.

31. Scalene triangle
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
D= sv3
Square the differences between each coordinate - then square root the sum

32. Two vectors are perpendicular if
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)]
Their dot product = 0
x = -b/2a y= c - (b²/4a)
An = a1rn?¹

33. Formula for arithmetic sequence
(y-k)²/a² - (x-h)²/b² = 1
Adding or subtracting 180 to ? and reversing the sign of r.
Parentheses - exponents - multiplication - division - addition - subtraction
An = a1 + (n-1)d

34. Complimentary angles add up to
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Arc length equals = (degree of the arc / 360)(circumference)
90°
Between the vertex and the minor axis on the major axis

35. What is the order of operations?
Hypotenuse is 2x - short side is x - long side is xv3
D = v(l²+w²+h²)
D= sv3
Parentheses - exponents - multiplication - division - addition - subtraction

36. Standard form equation for an ellipse
An = a1rn?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.
(n/2)(a1 + an)
(1-r/1-r)

37. Law of Cosines
NCr = nPr / r! = n! / (n-r)!r!
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
No equal sides and no equal angles
C² = a² + b² - 2abcos(C)

38. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
x = -b/2a y= c - (b²/4a)
(1-r/1-r)
NCr = nPr / r! = n! / (n-r)!r!
V = (4/3)pr³

39. How to find the distance between two points in 3d plane?
F(x) = f(-x)
The greatest common factor is 1 - but the numbers are not necessarily prime.
Square the differences between each coordinate - then square root the sum
x = -b/2a y= c - (b²/4a)

40. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
Adding or subtracting 180 to ? and reversing the sign of r.
Hypotenuse is 2x - short side is x - long side is xv3
y-y1 = m(x-x1)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

41. Standard form for a hyperbola that opens to the sides
An = a1rn?¹
An = a1 + (n-1)d
Hypotenuse is 2x - short side is x - long side is xv3
(x-h)²/a² - (y-k)²/b² = 1

42. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
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)]
D = v(l²+w²+h²)
N-1
(y-k)²/a² - (x-h)²/b² = 1

43. Sum of 2 Angles Formulas
Final amount = original amount x (1+growth rate)^number of changes
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-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.
Square the differences between each coordinate - then square root the sum

44. Formula for the diagonal length of a rectangular prism
NPr = n! / (n-r)!
SA = 4pr²
D = v(l²+w²+h²)
D= sv3

45. Volume of a sphere
D= sv3
V = (4/3)pr³
Parentheses - exponents - multiplication - division - addition - subtraction
NCr = nPr / r! = n! / (n-r)!r!

46. Surface area of a sphere
Between the vertex and the minor axis on the major axis
NCr = nPr / r! = n! / (n-r)!r!
SA = 4pr²
x = -b/2a y= c - (b²/4a)

47. Supplementary angles add up to
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
180°
NPr = n! / (n-r)!
90°

48. Formula for the area of a trapezoid
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)]
Arc length equals = (degree of the arc / 360)(circumference)
No equal sides and no equal angles
A = ((s1 + s2)h) / 2

49. Isosceles Triangles
Hypotenuse is xv2 - and the sides are x.
Two sides and two angle are equal
180°
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

50. 30-60-90 triangle
N-1
Parentheses - exponents - multiplication - division - addition - subtraction
Hypotenuse is xv2 - and the sides are x.
Hypotenuse is 2x - short side is x - long side is xv3