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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. Supplementary angles add up to
180°
The greatest common factor is 1 - but the numbers are not necessarily prime.
y-y1 = m(x-x1)
Square the differences between each coordinate - then square root the sum

2. What are the conversion equations for polar coordinates to normal coordinates?
An = a1rn?¹
x=rcos?(theta) y=rsin? (theta)
Hypotenuse is xv2 - and the sides are x.
(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.

3. 30-60-90 triangle
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Hypotenuse is 2x - short side is x - long side is xv3
a1 / 1-r
180°

4. How to find the distance between two points in 3d plane?
Square the differences between each coordinate - then square root the sum
The greatest common factor is 1 - but the numbers are not necessarily prime.
Multiply the inscribed angle by 2
An = a1rn?¹

5. Formula for geometric sequence
Square the differences between each coordinate - then square root the sum
An = a1rn?¹
SA = 4pr²
(1-r/1-r)

6. Two vectors are perpendicular if
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Their dot product = 0
(y-k)²/a² - (x-h)²/b² = 1
y-y1 = m(x-x1)

7. Isosceles Triangles
Two sides and two angle are equal
NPr = n! / (n-r)!
N!
Between the vertex and the minor axis on the major axis

8. Formula for the diagonal length of a rectangular prism
All whole numbers except for 0
D = v(l²+w²+h²)
D= sv3
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

9. Define an odd function.
y = a(x-h)² + k - where the vertex is (h -k)
F(x) = f(-x)
F(x) = -f(-x)
SA = pr² +prl

10. What is the form of a polar coordinate?
Arc length equals = (degree of the arc / 360)(circumference)
A = (degree of the arc / 360)(area of a circle)
D = v(l²+w²+h²)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

11. What are natural numbers?
Parentheses - exponents - multiplication - division - addition - subtraction
(n-2)180
x=rcos?(theta) y=rsin? (theta)
All whole numbers except for 0

12. How many ways can n elements be ordered?
N!
y-y1 = m(x-x1)
a1 / 1-r
Arc length equals = (degree of the arc / 360)(circumference)

13. Define an even function.
(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.
F(x) = -f(-x)
F(x) = f(-x)
Hypotenuse is 2x - short side is x - long side is xv3

14. Standard form of the equation of a parabola.
SA = 4pr²
V = (4/3)pr³
No equal sides and no equal angles
y = a(x-h)² + k - where the vertex is (h -k)

15. Complimentary angles add up to
x=rcos?(theta) y=rsin? (theta)
90°
a1 / 1-r
F(x) = f(-x)

16. What is the sum of the interior angles for a polygon with n sides?
Hypotenuse is 2x - short side is x - long side is xv3
An = a1 + (n-1)d
180°
(n-2)180

17. How can you determine the arc degree or central angle of an inscribed angle?
Their dot product = 0
x=rcos?(theta) y=rsin? (theta)
An = a1rn?¹
Multiply the inscribed angle by 2

18. What is the triangle inequality rule?
V = (1/3)bh
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Their dot product = 0
NPr = n! / (n-r)!

19. Sum of finite geometric series
V = (1/3)bh
180°
An = a1 + (n-1)d
(1-r/1-r)

20. Combination formula
Parentheses - exponents - multiplication - division - addition - subtraction
NPr = n! / (n-r)!
NCr = nPr / r! = n! / (n-r)!r!
Between the vertex and the minor axis on the major axis

21. In an ellipse - where are the foci?
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Between the vertex and the minor axis on the major axis
NPr = n! / (n-r)!
(n/2)(a1 + an)

22. Law of Cosines
a1 / 1-r
No equal sides and no equal angles
C² = a² + b² - 2abcos(C)
y-y1 = m(x-x1)

23. 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)]
(x-h)²/a² - (y-k)²/b² = 1
x=rcos?(theta) y=rsin? (theta)
Their dot product = 0

24. How to determine if a number is prime
y-y1 = m(x-x1)
D = v(l²+w²+h²)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

25. What is the order of operations?
Parentheses - exponents - multiplication - division - addition - subtraction
Their dot product = 0
N-1
V= (1/3)(pr²h)

26. Formula for arc length
90°
N-1
SA = 4pr²
Arc length equals = (degree of the arc / 360)(circumference)

27. How can multiple polar coordinates be made?
Adding or subtracting 180 to ? and reversing the sign of r.
Two sides and two angle are equal
F(x) = -f(-x)
C² = a² + b² - 2abcos(C)

28. Standard form for a hyperbola that opens vertically
Arc length equals = (degree of the arc / 360)(circumference)
(y-k)²/a² - (x-h)²/b² = 1
Between the vertex and the minor axis on the major axis
a1 / 1-r

29. Scalene triangle
x = -b/2a y= c - (b²/4a)
V = (4/3)pr³
No equal sides and no equal angles
Hypotenuse is 2x - short side is x - long side is xv3

30. Permutation formula (ordering)
NPr = n! / (n-r)!
Two sides and two angle are equal
D = v(l²+w²+h²)
Multiply the inscribed angle by 2

31. Formula for the area of a trapezoid
V = (1/3)bh
A = ((s1 + s2)h) / 2
(y-k)²/a² - (x-h)²/b² = 1
Hypotenuse is 2x - short side is x - long side is xv3

32. Pythagorean Identities
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(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.
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
An = a1rn?¹

33. Surface area of a sphere
SA = 4pr²
y-y1 = m(x-x1)
Two sides and two angle are equal
a1 / 1-r

34. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
Between the vertex and the minor axis on the major axis
Parentheses - exponents - multiplication - division - addition - subtraction
NCr = nPr / r! = n! / (n-r)!r!

35. Formula for the diagonal length of a cube
D= sv3
Two sides and two angle are equal
Arc length equals = (degree of the arc / 360)(circumference)
Parentheses - exponents - multiplication - division - addition - subtraction

36. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
An = a1rn?¹
Hypotenuse is 2x - short side is x - long side is xv3
x = -b/2a y= c - (b²/4a)
A = (degree of the arc / 360)(area of a circle)

37. Formula for the area of a sector
180°
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)]
A = (degree of the arc / 360)(area of a circle)

38. Surface area of a cone
Two sides and two angle are equal
N-1
An = a1 + (n-1)d
SA = pr² +prl

39. Where is tangent positive/negative?
(n-2)180
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
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

40. Volume of a pyramid
V = (1/3)bh
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)]
The greatest common factor is 1 - but the numbers are not necessarily prime.

41. Volume of a sphere
Adding or subtracting 180 to ? and reversing the sign of r.
A = ((s1 + s2)h) / 2
V = (4/3)pr³
C² = a² + b² - 2abcos(C)

42. Formula for arithmetic sequence
(x-h)²/a² - (y-k)²/b² = 1
An = a1 + (n-1)d
V= (1/3)(pr²h)
(n/2)(a1 + an)

43. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
Square the differences between each coordinate - then square root the sum
Hypotenuse is 2x - short side is x - long side is xv3
y-y1 = m(x-x1)
An = a1rn?¹

44. Sum of 2 Angles Formulas
F(x) = f(-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)]
Hypotenuse is xv2 - and the sides are x.
The greatest common factor is 1 - but the numbers are not necessarily prime.

45. What are relatively prime numbers?
SA = pr² +prl
F(x) = f(-x)
y-y1 = m(x-x1)
The greatest common factor is 1 - but the numbers are not necessarily prime.

46. Sum of infinite geometric series
a1 / 1-r
Arc length equals = (degree of the arc / 360)(circumference)
(1-r/1-r)
Between the vertex and the minor axis on the major axis

47. 45-45-90 triangle
D = v(l²+w²+h²)
Multiply the inscribed angle by 2
Parentheses - exponents - multiplication - division - addition - subtraction
Hypotenuse is xv2 - and the sides are x.

48. Standard form for a hyperbola that opens to the sides
(1-r/1-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.
(x-h)²/a² - (y-k)²/b² = 1
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

49. Standard form equation for circle
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
(n/2)(a1 + an)
a1 / 1-r
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

50. Formula for calculation exponential growth
SA = pr² +prl
NPr = n! / (n-r)!
Final amount = original amount x (1+growth rate)^number of changes
x=rcos?(theta) y=rsin? (theta)