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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. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
x = -b/2a y= c - (b²/4a)
V = (1/3)bh
Square the differences between each coordinate - then square root the sum
The greatest common factor is 1 - but the numbers are not necessarily prime.

2. In an ellipse - where are the foci?
F(x) = -f(-x)
Between the vertex and the minor axis on the major axis
y-y1 = m(x-x1)
Parentheses - exponents - multiplication - division - addition - subtraction

3. How many ways can n elements be ordered?
Hypotenuse is 2x - short side is x - long side is xv3
N!
a1 / 1-r
90°

4. Formula for arithmetic sequence
An = a1 + (n-1)d
(y-k)²/a² - (x-h)²/b² = 1
No equal sides and no equal angles
The greatest common factor is 1 - but the numbers are not necessarily prime.

5. Scalene triangle
x = -b/2a y= c - (b²/4a)
SA = pr² +prl
N-1
No equal sides and no equal angles

6. 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)]
F(x) = f(-x)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
(n-2)180

7. Standard form for a hyperbola that opens vertically
An = a1rn?¹
(n/2)(a1 + an)
(y-k)²/a² - (x-h)²/b² = 1
Parentheses - exponents - multiplication - division - addition - subtraction

8. Standard form for a hyperbola that opens to the sides
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(x-h)²/a² - (y-k)²/b² = 1
Final amount = original amount x (1+growth rate)^number of changes
Adding or subtracting 180 to ? and reversing the sign of r.

9. Volume of a sphere
D= sv3
(x-h)²/a² - (y-k)²/b² = 1
(1-r/1-r)
V = (4/3)pr³

10. 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)]
Their dot product = 0
Multiply the inscribed angle by 2
(y-k)²/a² - (x-h)²/b² = 1

11. Two vectors are perpendicular if
Their dot product = 0
Hypotenuse is xv2 - and the sides are x.
N!
V = (4/3)pr³

12. Formula for the diagonal length of a cube
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
D= sv3
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)]

13. Surface area of a cone
y = a(x-h)² + k - where the vertex is (h -k)
D = v(l²+w²+h²)
SA = pr² +prl
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

14. What are the conversion equations for polar coordinates to normal coordinates?
F(x) = f(-x)
90°
D = v(l²+w²+h²)
x=rcos?(theta) y=rsin? (theta)

15. How can multiple polar coordinates be made?
Adding or subtracting 180 to ? and reversing the sign of r.
All whole numbers except for 0
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)]
a1 / 1-r

16. Define an even function.
The greatest common factor is 1 - but the numbers are not necessarily prime.
An = a1rn?¹
F(x) = f(-x)
SA = pr² +prl

17. Formula for geometric sequence
Two sides and two angle are equal
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
An = a1rn?¹
y = a(x-h)² + k - where the vertex is (h -k)

18. Permutation formula (ordering)
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.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
NPr = n! / (n-r)!

19. What are relatively prime numbers?
Hypotenuse is xv2 - and the sides are x.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(1-r/1-r)
The greatest common factor is 1 - but the numbers are not necessarily prime.

20. Volume of a pyramid
SA = pr² +prl
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
NCr = nPr / r! = n! / (n-r)!r!
V = (1/3)bh

21. What is the order of operations?
F(x) = -f(-x)
Parentheses - exponents - multiplication - division - addition - subtraction
V = (4/3)pr³
SA = 4pr²

22. Pythagorean Identities
(n-2)180
V = (1/3)bh
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Final amount = original amount x (1+growth rate)^number of changes

23. Where is tangent positive/negative?
Their dot product = 0
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
SA = 4pr²
(n/2)(a1 + an)

24. Standard form equation for circle
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Final amount = original amount x (1+growth rate)^number of changes
SA = 4pr²
C² = a² + b² - 2abcos(C)

25. Isosceles Triangles
Final amount = original amount x (1+growth rate)^number of changes
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Multiply the inscribed angle by 2
Two sides and two angle are equal

26. Sum of n terms of an arithmetic sequence
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
a1 / 1-r
NCr = nPr / r! = n! / (n-r)!r!
(n/2)(a1 + an)

27. How can you determine the arc degree or central angle of an inscribed angle?
SA = pr² +prl
Multiply the inscribed angle by 2
90°
(n-2)180

28. Sum of finite geometric series
(n-2)180
N!
(1-r/1-r)
F(x) = -f(-x)

29. How to find the distance between two points in 3d plane?
Square the differences between each coordinate - then square root the sum
y = a(x-h)² + k - where the vertex is (h -k)
N-1
a1 / 1-r

30. Formula for the volume of a cone
Adding or subtracting 180 to ? and reversing the sign of r.
V= (1/3)(pr²h)
Multiply the inscribed angle by 2
D = v(l²+w²+h²)

31. Formula for the area of a sector
Multiply the inscribed angle by 2
V = (1/3)bh
x = -b/2a y= c - (b²/4a)
A = (degree of the arc / 360)(area of a circle)

32. Formula for calculation exponential growth
SA = pr² +prl
90°
(y-k)²/a² - (x-h)²/b² = 1
Final amount = original amount x (1+growth rate)^number of changes

33. Standard form of the equation of a parabola.
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
A = ((s1 + s2)h) / 2
N!
y = a(x-h)² + k - where the vertex is (h -k)

34. Define an odd function.
Square the differences between each coordinate - then square root the sum
F(x) = -f(-x)
(n-2)180
x = -b/2a y= c - (b²/4a)

35. Combination formula
a1 / 1-r
Arc length equals = (degree of the arc / 360)(circumference)
(n-2)180
NCr = nPr / r! = n! / (n-r)!r!

36. Law of Cosines
V = (4/3)pr³
Arc length equals = (degree of the arc / 360)(circumference)
C² = a² + b² - 2abcos(C)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

37. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
NCr = nPr / r! = n! / (n-r)!r!
V = (1/3)bh
N-1
x = -b/2a y= c - (b²/4a)

38. Double Angle Formulas
A = ((s1 + s2)h) / 2
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
No equal sides and no equal angles
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)]

39. What is the triangle inequality rule?
N-1
F(x) = -f(-x)
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= sv3

40. Surface area of a sphere
Their dot product = 0
SA = 4pr²
(n/2)(a1 + an)
Adding or subtracting 180 to ? and reversing the sign of r.

41. Supplementary angles add up to
Arc length equals = (degree of the arc / 360)(circumference)
Multiply the inscribed angle by 2
180°
C² = a² + b² - 2abcos(C)

42. Sum of infinite geometric series
No equal sides and no equal angles
V = (1/3)bh
a1 / 1-r
(n/2)(a1 + an)

43. How to determine if a number is prime
A = (degree of the arc / 360)(area of a circle)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
All whole numbers except for 0
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

44. Complimentary angles add up to
D= sv3
F(x) = f(-x)
All whole numbers except for 0
90°

45. What are natural numbers?
All whole numbers except for 0
Square the differences between each coordinate - then square root the sum
Two sides and two angle are equal
180°

46. Formula for the area of a trapezoid
Square the differences between each coordinate - then square root the sum
Final amount = original amount x (1+growth rate)^number of changes
Hypotenuse is xv2 - and the sides are x.
A = ((s1 + s2)h) / 2

47. Formula for the diagonal length of a rectangular prism
(x-h)²/a² - (y-k)²/b² = 1
Parentheses - exponents - multiplication - division - addition - subtraction
V = (1/3)bh
D = v(l²+w²+h²)

48. Difference between 2 Angles formulas
SA = pr² +prl
a1 / 1-r
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)]

49. 30-60-90 triangle
Parentheses - exponents - multiplication - division - addition - subtraction
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Hypotenuse is 2x - short side is x - long side is xv3
x=rcos?(theta) y=rsin? (theta)

50. Standard form equation for an ellipse
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.
Hypotenuse is 2x - short side is x - long side is xv3
x=rcos?(theta) y=rsin? (theta)