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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. Formula for calculation exponential growth
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Final amount = original amount x (1+growth rate)^number of changes
The greatest common factor is 1 - but the numbers are not necessarily prime.
C² = a² + b² - 2abcos(C)

2. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
x = -b/2a y= c - (b²/4a)
Square the differences between each coordinate - then square root the sum
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. Define an even function.
D = v(l²+w²+h²)
F(x) = f(-x)
Multiply the inscribed angle by 2
NCr = nPr / r! = n! / (n-r)!r!

4. Complimentary angles add up to
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
a1 / 1-r
N-1
90°

5. 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)]
NCr = nPr / r! = n! / (n-r)!r!
Between the vertex and the minor axis on the major axis
Final amount = original amount x (1+growth rate)^number of changes

6. Formula for the area of a trapezoid
Arc length equals = (degree of the arc / 360)(circumference)
A = ((s1 + s2)h) / 2
Parentheses - exponents - multiplication - division - addition - subtraction
An = a1 + (n-1)d

7. Formula for the diagonal length of a cube
x=rcos?(theta) y=rsin? (theta)
D= sv3
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)

8. Isosceles Triangles
V = (1/3)bh
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Two sides and two angle are equal

9. Two vectors are perpendicular if
No equal sides and no equal angles
Their dot product = 0
Arc length equals = (degree of the arc / 360)(circumference)
(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.

10. Combination formula
NPr = n! / (n-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.
Hypotenuse is xv2 - and the sides are x.
NCr = nPr / r! = n! / (n-r)!r!

11. Supplementary angles add up to
180°
y = a(x-h)² + k - where the vertex is (h -k)
An = a1 + (n-1)d
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

12. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
F(x) = -f(-x)
All whole numbers except for 0
D = v(l²+w²+h²)
y-y1 = m(x-x1)

13. 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.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
F(x) = f(-x)
(n/2)(a1 + an)

14. Formula for the area of a sector
A = (degree of the arc / 360)(area of a circle)
N-1
F(x) = f(-x)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

15. Standard form equation for circle
All whole numbers except for 0
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
y = a(x-h)² + k - where the vertex is (h -k)
F(x) = -f(-x)

16. How to determine if a number is prime
Hypotenuse is xv2 - and the sides are x.
V= (1/3)(pr²h)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
(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.

17. What are natural numbers?
SA = 4pr²
All whole numbers except for 0
Two sides and two angle are equal
Between the vertex and the minor axis on the major axis

18. Define an odd function.
N!
D= sv3
F(x) = -f(-x)
A = ((s1 + s2)h) / 2

19. How many ways can n elements be ordered?
N!
SA = 4pr²
An = a1rn?¹
180°

20. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
90°
N-1
Adding or subtracting 180 to ? and reversing the sign of r.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

21. Standard form equation for an ellipse
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.
A = (degree of the arc / 360)(area of a circle)
D= sv3

22. Scalene triangle
(x-h)²/a² - (y-k)²/b² = 1
C² = a² + b² - 2abcos(C)
Multiply the inscribed angle by 2
No equal sides and no equal angles

23. Surface area of a sphere
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
SA = 4pr²
F(x) = f(-x)
A = (degree of the arc / 360)(area of a circle)

24. Formula for arc length
Arc length equals = (degree of the arc / 360)(circumference)
y = a(x-h)² + k - where the vertex is (h -k)
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

25. Double Angle Formulas
(y-k)²/a² - (x-h)²/b² = 1
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
D = v(l²+w²+h²)

26. Formula for arithmetic sequence
(1-r/1-r)
C² = a² + b² - 2abcos(C)
Parentheses - exponents - multiplication - division - addition - subtraction
An = a1 + (n-1)d

27. What is the order of operations?
A = (degree of the arc / 360)(area of a circle)
Parentheses - exponents - multiplication - division - addition - subtraction
D= sv3
An = a1rn?¹

28. What are the conversion equations for polar coordinates to normal coordinates?
A = (degree of the arc / 360)(area of a circle)
All whole numbers except for 0
(1-r/1-r)
x=rcos?(theta) y=rsin? (theta)

29. In an ellipse - where are the foci?
N!
a1 / 1-r
Between the vertex and the minor axis on the major axis
C² = a² + b² - 2abcos(C)

30. What is the form of a polar coordinate?
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.
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
V= (1/3)(pr²h)

31. What are relatively prime numbers?
No equal sides and no equal angles
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)]
(n-2)180

32. What is the sum of the interior angles for a polygon with n sides?
Two sides and two angle are equal
Parentheses - exponents - multiplication - division - addition - subtraction
(n-2)180
An = a1rn?¹

33. Standard form for a hyperbola that opens to the sides
No equal sides and no equal angles
(x-h)²/a² - (y-k)²/b² = 1
An = a1 + (n-1)d
F(x) = -f(-x)

34. How to find the distance between two points in 3d plane?
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.
All whole numbers except for 0
Square the differences between each coordinate - then square root the sum

35. Formula for geometric sequence
(1-r/1-r)
An = a1rn?¹
Square the differences between each coordinate - then square root the sum
Two sides and two angle are equal

36. Surface area of a cone
A = ((s1 + s2)h) / 2
Square the differences between each coordinate - then square root the sum
An = a1 + (n-1)d
SA = pr² +prl

37. 30-60-90 triangle
NPr = n! / (n-r)!
Their dot product = 0
V= (1/3)(pr²h)
Hypotenuse is 2x - short side is x - long side is xv3

38. Volume of a pyramid
V = (1/3)bh
x = -b/2a y= c - (b²/4a)
a1 / 1-r
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

39. Sum of infinite geometric series
a1 / 1-r
Adding or subtracting 180 to ? and reversing the sign of r.
The length of a side of a triangle is less than the sum of and greater than the difference of the other two 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)]

40. Pythagorean Identities
Final amount = original amount x (1+growth rate)^number of changes
D= sv3
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)]
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

41. Standard form for a hyperbola that opens vertically
(n/2)(a1 + an)
A = ((s1 + s2)h) / 2
x = -b/2a y= c - (b²/4a)
(y-k)²/a² - (x-h)²/b² = 1

42. How can multiple polar coordinates be made?
C² = a² + b² - 2abcos(C)
V= (1/3)(pr²h)
Their dot product = 0
Adding or subtracting 180 to ? and reversing the sign of r.

43. Formula for the volume of a cone
A = (degree of the arc / 360)(area of a circle)
SA = 4pr²
All whole numbers except for 0
V= (1/3)(pr²h)

44. Where is tangent positive/negative?
(y-k)²/a² - (x-h)²/b² = 1
D = v(l²+w²+h²)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Final amount = original amount x (1+growth rate)^number of changes

45. Sum of finite geometric series
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
(1-r/1-r)
Parentheses - exponents - multiplication - division - addition - subtraction

46. Permutation formula (ordering)
(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.
C² = a² + b² - 2abcos(C)
NPr = n! / (n-r)!
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

47. 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)]
F(x) = f(-x)
SA = 4pr²
Two sides and two angle are equal

48. 45-45-90 triangle
(n/2)(a1 + an)
Hypotenuse is xv2 - and the sides are x.
N-1
V = (1/3)bh

49. Standard form of the equation of a parabola.
Parentheses - exponents - multiplication - division - addition - subtraction
(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.
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.

50. Volume of a sphere
Square the differences between each coordinate - then square root the sum
V = (4/3)pr³
A = ((s1 + s2)h) / 2
Arc length equals = (degree of the arc / 360)(circumference)