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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.
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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 arithmetic sequence
90°
Their dot product = 0
An = a1 + (n-1)d
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

2. Formula for geometric sequence
Final amount = original amount x (1+growth rate)^number of changes
F(x) = -f(-x)
An = a1rn?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)]

3. What are the conversion equations for polar coordinates to normal coordinates?
x=rcos?(theta) y=rsin? (theta)
D = v(l²+w²+h²)
180°
y = a(x-h)² + k - where the vertex is (h -k)

4. Volume of a sphere
Hypotenuse is 2x - short side is x - long side is xv3
V = (4/3)pr³
Multiply the inscribed angle by 2
F(x) = f(-x)

5. Standard form equation for circle
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
SA = 4pr²
(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

6. What is the triangle inequality rule?
Final amount = original amount x (1+growth rate)^number of changes
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
(n-2)180

7. 45-45-90 triangle
Arc length equals = (degree of the arc / 360)(circumference)
Hypotenuse is xv2 - and the sides are x.
180°
(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.

8. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
NPr = n! / (n-r)!
N-1
D = v(l²+w²+h²)
Arc length equals = (degree of the arc / 360)(circumference)

9. 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
The greatest common factor is 1 - but the numbers are not necessarily prime.
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Parentheses - exponents - multiplication - division - addition - subtraction

10. Sum of 2 Angles Formulas
N!
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
y-y1 = m(x-x1)
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)]

11. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
90°
All whole numbers except for 0
x = -b/2a y= c - (b²/4a)
(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.

12. Complimentary angles add up to
All whole numbers except for 0
90°
Parentheses - exponents - multiplication - division - addition - subtraction
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

13. Sum of infinite geometric series
a1 / 1-r
x = -b/2a y= c - (b²/4a)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

14. Sum of n terms of an arithmetic sequence
x = -b/2a y= c - (b²/4a)
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)(a1 + an)
V = (4/3)pr³

15. How can you determine the arc degree or central angle of an inscribed angle?
All whole numbers except for 0
Square the differences between each coordinate - then square root the sum
NCr = nPr / r! = n! / (n-r)!r!
Multiply the inscribed angle by 2

16. Standard form of the equation of a parabola.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
y = a(x-h)² + k - where the vertex is (h -k)
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.

17. Supplementary angles add up to
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Between the vertex and the minor axis on the major axis
Hypotenuse is xv2 - and the sides are x.
180°

18. What is the order of operations?
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
N!
Multiply the inscribed angle by 2
Parentheses - exponents - multiplication - division - addition - subtraction

19. Sum of finite geometric series
(1-r/1-r)
V = (1/3)bh
The greatest common factor is 1 - but the numbers are not necessarily prime.
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

20. How many ways can n elements be ordered?
N!
Square the differences between each coordinate - then square root the sum
N-1
Their dot product = 0

21. Surface area of a cone
SA = pr² +prl
(n/2)(a1 + an)
A = ((s1 + s2)h) / 2
An = a1rn?¹

22. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
C² = a² + b² - 2abcos(C)
Hypotenuse is xv2 - and the sides are x.
y-y1 = m(x-x1)
An = a1 + (n-1)d

23. Formula for calculation exponential growth
x=rcos?(theta) y=rsin? (theta)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Final amount = original amount x (1+growth rate)^number of changes
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

24. Standard form for a hyperbola that opens to the sides
Parentheses - exponents - multiplication - division - addition - subtraction
(x-h)²/a² - (y-k)²/b² = 1
(n-2)180
x=rcos?(theta) y=rsin? (theta)

25. Formula for the diagonal length of a cube
SA = 4pr²
Square the differences between each coordinate - then square root the sum
D= sv3
A = (degree of the arc / 360)(area of a circle)

26. How to determine if a number is prime
Parentheses - exponents - multiplication - division - addition - subtraction
D = v(l²+w²+h²)
Adding or subtracting 180 to ? and reversing the sign of r.
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

27. Difference between 2 Angles formulas
Two sides and two angle are equal
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
F(x) = -f(-x)

28. Standard form equation for an ellipse
F(x) = -f(-x)
a1 / 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.
D = v(l²+w²+h²)

29. Surface area of a sphere
SA = 4pr²
F(x) = -f(-x)
C² = a² + b² - 2abcos(C)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

30. What are relatively prime numbers?
V = (1/3)bh
SA = 4pr²
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
The greatest common factor is 1 - but the numbers are not necessarily prime.

31. Standard form for a hyperbola that opens vertically
V= (1/3)(pr²h)
(y-k)²/a² - (x-h)²/b² = 1
No equal sides and no equal angles
V = (4/3)pr³

32. Isosceles Triangles
(x-h)²/a² - (y-k)²/b² = 1
Two sides and two angle are equal
y-y1 = m(x-x1)
No equal sides and no equal angles

33. Volume of a pyramid
NPr = n! / (n-r)!
(n/2)(a1 + an)
y = a(x-h)² + k - where the vertex is (h -k)
V = (1/3)bh

34. How to find the distance between two points in 3d plane?
No equal sides and no equal angles
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
(x-h)²/a² - (y-k)²/b² = 1
Square the differences between each coordinate - then square root the sum

35. What is the sum of the interior angles for a polygon with n sides?
(n-2)180
Hypotenuse is xv2 - and the sides are x.
An = a1rn?¹
Hypotenuse is 2x - short side is x - long side is xv3

36. Where is tangent positive/negative?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
SA = pr² +prl
Hypotenuse is 2x - short side is x - long side is xv3

37. Two vectors are perpendicular if
Hypotenuse is 2x - short side is x - long side is xv3
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Multiply the inscribed angle by 2
Their dot product = 0

38. Define an even function.
a1 / 1-r
Final amount = original amount x (1+growth rate)^number of changes
All whole numbers except for 0
F(x) = f(-x)

39. Law of Cosines
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
V= (1/3)(pr²h)
C² = a² + b² - 2abcos(C)

40. Formula for arc length
The greatest common factor is 1 - but the numbers are not necessarily prime.
V = (1/3)bh
Arc length equals = (degree of the arc / 360)(circumference)
N!

41. Formula for the volume of a cone
V= (1/3)(pr²h)
(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-1
(n-2)180

42. Formula for the diagonal length of a rectangular prism
SA = pr² +prl
D = v(l²+w²+h²)
V = (1/3)bh
y = a(x-h)² + k - where the vertex is (h -k)

43. Formula for the area of a sector
Hypotenuse is 2x - short side is x - long side is xv3
NPr = n! / (n-r)!
(1-r/1-r)
A = (degree of the arc / 360)(area of a circle)

44. Double Angle Formulas
(n-2)180
N!
V = (1/3)bh
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

45. Formula for the area of a trapezoid
A = (degree of the arc / 360)(area of a circle)
A = ((s1 + s2)h) / 2
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
(x-h)²/a² - (y-k)²/b² = 1

46. What are natural numbers?
Hypotenuse is 2x - short side is x - long side is xv3
Hypotenuse is xv2 - and the sides are x.
(y-k)²/a² - (x-h)²/b² = 1
All whole numbers except for 0

47. Define an odd function.
y-y1 = m(x-x1)
F(x) = -f(-x)
y = a(x-h)² + k - where the vertex is (h -k)
All whole numbers except for 0

48. How can multiple polar coordinates be made?
Adding or subtracting 180 to ? and reversing the sign of r.
(y-k)²/a² - (x-h)²/b² = 1
V = (4/3)pr³
(n/2)(a1 + an)

49. Pythagorean Identities
(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.
Final amount = original amount x (1+growth rate)^number of changes
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Hypotenuse is 2x - short side is x - long side is xv3

50. In an ellipse - where are the foci?
Adding or subtracting 180 to ? and reversing the sign of r.
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
No equal sides and no equal angles
Between the vertex and the minor axis on the major axis

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SAT Math 2

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