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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 the diagonal length of a cube
D= sv3
All whole numbers except for 0
SA = pr² +prl
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

2. Formula for geometric sequence
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
An = a1rn?¹
y = a(x-h)² + k - where the vertex is (h -k)
Between the vertex and the minor axis on the major axis

3. Supplementary angles add up to
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
x = -b/2a y= c - (b²/4a)
180°
F(x) = f(-x)

4. Combination formula
NCr = nPr / r! = n! / (n-r)!r!
(x-h)²/a² - (y-k)²/b² = 1
90°
y = a(x-h)² + k - where the vertex is (h -k)

5. What is the sum of the interior angles for a polygon with n sides?
(n-2)180
D= sv3
y-y1 = m(x-x1)
Parentheses - exponents - multiplication - division - addition - subtraction

6. Isosceles Triangles
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)]
Two sides and two angle are equal
Hypotenuse is 2x - short side is x - long side is xv3
Adding or subtracting 180 to ? and reversing the sign of r.

7. Formula for the diagonal length of a rectangular prism
180°
A = (degree of the arc / 360)(area of a circle)
D = v(l²+w²+h²)
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)]

8. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
90°
x = -b/2a y= c - (b²/4a)
F(x) = f(-x)
A = ((s1 + s2)h) / 2

9. What is the order of operations?
Parentheses - exponents - multiplication - division - addition - subtraction
x = -b/2a y= c - (b²/4a)
x=rcos?(theta) y=rsin? (theta)
A = (degree of the arc / 360)(area of a circle)

10. What is the triangle inequality rule?
(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.
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
An = a1 + (n-1)d
A = ((s1 + s2)h) / 2

11. How to find the distance between two points in 3d plane?
x=rcos?(theta) y=rsin? (theta)
180°
Square the differences between each coordinate - then square root the sum
Their dot product = 0

12. What are relatively prime numbers?
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)]
(n/2)(a1 + an)
The greatest common factor is 1 - but the numbers are not necessarily prime.

13. Where is tangent positive/negative?
V = (4/3)pr³
Their dot product = 0
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
F(x) = -f(-x)

14. Standard form for a hyperbola that opens to the sides
(x-h)²/a² - (y-k)²/b² = 1
NPr = n! / (n-r)!
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
An = a1rn?¹

15. Difference between 2 Angles formulas
(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=rcos?(theta) y=rsin? (theta)
a1 / 1-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)]

16. How can multiple polar coordinates be made?
C² = a² + b² - 2abcos(C)
Final amount = original amount x (1+growth rate)^number of changes
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Adding or subtracting 180 to ? and reversing the sign of r.

17. Two vectors are perpendicular if
x=rcos?(theta) y=rsin? (theta)
An = a1 + (n-1)d
All whole numbers except for 0
Their dot product = 0

18. Pythagorean Identities
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
C² = a² + b² - 2abcos(C)
SA = 4pr²
V= (1/3)(pr²h)

19. Volume of a pyramid
Final amount = original amount x (1+growth rate)^number of changes
No equal sides and no equal angles
V = (1/3)bh
y = a(x-h)² + k - where the vertex is (h -k)

20. How can you determine the arc degree or central angle of an inscribed angle?
D= sv3
Hypotenuse is 2x - short side is x - long side is xv3
90°
Multiply the inscribed angle by 2

21. Formula for arc length
(n/2)(a1 + an)
A = (degree of the arc / 360)(area of a circle)
(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.
Arc length equals = (degree of the arc / 360)(circumference)

22. Volume of a sphere
All whole numbers except for 0
Multiply the inscribed angle by 2
V = (4/3)pr³
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

23. Standard form of the equation of a parabola.
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)
Between the vertex and the minor axis on the major axis
x=rcos?(theta) y=rsin? (theta)

24. Formula for arithmetic sequence
Hypotenuse is 2x - short side is x - long side is xv3
SA = 4pr²
An = a1 + (n-1)d
NCr = nPr / r! = n! / (n-r)!r!

25. What are natural numbers?
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
All whole numbers except for 0
180°

26. Standard form equation for circle
90°
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
F(x) = f(-x)

27. Complimentary angles add up to
a1 / 1-r
F(x) = f(-x)
180°
90°

28. Define an even function.
D = v(l²+w²+h²)
F(x) = f(-x)
(x-h)²/a² - (y-k)²/b² = 1
(1-r/1-r)

29. Surface area of a cone
SA = pr² +prl
(1-r/1-r)
V= (1/3)(pr²h)
F(x) = -f(-x)

30. Standard form equation for an ellipse
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(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
Between the vertex and the minor axis on the major axis

31. Formula for the area of a trapezoid
A = ((s1 + s2)h) / 2
90°
F(x) = f(-x)
N!

32. Scalene triangle
No equal sides and no equal angles
(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.
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)]

33. 45-45-90 triangle
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Hypotenuse is xv2 - and the sides are x.
F(x) = f(-x)

34. What are the conversion equations for polar coordinates to normal coordinates?
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)]
x=rcos?(theta) y=rsin? (theta)
All whole numbers except for 0

35. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
y-y1 = m(x-x1)
Multiply the inscribed angle by 2
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
SA = pr² +prl

36. How to determine if a number is prime
Between the vertex and the minor axis on the major axis
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Adding or subtracting 180 to ? and reversing the sign of r.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

37. Formula for the volume of a cone
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=rcos?(theta) y=rsin? (theta)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
V= (1/3)(pr²h)

38. Sum of infinite geometric series
(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
a1 / 1-r
NPr = n! / (n-r)!

39. In an ellipse - where are the foci?
Between the vertex and the minor axis on the major axis
(n-2)180
V = (1/3)bh
Adding or subtracting 180 to ? and reversing the sign of r.

40. Sum of finite geometric series
SA = pr² +prl
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
(1-r/1-r)
(n/2)(a1 + an)

41. Sum of n terms of an arithmetic sequence
(n/2)(a1 + an)
Between the vertex and the minor axis on the major axis
x=rcos?(theta) y=rsin? (theta)
SA = pr² +prl

42. Standard form for a hyperbola that opens vertically
V= (1/3)(pr²h)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(y-k)²/a² - (x-h)²/b² = 1
180°

43. Sum of 2 Angles Formulas
Hypotenuse is 2x - short side is x - long side is xv3
D = v(l²+w²+h²)
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)]
Adding or subtracting 180 to ? and reversing the sign of r.

44. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
(y-k)²/a² - (x-h)²/b² = 1
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
No equal sides and no equal angles
N-1

45. Formula for the area of a sector
90°
A = (degree of the arc / 360)(area of a circle)
y = a(x-h)² + k - where the vertex is (h -k)
V = (4/3)pr³

46. Define an odd function.
y-y1 = m(x-x1)
Square the differences between each coordinate - then square root the sum
V= (1/3)(pr²h)
F(x) = -f(-x)

47. How many ways can n elements be ordered?
No equal sides and no equal angles
Hypotenuse is 2x - short side is x - long side is xv3
x=rcos?(theta) y=rsin? (theta)
N!

48. Formula for calculation exponential growth
Final amount = original amount x (1+growth rate)^number of changes
SA = 4pr²
Their dot product = 0
(n/2)(a1 + an)

49. Law of Cosines
(n/2)(a1 + an)
V= (1/3)(pr²h)
C² = a² + b² - 2abcos(C)
Adding or subtracting 180 to ? and reversing the sign of r.

50. Permutation formula (ordering)
x = -b/2a y= c - (b²/4a)
(n-2)180
NPr = n! / (n-r)!
y-y1 = m(x-x1)