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SAT Math 2

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. How can multiple polar coordinates be made?
Adding or subtracting 180 to ? and reversing the sign of r.
Hypotenuse is xv2 - and the sides are x.
SA = 4pr²
Multiply the inscribed angle by 2

2. What is the order of operations?
Their dot product = 0
(n-2)180
Parentheses - exponents - multiplication - division - addition - subtraction
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

3. Sum of n terms of an arithmetic sequence
(n/2)(a1 + an)
Hypotenuse is 2x - short side is x - long side is xv3
x = -b/2a y= c - (b²/4a)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

4. Two vectors are perpendicular if
An = a1rn?¹
All whole numbers except for 0
V = (4/3)pr³
Their dot product = 0

5. 30-60-90 triangle
Hypotenuse is 2x - short side is x - long side is xv3
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)]
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

6. Difference between 2 Angles formulas
(x-h)²/a² - (y-k)²/b² = 1
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)]
(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.

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

8. 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)
N!
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Square the differences between each coordinate - then square root the sum

9. What are natural numbers?
F(x) = -f(-x)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
a1 / 1-r
All whole numbers except for 0

10. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
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)]
An = a1 + (n-1)d
N-1

11. Standard form of the equation of a parabola.
y = a(x-h)² + k - where the vertex is (h -k)
F(x) = f(-x)
V= (1/3)(pr²h)
x = -b/2a y= c - (b²/4a)

12. What is the form of a polar coordinate?
V= (1/3)(pr²h)
SA = pr² +prl
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

13. Volume of a sphere
V = (4/3)pr³
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Final amount = original amount x (1+growth rate)^number of changes
A = (degree of the arc / 360)(area of a circle)

14. Formula for arc length
D= sv3
F(x) = -f(-x)
Two sides and two angle are equal
Arc length equals = (degree of the arc / 360)(circumference)

15. Formula for the area of a trapezoid
V = (4/3)pr³
A = ((s1 + s2)h) / 2
Their dot product = 0
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

16. What are the conversion equations for polar coordinates to normal coordinates?
F(x) = -f(-x)
x=rcos?(theta) y=rsin? (theta)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

17. Define an odd function.
F(x) = -f(-x)
Adding or subtracting 180 to ? and reversing the sign of r.
Multiply the inscribed angle by 2
V = (1/3)bh

18. Standard form for a hyperbola that opens vertically
N!
Their dot product = 0
F(x) = f(-x)
(y-k)²/a² - (x-h)²/b² = 1

19. Complimentary angles add up to
(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.
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Arc length equals = (degree of the arc / 360)(circumference)
90°

20. Supplementary angles add up to
(n/2)(a1 + an)
y = a(x-h)² + k - where the vertex is (h -k)
Adding or subtracting 180 to ? and reversing the sign of r.
180°

21. Formula for arithmetic sequence
(x-h)²/a² - (y-k)²/b² = 1
F(x) = f(-x)
Final amount = original amount x (1+growth rate)^number of changes
An = a1 + (n-1)d

22. Sum of infinite geometric series
Adding or subtracting 180 to ? and reversing the sign of r.
a1 / 1-r
180°
90°

23. Permutation formula (ordering)
Adding or subtracting 180 to ? and reversing the sign of r.
N-1
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.

24. Isosceles Triangles
Two sides and two angle are equal
A = (degree of the arc / 360)(area of a circle)
An = a1 + (n-1)d
No equal sides and no equal angles

25. Formula for the area of a sector
A = (degree of the arc / 360)(area of a circle)
(n-2)180
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Arc length equals = (degree of the arc / 360)(circumference)

26. How many ways can n elements be ordered?
N!
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)]
Arc length equals = (degree of the arc / 360)(circumference)
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)]

27. Where is tangent positive/negative?
90°
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
(n/2)(a1 + an)

28. Standard form equation for an ellipse
Final amount = original amount x (1+growth rate)^number of changes
F(x) = -f(-x)
Between the vertex and the minor axis on the major 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.

29. Standard form for a hyperbola that opens to the sides
An = a1 + (n-1)d
F(x) = f(-x)
(x-h)²/a² - (y-k)²/b² = 1
a1 / 1-r

30. Surface area of a cone
The greatest common factor is 1 - but the numbers are not necessarily prime.
Square the differences between each coordinate - then square root the sum
SA = pr² +prl
V= (1/3)(pr²h)

31. How can you determine the arc degree or central angle of an inscribed angle?
Multiply the inscribed angle by 2
(n-2)180
Arc length equals = (degree of the arc / 360)(circumference)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

32. Formula for the diagonal length of a rectangular prism
NPr = n! / (n-r)!
A = ((s1 + s2)h) / 2
D = v(l²+w²+h²)
F(x) = -f(-x)

33. Pythagorean Identities
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
a1 / 1-r
Their dot product = 0
Two sides and two angle are equal

34. Law of Cosines
D= sv3
All whole numbers except for 0
C² = a² + b² - 2abcos(C)
An = a1 + (n-1)d

35. How to determine if a number is prime
Multiply the inscribed angle by 2
Square the differences between each coordinate - then square root the sum
N-1
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

36. In an ellipse - where are the foci?
C² = a² + b² - 2abcos(C)
Between the vertex and the minor axis on the major axis
N-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)]

37. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
An = a1 + (n-1)d
x = -b/2a y= c - (b²/4a)
Multiply the inscribed angle by 2
A = (degree of the arc / 360)(area of a circle)

38. Formula for the diagonal length of a cube
Arc length equals = (degree of the arc / 360)(circumference)
N-1
V = (4/3)pr³
D= sv3

39. Combination formula
90°
D= sv3
An = a1rn?¹
NCr = nPr / r! = n! / (n-r)!r!

40. Define an even function.
Hypotenuse is xv2 - and the sides are x.
SA = 4pr²
F(x) = f(-x)
F(x) = -f(-x)

41. Surface area of a sphere
SA = 4pr²
x = -b/2a y= c - (b²/4a)
A = (degree of the arc / 360)(area of a circle)
No equal sides and no equal angles

42. 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)]
N-1
V= (1/3)(pr²h)
D= sv3

43. Scalene triangle
V = (1/3)bh
(y-k)²/a² - (x-h)²/b² = 1
No equal sides and no equal angles
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

44. Double Angle Formulas
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
The greatest common factor is 1 - but the numbers are not necessarily prime.
SA = 4pr²

45. What is the triangle inequality rule?
Adding or subtracting 180 to ? and reversing the sign of r.
Two sides and two angle are equal
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
(n-2)180

46. 45-45-90 triangle
Final amount = original amount x (1+growth rate)^number of changes
Hypotenuse is xv2 - and the sides are x.
F(x) = -f(-x)
NCr = nPr / r! = n! / (n-r)!r!

47. Volume of a pyramid
D = v(l²+w²+h²)
D= sv3
An = a1 + (n-1)d
V = (1/3)bh

48. Formula for geometric sequence
An = a1rn?¹
F(x) = f(-x)
V = (4/3)pr³
V= (1/3)(pr²h)

49. Formula for calculation exponential growth
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)]
Final amount = original amount x (1+growth rate)^number of changes
y = a(x-h)² + k - where the vertex is (h -k)
An = a1rn?¹

50. Sum of 2 Angles Formulas
N-1
(1-r/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)]
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis