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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. Formula for the area of a trapezoid
A = ((s1 + s2)h) / 2
(y-k)²/a² - (x-h)²/b² = 1
Their dot product = 0
The greatest common factor is 1 - but the numbers are not necessarily prime.

2. Standard form equation for circle
NPr = n! / (n-r)!
(1-r/1-r)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
F(x) = f(-x)

3. What are natural numbers?
All whole numbers except for 0
F(x) = f(-x)
V = (4/3)pr³
(x-h)²/a² - (y-k)²/b² = 1

4. Permutation formula (ordering)
NPr = n! / (n-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)]
y = a(x-h)² + k - where the vertex is (h -k)
D= sv3

5. Scalene triangle
No equal sides and no equal angles
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.
Parentheses - exponents - multiplication - division - addition - subtraction

6. Sum of n terms of an arithmetic sequence
(n/2)(a1 + an)
An = a1 + (n-1)d
Square the differences between each coordinate - then square root the sum
SA = 4pr²

7. Formula for calculation exponential growth
All whole numbers except for 0
Final amount = original amount x (1+growth rate)^number of changes
(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.
SA = pr² +prl

8. Where is tangent positive/negative?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Square the differences between each coordinate - then square root the sum
Hypotenuse is xv2 - and the sides are x.
F(x) = -f(-x)

9. Sum of 2 Angles Formulas
F(x) = f(-x)
SA = 4pr²
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 + (y-k)² = r² - where (h -k) is the center of the circle

10. 30-60-90 triangle
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
180°
Hypotenuse is 2x - short side is x - long side is xv3
NCr = nPr / r! = n! / (n-r)!r!

11. Formula for the volume of a cone
N-1
V= (1/3)(pr²h)
Their dot product = 0
Two sides and two angle are equal

12. What is the triangle inequality rule?
The greatest common factor is 1 - but the numbers are not necessarily prime.
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!
(n-2)180

13. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
(n-2)180
An = a1rn?¹
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
x = -b/2a y= c - (b²/4a)

14. Standard form equation for an ellipse
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
y = a(x-h)² + k - where the vertex is (h -k)
(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

15. 45-45-90 triangle
x=rcos?(theta) y=rsin? (theta)
180°
Hypotenuse is xv2 - and the sides are x.
Arc length equals = (degree of the arc / 360)(circumference)

16. How can multiple polar coordinates be made?
x = -b/2a y= c - (b²/4a)
Adding or subtracting 180 to ? and reversing the sign of r.
Parentheses - exponents - multiplication - division - addition - subtraction
(n/2)(a1 + an)

17. Combination formula
Multiply the inscribed angle by 2
An = a1 + (n-1)d
NCr = nPr / r! = n! / (n-r)!r!
V= (1/3)(pr²h)

18. Standard form of the equation of a parabola.
y = a(x-h)² + k - where the vertex is (h -k)
90°
Adding or subtracting 180 to ? and reversing the sign of r.
Hypotenuse is xv2 - and the sides are x.

19. Formula for the area of a sector
y-y1 = m(x-x1)
A = (degree of the arc / 360)(area of a circle)
Final amount = original amount x (1+growth rate)^number of changes
(1-r/1-r)

20. How to determine if a number is prime
SA = 4pr²
NPr = n! / (n-r)!
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
An = a1 + (n-1)d

21. Formula for arithmetic sequence
An = a1 + (n-1)d
Between the vertex and the minor axis on the major axis
Multiply the inscribed angle by 2
Square the differences between each coordinate - then square root the sum

22. Sum of finite geometric series
x = -b/2a y= c - (b²/4a)
V = (1/3)bh
(y-k)²/a² - (x-h)²/b² = 1
(1-r/1-r)

23. Pythagorean Identities
V = (4/3)pr³
Final amount = original amount x (1+growth rate)^number of changes
(y-k)²/a² - (x-h)²/b² = 1
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

24. Define an odd function.
All whole numbers except for 0
NPr = n! / (n-r)!
F(x) = -f(-x)
V= (1/3)(pr²h)

25. In an ellipse - where are the foci?
Between the vertex and the minor axis on the major axis
F(x) = -f(-x)
y-y1 = m(x-x1)
All whole numbers except for 0

26. Double Angle Formulas
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
F(x) = f(-x)
A = (degree of the arc / 360)(area of a circle)
N!

27. Difference between 2 Angles formulas
Two sides and two angle are equal
SA = pr² +prl
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)

28. How to find the distance between two points in 3d plane?
Between the vertex and the minor axis on the major axis
Square the differences between each coordinate - then square root the sum
a1 / 1-r
y-y1 = m(x-x1)

29. What is the form of a polar coordinate?
NCr = nPr / r! = n! / (n-r)!r!
Multiply the inscribed angle by 2
(n/2)(a1 + an)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

30. Formula for the diagonal length of a rectangular prism
D = v(l²+w²+h²)
F(x) = -f(-x)
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)]

31. Volume of a sphere
F(x) = -f(-x)
V = (4/3)pr³
(x-h)²/a² - (y-k)²/b² = 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)]

32. Two vectors are perpendicular if
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)]
Their dot product = 0
y-y1 = m(x-x1)

33. What are relatively prime numbers?
The greatest common factor is 1 - but the numbers are not necessarily prime.
90°
Adding or subtracting 180 to ? and reversing the sign of r.
Parentheses - exponents - multiplication - division - addition - subtraction

34. Surface area of a cone
Multiply the inscribed angle by 2
SA = pr² +prl
y = a(x-h)² + k - where the vertex is (h -k)
(n/2)(a1 + an)

35. How many ways can n elements be ordered?
Two sides and two angle are equal
(n-2)180
Parentheses - exponents - multiplication - division - addition - subtraction
N!

36. Sum of infinite geometric series
a1 / 1-r
NPr = n! / (n-r)!
An = a1rn?¹
Their dot product = 0

37. Formula for arc length
Hypotenuse is xv2 - and the sides are x.
An = a1rn?¹
A = ((s1 + s2)h) / 2
Arc length equals = (degree of the arc / 360)(circumference)

38. Volume of a pyramid
V= (1/3)(pr²h)
An = a1rn?¹
V = (1/3)bh
Parentheses - exponents - multiplication - division - addition - subtraction

39. How can you determine the arc degree or central angle of an inscribed angle?
(n-2)180
D= sv3
Multiply the inscribed angle by 2
(x-h)²/a² - (y-k)²/b² = 1

40. What is the sum of the interior angles for a polygon with n sides?
V = (4/3)pr³
An = a1 + (n-1)d
180°
(n-2)180

41. Formula for the diagonal length of a cube
90°
D= sv3
SA = 4pr²
Final amount = original amount x (1+growth rate)^number of changes

42. What are the conversion equations for polar coordinates to normal coordinates?
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
x=rcos?(theta) y=rsin? (theta)
An = a1 + (n-1)d

43. Define an even function.
F(x) = f(-x)
F(x) = -f(-x)
(y-k)²/a² - (x-h)²/b² = 1
(1-r/1-r)

44. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
y-y1 = m(x-x1)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
A = ((s1 + s2)h) / 2

45. Law of Cosines
V= (1/3)(pr²h)
V = (1/3)bh
180°
C² = a² + b² - 2abcos(C)

46. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
180°
No equal sides and no equal angles
An = a1 + (n-1)d

47. Standard form for a hyperbola that opens vertically
Hypotenuse is xv2 - and the sides are x.
(y-k)²/a² - (x-h)²/b² = 1
V= (1/3)(pr²h)
N!

48. Formula for geometric sequence
An = a1rn?¹
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-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.
A = (degree of the arc / 360)(area of a circle)

49. Supplementary angles add up to
180°
An = a1 + (n-1)d
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 = v(l²+w²+h²)

50. Isosceles Triangles
Adding or subtracting 180 to ? and reversing the sign of r.
x = -b/2a y= c - (b²/4a)
180°
Two sides and two angle are equal