Test your basic knowledge |

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. Supplementary angles add up to
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)]
D = v(l²+w²+h²)
180°
Hypotenuse is 2x - short side is x - long side is xv3

2. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
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)]
N-1
(1-r/1-r)

3. What is the triangle inequality rule?
NCr = nPr / r! = n! / (n-r)!r!
C² = a² + b² - 2abcos(C)
Hypotenuse is 2x - short side is x - long side is xv3
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

4. Volume of a pyramid
(n/2)(a1 + an)
V = (1/3)bh
x = -b/2a y= c - (b²/4a)
Multiply the inscribed angle by 2

5. Standard form equation for an ellipse
x=rcos?(theta) y=rsin? (theta)
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.
Their dot product = 0

6. What is the sum of the interior angles for a polygon with n sides?
All whole numbers except for 0
(n-2)180
Multiply the inscribed angle by 2
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

7. Permutation formula (ordering)
NPr = n! / (n-r)!
No equal sides and no equal angles
F(x) = f(-x)
Adding or subtracting 180 to ? and reversing the sign of r.

8. How to determine if a number is prime
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
x=rcos?(theta) y=rsin? (theta)
F(x) = f(-x)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

9. Where is tangent positive/negative?
Arc length equals = (degree of the arc / 360)(circumference)
Between the vertex and the minor axis on the major axis
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
180°

10. Formula for geometric sequence
y-y1 = m(x-x1)
An = a1rn?¹
x=rcos?(theta) y=rsin? (theta)
D= sv3

11. 30-60-90 triangle
x=rcos?(theta) y=rsin? (theta)
90°
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Hypotenuse is 2x - short side is x - long side is xv3

12. Complimentary angles add up to
Multiply the inscribed angle by 2
Parentheses - exponents - multiplication - division - addition - subtraction
a1 / 1-r
90°

13. Isosceles Triangles
(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)
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.

14. Sum of n terms of an arithmetic sequence
Between the vertex and the minor axis on the major axis
SA = pr² +prl
(n/2)(a1 + an)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

15. How to find the distance between two points in 3d plane?
An = a1rn?¹
V = (1/3)bh
N-1
Square the differences between each coordinate - then square root the sum

16. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
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-1
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

17. 45-45-90 triangle
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
C² = a² + b² - 2abcos(C)
Parentheses - exponents - multiplication - division - addition - subtraction
Hypotenuse is xv2 - and the sides are x.

18. Formula for arithmetic sequence
Final amount = original amount x (1+growth rate)^number of changes
An = a1 + (n-1)d
SA = 4pr²
a1 / 1-r

19. Standard form for a hyperbola that opens to the sides
a1 / 1-r
C² = a² + b² - 2abcos(C)
(x-h)²/a² - (y-k)²/b² = 1
Adding or subtracting 180 to ? and reversing the sign of r.

20. Sum of 2 Angles Formulas
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
(x-h)²/a² - (y-k)²/b² = 1
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
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)]

21. Surface area of a sphere
(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 = 4pr²
(n/2)(a1 + an)
N!

22. Sum of infinite geometric series
N-1
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Hypotenuse is 2x - short side is x - long side is xv3
a1 / 1-r

23. In an ellipse - where are the foci?
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)]
Square the differences between each coordinate - then square root the sum
Parentheses - exponents - multiplication - division - addition - subtraction
Between the vertex and the minor axis on the major axis

24. What are relatively prime numbers?
V = (4/3)pr³
Parentheses - exponents - multiplication - division - addition - subtraction
The greatest common factor is 1 - but the numbers are not necessarily prime.
V = (1/3)bh

25. How can you determine the arc degree or central angle of an inscribed angle?
Two sides and two angle are equal
V = (4/3)pr³
Multiply the inscribed angle by 2
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

26. Formula for the diagonal length of a rectangular prism
D = v(l²+w²+h²)
N-1
NPr = n! / (n-r)!
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

27. Law of Cosines
Square the differences between each coordinate - then square root the sum
C² = a² + b² - 2abcos(C)
V = (1/3)bh
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

28. 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)]
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)]
Square the differences between each coordinate - then square root the sum
F(x) = -f(-x)

29. Standard form for a hyperbola that opens vertically
(y-k)²/a² - (x-h)²/b² = 1
An = a1rn?¹
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
All whole numbers except for 0

30. Combination formula
F(x) = -f(-x)
N-1
A = ((s1 + s2)h) / 2
NCr = nPr / r! = n! / (n-r)!r!

31. Formula for the area of a trapezoid
(y-k)²/a² - (x-h)²/b² = 1
A = ((s1 + s2)h) / 2
V= (1/3)(pr²h)
An = a1 + (n-1)d

32. Two vectors are perpendicular if
N-1
x = -b/2a y= c - (b²/4a)
Their dot product = 0
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

33. Surface area of a cone
N-1
V = (1/3)bh
D = v(l²+w²+h²)
SA = pr² +prl

34. Formula for the area of a sector
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.
x = -b/2a y= c - (b²/4a)
Multiply the inscribed angle by 2

35. Formula for the volume of a cone
V= (1/3)(pr²h)
C² = a² + b² - 2abcos(C)
(n/2)(a1 + an)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

36. What is the order of operations?
Hypotenuse is 2x - short side is x - long side is xv3
Parentheses - exponents - multiplication - division - addition - subtraction
(y-k)²/a² - (x-h)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)]

37. Standard form equation for circle
(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
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
NCr = nPr / r! = n! / (n-r)!r!

38. Formula for calculation exponential growth
V = (1/3)bh
Final amount = original amount x (1+growth rate)^number of changes
F(x) = -f(-x)
Arc length equals = (degree of the arc / 360)(circumference)

39. What are the conversion equations for polar coordinates to normal coordinates?
x=rcos?(theta) y=rsin? (theta)
SA = 4pr²
Adding or subtracting 180 to ? and reversing the sign of r.
y-y1 = m(x-x1)

40. Scalene triangle
Adding or subtracting 180 to ? and reversing the sign of r.
No equal sides and no equal angles
a1 / 1-r
Final amount = original amount x (1+growth rate)^number of changes

41. How many ways can n elements be ordered?
Arc length equals = (degree of the arc / 360)(circumference)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
N!
Square the differences between each coordinate - then square root the sum

42. What is the form of a polar coordinate?
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
An = a1 + (n-1)d
NCr = nPr / r! = n! / (n-r)!r!
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

43. Volume of a sphere
V = (4/3)pr³
Their dot product = 0
NCr = nPr / r! = n! / (n-r)!r!
90°

44. How can multiple polar coordinates be made?
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.
Two sides and two angle are equal
D= sv3

45. Double Angle Formulas
D= sv3
SA = pr² +prl
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Arc length equals = (degree of the arc / 360)(circumference)

46. Define an even function.
F(x) = f(-x)
Adding or subtracting 180 to ? and reversing the sign of r.
Parentheses - exponents - multiplication - division - addition - subtraction
x=rcos?(theta) y=rsin? (theta)

47. Formula for arc length
Arc length equals = (degree of the arc / 360)(circumference)
Hypotenuse is 2x - short side is x - long side is xv3
An = a1 + (n-1)d
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)]

48. What are natural numbers?
A = (degree of the arc / 360)(area of a circle)
Hypotenuse is xv2 - and the sides are x.
F(x) = f(-x)
All whole numbers except for 0

49. Define an odd function.
An = a1rn?¹
All whole numbers except for 0
y = a(x-h)² + k - where the vertex is (h -k)
F(x) = -f(-x)

50. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
NPr = n! / (n-r)!
y-y1 = m(x-x1)
Between the vertex and the minor axis on the major axis