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. What is the triangle inequality rule?
Hypotenuse is xv2 - and the sides are 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.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Multiply the inscribed angle by 2

2. 45-45-90 triangle
N-1
(n/2)(a1 + an)
A = (degree of the arc / 360)(area of a circle)
Hypotenuse is xv2 - and the sides are x.

3. What are relatively prime numbers?
An = a1 + (n-1)d
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
V = (4/3)pr³
The greatest common factor is 1 - but the numbers are not necessarily prime.

4. 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
Their dot product = 0
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

5. Pythagorean Identities
(1-r/1-r)
y-y1 = m(x-x1)
N-1
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

6. Complimentary angles add up to
(n/2)(a1 + an)
A = (degree of the arc / 360)(area of a circle)
90°
Adding or subtracting 180 to ? and reversing the sign of r.

7. What is the sum of the interior angles for a polygon with n sides?
SA = pr² +prl
Arc length equals = (degree of the arc / 360)(circumference)
An = a1rn?¹
(n-2)180

8. Surface area of a cone
A = ((s1 + s2)h) / 2
V = (4/3)pr³
SA = pr² +prl
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

9. Permutation formula (ordering)
a1 / 1-r
NPr = n! / (n-r)!
Square the differences between each coordinate - then square root the sum
V = (4/3)pr³

10. Standard form of the equation of a parabola.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
C² = a² + b² - 2abcos(C)
The greatest common factor is 1 - but the numbers are not necessarily prime.
y = a(x-h)² + k - where the vertex is (h -k)

11. What is the order of operations?
180°
Parentheses - exponents - multiplication - division - addition - subtraction
D= sv3
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

12. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
(1-r/1-r)
x = -b/2a y= c - (b²/4a)
An = a1rn?¹
V= (1/3)(pr²h)

13. How can you determine the arc degree or central angle of an inscribed angle?
Between the vertex and the minor axis on the major axis
An = a1rn?¹
Multiply the inscribed angle by 2
Square the differences between each coordinate - then square root the sum

14. Combination formula
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
A = (degree of the arc / 360)(area of a circle)
NCr = nPr / r! = n! / (n-r)!r!
Square the differences between each coordinate - then square root the sum

15. Sum of 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)]
(x-h)²/a² - (y-k)²/b² = 1
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Between the vertex and the minor axis on the major axis

16. How can multiple polar coordinates be made?
No equal sides and no equal angles
Adding or subtracting 180 to ? and reversing the sign of r.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
C² = a² + b² - 2abcos(C)

17. Sum of n terms of an arithmetic sequence
An = a1 + (n-1)d
(n/2)(a1 + an)
Multiply the inscribed angle by 2
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

18. Two vectors are perpendicular if
Their dot product = 0
(x-h)²/a² - (y-k)²/b² = 1
F(x) = f(-x)
Final amount = original amount x (1+growth rate)^number of changes

19. Formula for the diagonal length of a rectangular prism
(1-r/1-r)
D = v(l²+w²+h²)
NPr = n! / (n-r)!
Adding or subtracting 180 to ? and reversing the sign of r.

20. 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
N-1
An = a1rn?¹
V = (1/3)bh

21. How to find the distance between two points in 3d plane?
N-1
Parentheses - exponents - multiplication - division - addition - subtraction
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Square the differences between each coordinate - then square root the sum

22. 30-60-90 triangle
F(x) = f(-x)
NPr = n! / (n-r)!
A = ((s1 + s2)h) / 2
Hypotenuse is 2x - short side is x - long side is xv3

23. Standard form equation for circle
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
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-k)²/a² - (x-h)²/b² = 1
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

24. Formula for the area of a trapezoid
D = v(l²+w²+h²)
A = ((s1 + s2)h) / 2
All whole numbers except for 0
N-1

25. Define an odd function.
Parentheses - exponents - multiplication - division - addition - subtraction
Multiply the inscribed angle by 2
An = a1 + (n-1)d
F(x) = -f(-x)

26. Formula for calculation exponential growth
90°
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
V= (1/3)(pr²h)

27. Supplementary angles add up to
(n/2)(a1 + an)
180°
x=rcos?(theta) y=rsin? (theta)
N!

28. Where is tangent positive/negative?
Hypotenuse is 2x - short side is x - long side is xv3
Final amount = original amount x (1+growth rate)^number of changes
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

29. How many ways can n elements be ordered?
N!
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
A = ((s1 + s2)h) / 2
F(x) = f(-x)

30. 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)
a1 / 1-r
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
180°

31. How to determine if a number is prime
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Parentheses - exponents - multiplication - division - addition - subtraction
Their dot product = 0
NCr = nPr / r! = n! / (n-r)!r!

32. What are natural numbers?
y-y1 = m(x-x1)
(n-2)180
All whole numbers except for 0
(x-h)²/a² - (y-k)²/b² = 1

33. Sum of finite geometric series
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)]
(1-r/1-r)
Hypotenuse is 2x - short side is x - long side is xv3

34. Sum of infinite geometric series
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)]
90°
y-y1 = m(x-x1)
a1 / 1-r

35. Formula for the area of a sector
A = (degree of the arc / 360)(area of a circle)
(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
SA = 4pr²

36. Formula for the volume of a cone
A = ((s1 + s2)h) / 2
(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)]
V= (1/3)(pr²h)

37. Formula for arc length
Final amount = original amount x (1+growth rate)^number of changes
(1-r/1-r)
Hypotenuse is 2x - short side is x - long side is xv3
Arc length equals = (degree of the arc / 360)(circumference)

38. Volume of a sphere
The greatest common factor is 1 - but the numbers are not necessarily prime.
V = (4/3)pr³
Hypotenuse is 2x - short side is x - long side is xv3
90°

39. Law of Cosines
90°
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
C² = a² + b² - 2abcos(C)
D= sv3

40. Difference between 2 Angles formulas
An = a1rn?¹
Between the vertex and the minor axis on the major axis
90°
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)]

41. Define an even function.
y-y1 = m(x-x1)
F(x) = f(-x)
(n-2)180
N-1

42. Standard form for a hyperbola that opens to the sides
y = a(x-h)² + k - where the vertex is (h -k)
(x-h)²/a² - (y-k)²/b² = 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.

43. Formula for the diagonal length of a cube
y-y1 = m(x-x1)
Their dot product = 0
C² = a² + b² - 2abcos(C)
D= sv3

44. Formula for arithmetic sequence
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
V = (1/3)bh
An = a1 + (n-1)d
NPr = n! / (n-r)!

45. Scalene triangle
Square the differences between each coordinate - then square root the sum
y = a(x-h)² + k - where the vertex is (h -k)
No equal sides and no equal angles
A = (degree of the arc / 360)(area of a circle)

46. Volume of a pyramid
(n-2)180
No equal sides and no equal angles
V = (1/3)bh
An = a1rn?¹

47. Standard form equation for an ellipse
Their dot product = 0
(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
Multiply the inscribed angle by 2

48. In an ellipse - where are the foci?
Between the vertex and the minor axis on 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.
x = -b/2a y= c - (b²/4a)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

49. 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
Square the differences between each coordinate - then square root the sum
No equal sides and no equal angles
(1-r/1-r)

50. What are the conversion equations for polar coordinates to normal coordinates?
y = a(x-h)² + k - where the vertex is (h -k)
a1 / 1-r
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
x=rcos?(theta) y=rsin? (theta)