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Test your basic knowledge |
SAT Math 2
Start Test
Study First
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. Surface area of a cone
SA = pr² +prl
90°
D = v(l²+w²+h²)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
2. What is the form of a polar coordinate?
Parentheses - exponents - multiplication - division - addition - subtraction
N!
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(1-r/1-r)
3. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
V= (1/3)(pr²h)
y-y1 = m(x-x1)
Multiply the inscribed angle by 2
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
4. Volume of a pyramid
V= (1/3)(pr²h)
V = (4/3)pr³
V = (1/3)bh
F(x) = f(-x)
5. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
x = -b/2a y= c - (b²/4a)
V = (4/3)pr³
N!
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
6. Sum of finite geometric series
Multiply the inscribed angle by 2
Hypotenuse is xv2 - and the sides are x.
NCr = nPr / r! = n! / (n-r)!r!
(1-r/1-r)
7. Standard form for a hyperbola that opens vertically
y = a(x-h)² + k - where the vertex is (h -k)
N-1
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
(y-k)²/a² - (x-h)²/b² = 1
8. Two vectors are perpendicular if
(n-2)180
Parentheses - exponents - multiplication - division - addition - subtraction
The greatest common factor is 1 - but the numbers are not necessarily prime.
Their dot product = 0
9. Isosceles Triangles
SA = pr² +prl
Square the differences between each coordinate - then square root the sum
Two sides and two angle are equal
(x-h)²/a² - (y-k)²/b² = 1
10. In an ellipse - where are the foci?
A = ((s1 + s2)h) / 2
Parentheses - exponents - multiplication - division - addition - subtraction
Between the vertex and the minor axis on the major axis
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
11. What is the triangle inequality rule?
y-y1 = m(x-x1)
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)
Final amount = original amount x (1+growth rate)^number of changes
12. What is the sum of the interior angles for a polygon with n sides?
x=rcos?(theta) y=rsin? (theta)
N-1
SA = 4pr²
(n-2)180
13. Combination formula
SA = pr² +prl
NCr = nPr / r! = n! / (n-r)!r!
SA = 4pr²
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
14. Define an odd function.
F(x) = -f(-x)
N!
The greatest common factor is 1 - but the numbers are not necessarily prime.
x=rcos?(theta) y=rsin? (theta)
15. How can multiple polar coordinates be made?
(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)
N-1
Adding or subtracting 180 to ? and reversing the sign of r.
16. How to find the distance between two points in 3d plane?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Square the differences between each coordinate - then square root the sum
F(x) = f(-x)
NPr = n! / (n-r)!
17. What are the conversion equations for polar coordinates to normal coordinates?
y = a(x-h)² + k - where the vertex is (h -k)
(x-h)²/a² - (y-k)²/b² = 1
x=rcos?(theta) y=rsin? (theta)
x = -b/2a y= c - (b²/4a)
18. Formula for arc length
a1 / 1-r
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Adding or subtracting 180 to ? and reversing the sign of r.
Arc length equals = (degree of the arc / 360)(circumference)
19. Formula for the diagonal length of a rectangular prism
(x-h)²/a² - (y-k)²/b² = 1
a1 / 1-r
V= (1/3)(pr²h)
D = v(l²+w²+h²)
20. Law of Cosines
(1-r/1-r)
Square the differences between each coordinate - then square root the sum
Between the vertex and the minor axis on the major axis
C² = a² + b² - 2abcos(C)
21. Sum of n terms of an arithmetic sequence
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
N!
(n/2)(a1 + an)
22. Scalene triangle
No equal sides and no equal angles
Adding or subtracting 180 to ? and reversing the sign of r.
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
90°
23. Sum of infinite geometric series
a1 / 1-r
x=rcos?(theta) y=rsin? (theta)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
D= sv3
24. Volume of a sphere
y-y1 = m(x-x1)
V = (4/3)pr³
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Their dot product = 0
25. Define an even function.
F(x) = f(-x)
V= (1/3)(pr²h)
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)]
Parentheses - exponents - multiplication - division - addition - subtraction
26. What are relatively prime numbers?
(1-r/1-r)
The greatest common factor is 1 - but the numbers are not necessarily prime.
N-1
Two sides and two angle are equal
27. Standard form for a hyperbola that opens to the sides
Square the differences between each coordinate - then square root the sum
Adding or subtracting 180 to ? and reversing the sign of r.
(x-h)²/a² - (y-k)²/b² = 1
N!
28. Formula for the area of a trapezoid
An = a1rn?¹
Final amount = original amount x (1+growth rate)^number of changes
A = ((s1 + s2)h) / 2
N-1
29. 45-45-90 triangle
V = (4/3)pr³
C² = a² + b² - 2abcos(C)
Multiply the inscribed angle by 2
Hypotenuse is xv2 - and the sides are x.
30. What is the order of operations?
Arc length equals = (degree of the arc / 360)(circumference)
(n-2)180
C² = a² + b² - 2abcos(C)
Parentheses - exponents - multiplication - division - addition - subtraction
31. Double Angle Formulas
An = a1rn?¹
V = (1/3)bh
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Between the vertex and the minor axis on the major axis
32. How to determine if a number is prime
(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.
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
x = -b/2a y= c - (b²/4a)
33. Formula for the volume of a cone
V= (1/3)(pr²h)
(n-2)180
Multiply the inscribed angle by 2
F(x) = -f(-x)
34. Formula for calculation exponential growth
a1 / 1-r
Final amount = original amount x (1+growth rate)^number of changes
(n-2)180
x = -b/2a y= c - (b²/4a)
35. Standard form of the equation of a parabola.
(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.
No equal sides and no equal angles
y = a(x-h)² + k - where the vertex is (h -k)
a1 / 1-r
36. Formula for the area of a sector
A = (degree of the arc / 360)(area of a circle)
(1-r/1-r)
x=rcos?(theta) y=rsin? (theta)
NPr = n! / (n-r)!
37. 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)]
V = (4/3)pr³
Between the vertex and the minor axis on the major axis
38. Sum of 2 Angles Formulas
V = (1/3)bh
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)]
39. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
NCr = nPr / r! = n! / (n-r)!r!
y-y1 = m(x-x1)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
40. Standard form equation for circle
C² = a² + b² - 2abcos(C)
(x-h)²/a² - (y-k)²/b² = 1
NCr = nPr / r! = n! / (n-r)!r!
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
41. Formula for the diagonal length of a cube
Between the vertex and the minor axis on the major axis
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
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)]
42. Where is tangent positive/negative?
Adding or subtracting 180 to ? and reversing the sign of r.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
N-1
x=rcos?(theta) y=rsin? (theta)
43. Pythagorean Identities
(y-k)²/a² - (x-h)²/b² = 1
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
SA = 4pr²
A = ((s1 + s2)h) / 2
44. Supplementary angles add up to
F(x) = -f(-x)
D = v(l²+w²+h²)
180°
A = (degree of the arc / 360)(area of a circle)
45. Formula for geometric sequence
V= (1/3)(pr²h)
An = a1rn?¹
F(x) = -f(-x)
No equal sides and no equal angles
46. Permutation formula (ordering)
(1-r/1-r)
F(x) = -f(-x)
No equal sides and no equal angles
NPr = n! / (n-r)!
47. 30-60-90 triangle
Hypotenuse is 2x - short side is x - long side is xv3
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)
y = a(x-h)² + k - where the vertex is (h -k)
48. Standard form equation for an ellipse
C² = a² + b² - 2abcos(C)
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.
49. What are natural numbers?
V= (1/3)(pr²h)
All whole numbers except for 0
Hypotenuse is 2x - short side is x - long side is xv3
(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.
50. Surface area of a sphere
180°
SA = pr² +prl
Square the differences between each coordinate - then square root the sum
SA = 4pr²