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