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GRE Math: Facts

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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 relationship between a radius of a circle and a line that is tangent to the circle?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Shifted right 2 units.
No matter how many angles there are - the sum around the point is 360°.

2. Properties of one 4
For any number n: x^-n means 1/x^n.
If a is negative and b is positive - then a < 0 < b.
M = (y2 - y1)/(x2 - x1)
1 is the smallest positive odd integer.

3. What are the important properties of a 45-45 - 90 triangle?
0 is a multiple of every integer.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
The longest side is opposite the largest angle - the shortest side is opposite the smallest angle - and same length sides are opposite same measure angles.

4. How do you convert a percent to a fraction or a decimal?
The two pairs of opposite angles formed are equal to each other.
Write the percent over 100 and reduce.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

5. What is the formula for the surface area of a rectangular solid?
Same as a parallelogram and a rectangle - as well as all four sides are the same length - the diagonals are perpendicular - and each diagonal divides the square into a 45-45-90 isosceles right triangle.
If the line is not perpendicular - all four acute angles have the same measure - all four obtuse have the same measure - and the sum of any one acute and one obtuse angle is 180°.
V = pr^2h
A = 2(lw + lh + hw)

6. Law of exponents 2
B^m/b^n = b^m-n
For any integer n: 1^n = 1.
A^m*b^m = (ab)^m
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

7. What is a prime number?
An integer divisible by only one and itself. 1 is not - 2 is the only even - and 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and 29 are the 10 smallest.
An equation that states that two ratios are equivalent. 4/6 = 10/15
(n - 2)(180°)
Shifted right 2 units.

8. What is the formula for the volume of a cylinder?
V = pr^2h
Cannot is 0 - must is 1 - all others are in between.
If a is negative and b is positive - then a < 0 < b.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

9. What are the properties of a square?
Same as a parallelogram and a rectangle - as well as all four sides are the same length - the diagonals are perpendicular - and each diagonal divides the square into a 45-45-90 isosceles right triangle.
Area = (x°/360)(pr^2) where x is the central angle.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

10. What is the sum of the measures of the n angles of a polygon with n sides?
Shifted down 2 units.
Equal slopes.
(n - 2)(180°)
For any number n: x^-n means 1/x^n.

11. How do you find the area of a sector of a circle?
(Circumference/diameter) of a circle - or approximately 3.14.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Area = (x°/360)(pr^2) where x is the central angle.
At least one of the factors is 0.

12. What is the ratio of similitude?
Write the percent as a decimal - and multiply.
(n - 2)(180°)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The ratio of corresponding sides of similar triangles.

13. Properties of one 3
360°
1 is a divisor (or factor) of every integer.
0 is the only number that is neither positive nor negative.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

14. What are the quotient and the remainder?

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15. What is the volume of a cube?
360°
V = l^3
Write the percent over 100 and reduce.
Then the product xy is a constant.

16. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Shifted right 2 units.
A = lw

17. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
0 is the only number that is neither positive nor negative.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

18. Properties of zero 5
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
M = (y2 - y1)/(x2 - x1)
V = lwh
For any number b: b = -b if and only if b = 0.

19. What is true about the slopes of perpendicular lines?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
An integer divisible by only one and itself. 1 is not - 2 is the only even - and 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and 29 are the 10 smallest.
The product of their slopes is -1 (negative reciprocal).
Even numbers are divisible by 2 and odd numbers are not.

20. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
For any number a: a * 1 = a and a / 1 = a.
Their sum is 90°.
Divide - then multiply by 100.
Shifted up 2 units.

21. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
No matter how many angles there are - the sum around the point is 360°.
180°. If two or more angles form a straight angle - their sum is 180°.
An angle formed by extending the side of the polygon.
360°

22. If you were given the graph of y = f(x) - what does f(a) represent?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Then the quotient y/x is a constant.
V = pr^2h
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

23. In a circle of radius r - what is the formula for the area?
A = pr^2
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(x + y)(x - y) = x^2 - y^2
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

24. What is the measure of a straight angle?
The ratio of corresponding sides of similar triangles.
How steep the line is. Horizontal line = 0 - vertical has no slope.
(x + y)(x - y) = x^2 - y^2
180°. If two or more angles form a straight angle - their sum is 180°.

25. If the product of two or more numbers is 0 - what do you know about the numbers?
Corresponding sides of similar triangles are in proportion.
At least one of the factors is 0.
For any number b: b = -b if and only if b = 0.
How steep the line is. Horizontal line = 0 - vertical has no slope.

26. What is the distance formula?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
D = 2r
An integer greater than one that is not prime.

27. Properties of zero 3
Write the percent over 100 and reduce.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
0 is a multiple of every integer.
A = (1/2)bh.

28. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
360°
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

29. What is the graph of a function?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The set of all ordered pairs (x -y) such that y = f(x).
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

30. What are the properties of a rectangle?
Same as a parallelogram and a rectangle - as well as all four sides are the same length - the diagonals are perpendicular - and each diagonal divides the square into a 45-45-90 isosceles right triangle.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = 6(l^2)
B^m/b^n = b^m-n

31. What is an exponent?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
In the expression x^b - x is the base and b is the exponent.
If the line is not perpendicular - all four acute angles have the same measure - all four obtuse have the same measure - and the sum of any one acute and one obtuse angle is 180°.
Avg = sum of n numbers/n

32. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
Shifted right 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(b^m)^n = b^mn

33. What is the formula for the area of a triangle?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A = bh
A = pr^2
A = (1/2)bh.

34. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
No matter how many angles there are - the sum around the point is 360°.
(Circumference/diameter) of a circle - or approximately 3.14.

35. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Their sum is 180°.
At least one of the factors is 0.
Shifted right 2 units.
V = pr^2h

36. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Arc = (x°/360)(2pr) where x is the central angle.
For any integer n: 1^n = 1.
If the line is not perpendicular - all four acute angles have the same measure - all four obtuse have the same measure - and the sum of any one acute and one obtuse angle is 180°.

37. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
C = p2r
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The longest side is opposite the largest angle - the shortest side is opposite the smallest angle - and same length sides are opposite same measure angles.
For any number b: b = -b if and only if b = 0.

38. What is an exterior angle of a triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
[(x1 + x2)/2] -[(y1 + y2)/2]

39. How do you calculate a weighted average?
A = 6(l^2)
360°
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A^m/b^m = (a/b)^m

40. What are the properties of a parallelogram?
Shifted up 2 units.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
(b^m)^n = b^mn
For any number a: a * 1 = a and a / 1 = a.

41. Properties of zero 4
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For any integer n: 1^n = 1.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any number b: b = -b if and only if b = 0.

42. What is the midpoint formula?
Shifted down 2 units.
[(x1 + x2)/2] -[(y1 + y2)/2]
V = l^3
Set x = 0 - and solve.

43. What are the important properties of 30-60-90 triangle?
V = l^3
The product of their slopes is -1 (negative reciprocal).
Is a right triangle with a ratio of sides x:xv3:2x.
(x + y)(x - y) = x^2 - y^2

44. What is a ratio?

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45. What is true about the slopes of parallel lines?
A = s^2 or A =d^2/2 where d is the diagonal
V = lwh
Equal slopes.
For any number n: x^-n means 1/x^n.

46. What is true about the measures of the four angles formed by two intersecting lines?
V = pr^2h
In the expression x^b - x is the base and b is the exponent.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The two pairs of opposite angles formed are equal to each other.

47. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = bh
Corresponding sides of similar triangles are in proportion.
1 is a divisor (or factor) of every integer.

48. What are similar triangles?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The set of all ordered pairs (x -y) such that y = f(x).
Shifted down 2 units.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

49. What is an exterior angle of a polygon?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Shifted left 2 units.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
An angle formed by extending the side of the polygon.

50. Properties of zero 1
V = l^3
0 is the only number that is neither positive nor negative.
Corresponding sides of similar triangles are in proportion.
The two pairs of opposite angles formed are equal to each other.

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