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GRE Math: Facts

Subjects : gre, 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. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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°.
Shifted right 2 units.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

2. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Their sum is 90°.
1 is the smallest positive odd integer.
1 is a divisor (or factor) of every integer.
360°

3. How do we write the equation of a line?
Their sum is 180°.
The product of their slopes is -1 (negative reciprocal).
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Then the product xy is a constant.

4. What is a function?
The sum of the length of any two sides of the triangle is greater than the length of the third side i.e. x + y > z - x + z > y - & y + z > x.
Cannot is 0 - must is 1 - all others are in between.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

5. What is the formula for the volume of a cylinder?
V = pr^2h
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
If a is negative and b is positive - then a < 0 < b.

6. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Write the percent as a decimal - and multiply.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

7. What is a fractional exponent?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Even numbers are divisible by 2 and odd numbers are not.
A = 6(l^2)
Write the percent over 100 and reduce.

8. For what values of a function is the function undefined?
A multiple of an integer - n - is any integer that is a product of n and another integer i.e. 12 is a multiple of 3 and 3 is a divisor of 12.
At least one of the factors is 0.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

9. What is the formula for the area of a triangle?
For any right triangle - a^2 + b^2 = c^2.
A = (1/2)bh.
Is a right triangle with a ratio of sides x:xv3:2x.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

10. Properties of one 3
1 is a divisor (or factor) of every integer.
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.
Divide - then multiply by 100.
Then the quotient y/x is a constant.

11. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
An integer greater than one that is not prime.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Their sum is 90°.

12. Properties of square roots
The product of their slopes is -1 (negative reciprocal).
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = bh

13. Law of exponents 3
Then the quotient y/x is a constant.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(b^m)^n = b^mn
A = bh

14. Properties of zero 5
Shifted left 2 units.
A^m*b^m = (ab)^m
For any number b: b = -b if and only if b = 0.
A fraction whose denominator is 100 i.e. 17% = 17/100

15. Properties of zero 2
A fraction whose denominator is 100 i.e. 17% = 17/100
(n - 2)(180°)
If a is negative and b is positive - then a < 0 < b.
1 is the smallest positive odd integer.

16. Properties of zero 4
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.
Divide - then multiply by 100.
Area = (x°/360)(pr^2) where x is the central angle.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

17. Law of exponents 2
B^m/b^n = b^m-n
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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.
B^m*b^n = b^m+n

18. What is true about the measures of the two acute angles in a right triangle?
Set y = 0 - and solve.
Their sum is 90°.
A^m*b^m = (ab)^m
Write the percent as a decimal - and multiply.

19. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
V = l^3
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

20. What does it mean if y is directly proportional to x?
A^m/b^m = (a/b)^m
Then the quotient y/x is a constant.
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°.
(Circumference/diameter) of a circle - or approximately 3.14.

21. What formula is used for an average?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A multiple of an integer - n - is any integer that is a product of n and another integer i.e. 12 is a multiple of 3 and 3 is a divisor of 12.
Avg = sum of n numbers/n
1 is a divisor (or factor) of every integer.

22. What is true about the measures of the three angles in a triangle?
All positive and negative whole numbers - and zero.
Avg = sum of n numbers/n
The sum of the length of any two sides of the triangle is greater than the length of the third side i.e. x + y > z - x + z > y - & y + z > x.
Their sum is 180°.

23. What is the formula for the area of a parallelogram?
Avg = sum of n numbers/n
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A fraction whose denominator is 100 i.e. 17% = 17/100
A = bh

24. What are the important properties of 30-60-90 triangle?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The two pairs of opposite angles formed are equal to each other.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Is a right triangle with a ratio of sides x:xv3:2x.

25. Law of exponents 4
A^m*b^m = (ab)^m
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Then the quotient y/x is a constant.
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.

26. What is a percent?
A = pr^2
D = 2r
A fraction whose denominator is 100 i.e. 17% = 17/100
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.

27. What is the square root of a number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A fraction whose denominator is 100 i.e. 17% = 17/100
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

28. What is a Venn diagram?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = bh
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

29. What are similar triangles?
0 is a multiple of every integer.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Even numbers are divisible by 2 and odd numbers are not.

30. What is the graph of a function?
A^m/b^m = (a/b)^m
The set of all ordered pairs (x -y) such that y = f(x).
Divide - then multiply by 100.
The median is the middle number (for odd total) or average of two middle numbers (for even total). The mode is the number that appears most often.

31. How do you find a percent of a number?
0 is a multiple of every integer.
Shifted left 2 units.
Shifted right 2 units.
Write the percent as a decimal - and multiply.

32. How do you find the length of an arc of a circle?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Arc = (x°/360)(2pr) where x is the central angle.
A multiple of an integer - n - is any integer that is a product of n and another integer i.e. 12 is a multiple of 3 and 3 is a divisor of 12.
A^m*b^m = (ab)^m

33. What is the formula for the volume of a rectangular solid?
For any right triangle - a^2 + b^2 = c^2.
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°.
M = (y2 - y1)/(x2 - x1)
V = lwh

34. Law of exponents 1
Shifted down 2 units.
A = 2(lw + lh + hw)
B^m*b^n = b^m+n
(n - 2)(180°)

35. Properties of one 4
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
In the expression x^b - x is the base and b is the exponent.
1 is the smallest positive odd integer.
A^m/b^m = (a/b)^m

36. What are the important properties of a 45-45 - 90 triangle?
Set x = 0 - and solve.
The ratio of corresponding sides of similar triangles.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
(n - 2)(180°)

37. What is an integer?
Write the percent as a decimal - and multiply.
All positive and negative whole numbers - and zero.
M = (y2 - y1)/(x2 - x1)
D = 2r

38. Properties of zero 1
At least one of the factors is 0.
B^m*b^n = b^m+n
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
0 is the only number that is neither positive nor negative.

39. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
[(x1 + x2)/2] -[(y1 + y2)/2]
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

40. What is a composite number?
0 is a multiple of every integer.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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°.
An integer greater than one that is not prime.

41. What is the triangle inequality?
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°.
The sum of the length of any two sides of the triangle is greater than the length of the third side i.e. x + y > z - x + z > y - & y + z > x.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any number a: a * 1 = a and a / 1 = a.

42. Properties of one 1
M = (y2 - y1)/(x2 - x1)
1 is the smallest positive odd integer.
A = 6(l^2)
For any number a: a * 1 = a and a / 1 = a.

43. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Is a right triangle with a ratio of sides x:xv3:2x.
Shifted up 2 units.
Then the product xy is a constant.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

44. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
M = (y2 - y1)/(x2 - x1)
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
C = p2r

45. What is an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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.
B^m/b^n = b^m-n

46. In a circle of radius r - what is the formula for the diameter?
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.
D = 2r
V = pr^2h
360°

47. Properties of one 2
No matter how many angles there are - the sum around the point is 360°.
A = (1/2)bh.
For any integer n: 1^n = 1.
0 is a multiple of every integer.

48. Important binomial 1
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(x + y)(x - y) = x^2 - y^2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Cannot is 0 - must is 1 - all others are in between.

49. If you were given the graph of y = f(x) - what does f(a) represent?
The product of their slopes is -1 (negative reciprocal).
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
An integer greater than one that is not prime.
In the expression x^b - x is the base and b is the exponent.

50. What is true about the areas of similar triangles?
The sum of the length of any two sides of the triangle is greater than the length of the third side i.e. x + y > z - x + z > y - & y + z > x.
An integer greater than one that is not prime.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For any integer n: 1^n = 1.