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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. What is a divisor and a factor of an integer?
At least one of the factors is 0.
Write the percent as a decimal - and multiply.
V = pr^2h
They are both the same. A divisor or factor of an integer leaves no remainder.

2. Properties of zero 4
Write the percent over 100 and reduce.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Is a right triangle with a ratio of sides x:xv3:2x.

3. What does it mean if y is inversely proportional to x?
360°
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(Circumference/diameter) of a circle - or approximately 3.14.
Then the product xy is a constant.

4. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
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.
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.
Shifted left 2 units.
360°

5. What is the volume of a cube?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
V = l^3
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
(n - 2)(180°)

6. Properties of zero 5
For any number b: b = -b if and only if b = 0.
Avg = sum of n numbers/n
Then the quotient y/x is a constant.
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.

7. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
Set x = 0 - and solve.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

8. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = [(s^2*v3)/4]
For any number b: b = -b if and only if b = 0.
The set of all ordered pairs (x -y) such that y = f(x).

9. What is a composite number?
An integer greater than one that is not prime.
A = pr^2
At least one of the factors is 0.
360°

10. How do you find a percent of a number?
An integer greater than one that is not prime.
(n - 2)(180°)
Write the percent as a decimal - and multiply.
D = 2r

11. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
Set x = 0 - and solve.
They are both the same. A divisor or factor of an integer leaves no remainder.
For any number n: x^-n means 1/x^n.

12. What is the measure of a straight angle?
Shifted right 2 units.
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.
180°. If two or more angles form a straight angle - their sum is 180°.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

13. What is the probability of an event that cannot occur? That must occur?
A = bh
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
V = l^3
Cannot is 0 - must is 1 - all others are in between.

14. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
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.
A^m/b^m = (a/b)^m
Write the percent over 100 and reduce.

15. What is the formula for the area of a parallelogram?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = bh
(n - 2)(180°)
C = p2r

16. What is an exterior angle of a polygon?
1 is the smallest positive odd integer.
Set x = 0 - and solve.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
An angle formed by extending the side of the polygon.

17. What is an even and an odd number?
A = bh
Even numbers are divisible by 2 and odd numbers are not.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

18. What is the formula for the surface area of a cube?
V = l^3
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = 6(l^2)

19. What is true about the slopes of perpendicular lines?
In the expression x^b - x is the base and b is the exponent.
The product of their slopes is -1 (negative reciprocal).
Is a right triangle with a ratio of sides x:xv3:2x.
D = 2r

20. How do you find the length of an arc of a circle?
180°. If two or more angles form a straight angle - their sum is 180°.
Avg = sum of n numbers/n
A fraction whose denominator is 100 i.e. 17% = 17/100
Arc = (x°/360)(2pr) where x is the central angle.

21. What is the relationship between a radius of a circle and a line that is tangent to the circle?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
B^m*b^n = b^m+n
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

22. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
How steep the line is. Horizontal line = 0 - vertical has no slope.
0 is a multiple of every integer.
(x + y)(x - y) = x^2 - y^2
Shifted right 2 units.

23. Properties of one 2
1 is the smallest positive odd integer.
For any integer n: 1^n = 1.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
At least one of the factors is 0.

24. What is a prime number?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The ratio of corresponding sides of similar triangles.
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.
A^m*b^m = (ab)^m

25. What formula is used for an average?
Divide - then multiply by 100.
Avg = sum of n numbers/n
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(x + y)(x - y) = x^2 - y^2

26. Properties of one 3
A^m*b^m = (ab)^m
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
1 is a divisor (or factor) of every integer.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

27. What are the important properties of 30-60-90 triangle?
Their sum is 180°.
Then the product xy is a constant.
Corresponding sides of similar triangles are in proportion.
Is a right triangle with a ratio of sides x:xv3:2x.

28. Properties of one 1
How steep the line is. Horizontal line = 0 - vertical has no slope.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For any number a: a * 1 = a and a / 1 = a.
(b^m)^n = b^mn

29. What is the distance formula?
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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = bh
Set x = 0 - and solve.

30. How do you convert a percent to a fraction or a decimal?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Write the percent over 100 and reduce.
V = l^3
A = 6(l^2)

31. If the product of two or more numbers is 0 - what do you know about the numbers?
Then the quotient y/x is a constant.
At least one of the factors is 0.
The ratio of corresponding sides of similar triangles.
Shifted down 2 units.

32. What does it mean if y is directly proportional to x?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Divide - then multiply by 100.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Then the quotient y/x is a constant.

33. What is the graph of a function?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
The set of all ordered pairs (x -y) such that y = f(x).
(x + y)(x - y) = x^2 - y^2
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.

34. Law of exponents 1
B^m*b^n = b^m+n
Even numbers are divisible by 2 and odd numbers are not.
Divide - then multiply by 100.
180°. If two or more angles form a straight angle - their sum is 180°.

35. What are the important properties of a 45-45 - 90 triangle?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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.
A = lw
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

36. What are the sum - difference - products - and quotient of two numbers?
Corresponding sides of similar triangles are in proportion.
The product of their slopes is -1 (negative reciprocal).
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Set y = 0 - and solve.

37. Law of exponents 2
180°. If two or more angles form a straight angle - their sum is 180°.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
B^m/b^n = b^m-n
D = 2r

38. What is the triangle inequality?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
D = 2r
Then the product xy is a constant.
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.

39. How do you find the probability that an event will occur?
1 is a divisor (or factor) of every integer.
(b^m)^n = b^mn
V = l^3
P(e) = (# of favorable outcomes)/(# of possible outcomes)

40. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
360°
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.
180°. If two or more angles form a straight angle - their sum is 180°.

41. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any integer n: 1^n = 1.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
B^m/b^n = b^m-n

42. What is a ratio?

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43. In a circle of radius r - what is the formula for the area?
C = p2r
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = pr^2
D = 2r

44. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
For any number n: x^-n means 1/x^n.
V = pr^2h
Their sum is 180°.

45. What is the sum of the measures of all angles around a point?
Shifted up 2 units.
0 is a multiple of every integer.
No matter how many angles there are - the sum around the point is 360°.
An angle formed by extending the side of the polygon.

46. How do you find the x-intercept of a graph?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Set y = 0 - and solve.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

47. How do you find the y-intercept of a graph?
Corresponding sides of similar triangles are in proportion.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.
Set x = 0 - and solve.

48. Important binomial 2
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
0 is the only number that is neither positive nor negative.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

49. What is special formula for the area of an equilateral triangle?
(n - 2)(180°)
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°.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A = [(s^2*v3)/4]

50. If you were given the graph of y = f(x) - what does f(a) represent?
B^m/b^n = b^m-n
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
An equation that states that two ratios are equivalent. 4/6 = 10/15
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.