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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 the formula for the volume of a rectangular solid?
In the expression x^b - x is the base and b is the exponent.
V = lwh
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = 2(lw + lh + hw)

2. 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.
(n - 2)(180°)
Equal slopes.
(b^m)^n = b^mn

3. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
360°
A = bh
A^m*b^m = (ab)^m

4. What are the quotient and the remainder?

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5. What are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
B^m/b^n = b^m-n
0 is the only number that is neither positive nor negative.
C = p2r

6. What are similar triangles?
Shifted left 2 units.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = lw
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

7. If you were given the graph of y = f(x) - what does f(a) represent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
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.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

8. What is the midpoint formula?
For any number n: x^-n means 1/x^n.
[(x1 + x2)/2] -[(y1 + y2)/2]
M = (y2 - y1)/(x2 - x1)
Then the quotient y/x is a constant.

9. In a circle of radius r - what is the formula for the diameter?
D = 2r
A^m*b^m = (ab)^m
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.
Shifted down 2 units.

10. What are the properties of a parallelogram?
Shifted left 2 units.
Shifted right 2 units.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

11. What is a divisor and a factor of an integer?
Write the percent over 100 and reduce.
They are both the same. A divisor or factor of an integer leaves no remainder.
For any integer n: 1^n = 1.
Then the quotient y/x is a constant.

12. What is the distributive law?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

13. What do we mean by the slope of the line?
A = 2(lw + lh + hw)
Arc = (x°/360)(2pr) where x is the central angle.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
How steep the line is. Horizontal line = 0 - vertical has no slope.

14. What is a proportion?
0 is a multiple of every integer.
The product of their slopes is -1 (negative reciprocal).
An equation that states that two ratios are equivalent. 4/6 = 10/15
D = 2r

15. What is the volume of a cube?
The ratio of corresponding sides of similar triangles.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
V = l^3
For any integer n: 1^n = 1.

16. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = (1/2)bh.
Area = (x°/360)(pr^2) 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.

17. Properties of zero 2
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
If a is negative and b is positive - then a < 0 < b.
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.

18. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Set y = 0 - and solve.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.

19. What is the triangle inequality?
An angle formed by extending the side of the polygon.
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 up 2 units.
A = lw

20. Properties of zero 3
360°
0 is a multiple of every integer.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Cannot is 0 - must is 1 - all others are in between.

21. What is an exterior angle of a polygon?
Set x = 0 - and solve.
V = pr^2h
An angle formed by extending the side of the polygon.
Even numbers are divisible by 2 and odd numbers are not.

22. 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.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Set x = 0 - and solve.
The ratio of corresponding sides of similar triangles.

23. What is a fractional exponent?
An integer greater than one that is not prime.
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.
The product of their slopes is -1 (negative reciprocal).
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

24. What is true about the measures of the four angles formed by two intersecting lines?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
The two pairs of opposite angles formed are equal to each other.
A = lw
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.

25. Properties of one 2
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.
D = 2r
0 is the only number that is neither positive nor negative.
For any integer n: 1^n = 1.

26. What is an even and an odd number?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Area = (x°/360)(pr^2) where x is the central angle.
Even numbers are divisible by 2 and odd numbers are not.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

27. What is the ratio of similitude?
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.
Then the quotient y/x is a constant.
The ratio of corresponding sides of similar triangles.
For any number a: a * 1 = a and a / 1 = a.

28. What is the measure of a straight angle?
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 = s^2 or A =d^2/2 where d is the diagonal
180°. If two or more angles form a straight angle - their sum is 180°.
Write the percent over 100 and reduce.

29. In a circle of radius r - what is the formula for the area?
Set x = 0 - and solve.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = pr^2

30. What is the formula for the area of a rectangle?
All positive and negative whole numbers - and zero.
A = lw
(b^m)^n = b^mn
A = pr^2

31. How do you find the probability that an event will occur?
The two pairs of opposite angles formed are equal to each other.
360°
Corresponding sides of similar triangles are in proportion.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

32. Law of exponents 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A = 6(l^2)
(b^m)^n = b^mn
For any number n: x^-n means 1/x^n.

33. What important property do similar triangles have?
A^m/b^m = (a/b)^m
Their sum is 180°.
V = lwh
Corresponding sides of similar triangles are in proportion.

34. Properties of one 3
1 is a divisor (or factor) of every integer.
An integer greater than one that is not prime.
A fraction whose denominator is 100 i.e. 17% = 17/100
A^m*b^m = (ab)^m

35. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
[(x1 + x2)/2] -[(y1 + y2)/2]
A^m/b^m = (a/b)^m
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.

36. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
V = lwh
Shifted up 2 units.
Shifted right 2 units.
At least one of the factors is 0.

37. In a circle of radius r - what is the formula for the circumference?
For any number b: b = -b if and only if b = 0.
For any number a: a * 1 = a and a / 1 = a.
Then the product xy is a constant.
C = p2r

38. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
For any number a: a * 1 = a and a / 1 = a.
360°
(n - 2)(180°)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

39. What is special formula for the area of an equilateral triangle?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A = [(s^2*v3)/4]
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Cannot is 0 - must is 1 - all others are in between.

40. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
At least one of the factors is 0.
Then the product xy is a constant.
Is a right triangle with a ratio of sides x:xv3:2x.

41. How do you calculate a weighted average?
Divide - then multiply by 100.
In the expression x^b - x is the base and b is the exponent.
Set y = 0 - and solve.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

42. What is true about the measures of the two acute angles in a right triangle?
For any number a: a * 1 = a and a / 1 = a.
If a is negative and b is positive - then a < 0 < b.
0 is a multiple of every integer.
Their sum is 90°.

43. How do you find the area of a sector of a circle?
Shifted right 2 units.
180°. If two or more angles form a straight angle - their sum is 180°.
The ratio of corresponding sides of similar triangles.
Area = (x°/360)(pr^2) where x is the central angle.

44. Law of exponents 1
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
B^m*b^n = b^m+n
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

45. What is p?
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°.
Even numbers are divisible by 2 and odd numbers are not.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
(Circumference/diameter) of a circle - or approximately 3.14.

46. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
B^m*b^n = b^m+n
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted left 2 units.

47. 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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = [(s^2*v3)/4]
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.

48. How do you find the length of an arc of a circle?
B^m/b^n = b^m-n
Arc = (x°/360)(2pr) where x is the central angle.
Is a right triangle with a ratio of sides x:xv3:2x.
Corresponding sides of similar triangles are in proportion.

49. What is true about the areas of similar triangles?
A = 2(lw + lh + hw)
All positive and negative whole numbers - and zero.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Set y = 0 - and solve.

50. What is the sum of the measures of the four angles in a quadrilateral?
B^m*b^n = b^m+n
They are both the same. A divisor or factor of an integer leaves no remainder.
360°
(n - 2)(180°)