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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 sum of the measures of the four angles in a quadrilateral?
Write the percent over 100 and reduce.
C = p2r
Their sum is 180°.
360°

2. Properties of one 4
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Divide - then multiply by 100.
1 is the smallest positive odd integer.

3. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Shifted right 2 units.
360°
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A fraction whose denominator is 100 i.e. 17% = 17/100

4. What is p?
Corresponding sides of similar triangles are in proportion.
(Circumference/diameter) of a circle - or approximately 3.14.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Divide - then multiply by 100.

5. What is the formula for the area of a rectangle?
A = lw
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
1 is a divisor (or factor) of every integer.
[(x1 + x2)/2] -[(y1 + y2)/2]

6. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
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.
Divide - then multiply by 100.

7. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
A^m/b^m = (a/b)^m
Set x = 0 - and solve.
B^m*b^n = b^m+n

8. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Shifted down 2 units.
1 is a divisor (or factor) of every integer.
Even numbers are divisible by 2 and odd numbers are not.

9. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
Corresponding sides of similar triangles are in proportion.
A fraction whose denominator is 100 i.e. 17% = 17/100
A = 6(l^2)

10. Properties of zero 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.
Then the product xy is a constant.
The ratio of corresponding sides of similar triangles.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

11. What is the volume of a cube?
V = l^3
V = pr^2h
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.
They are both the same. A divisor or factor of an integer leaves no remainder.

12. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
For any number n: x^-n means 1/x^n.
They are both the same. A divisor or factor of an integer leaves no remainder.
A = 2(lw + lh + hw)

13. What are the important properties of a 45-45 - 90 triangle?
Avg = sum of n numbers/n
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The set of all ordered pairs (x -y) such that y = f(x).

14. What is a Venn diagram?
For any integer n: 1^n = 1.
Then the product xy 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°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

15. How you convert a fraction or a decimal to a percent?
1 is a divisor (or factor) of every integer.
Their sum is 90°.
360°
Divide - then multiply by 100.

16. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For any number n: x^-n means 1/x^n.

17. What is the distributive law?
A fraction whose denominator is 100 i.e. 17% = 17/100
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Avg = sum of n numbers/n

18. What is the formula for the surface area of a rectangular solid?
Shifted up 2 units.
A = 2(lw + lh + hw)
V = lwh
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

19. What is true about the measures of the two acute angles in a right triangle?
Divide - then multiply by 100.
How steep the line is. Horizontal line = 0 - vertical has no slope.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Their sum is 90°.

20. What is true about the areas of similar triangles?
Divide - then multiply by 100.
(Circumference/diameter) of a circle - or approximately 3.14.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

21. What is the formula for the area of a parallelogram?
For any right triangle - a^2 + b^2 = c^2.
0 is a multiple of every integer.
A = bh
All positive and negative whole numbers - and zero.

22. In a circle of radius r - what is the formula for the circumference?
For any right triangle - a^2 + b^2 = c^2.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
C = p2r
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

23. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
Cannot is 0 - must is 1 - all others are in between.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For any number b: b = -b if and only if b = 0.

24. Law of exponents 1
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.
B^m*b^n = b^m+n
1 is the smallest positive odd integer.
If a is negative and b is positive - then a < 0 < b.

25. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Avg = sum of n numbers/n
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted up 2 units.
For any integer n: 1^n = 1.

26. What do we mean by the slope of the line?
An equation that states that two ratios are equivalent. 4/6 = 10/15
How steep the line is. Horizontal line = 0 - vertical has no slope.
Set x = 0 - and solve.
A = [(s^2*v3)/4]

27. What is an integer?
For any number a: a * 1 = a and a / 1 = a.
(x + y)(x - y) = x^2 - y^2
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
All positive and negative whole numbers - and zero.

28. In a circle of radius r - what is the formula for the area?
A = pr^2
M = (y2 - y1)/(x2 - x1)
[(x1 + x2)/2] -[(y1 + y2)/2]
If a is negative and b is positive - then a < 0 < b.

29. What is true about the measures of the four angles formed by two intersecting lines?
The two pairs of opposite angles formed are equal to each other.
A = pr^2
No matter how many angles there are - the sum around the point is 360°.
Their sum is 90°.

30. In a circle of radius r - what is the formula for the diameter?
V = l^3
A = 2(lw + lh + hw)
Write the percent over 100 and reduce.
D = 2r

31. What is true about the measures of the three angles in a triangle?
Write the percent over 100 and reduce.
Their sum is 180°.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
V = lwh

32. What is a function?
Write the percent over 100 and reduce.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

33. What is the ratio of similitude?
V = lwh
The ratio of corresponding sides of similar triangles.
Their sum is 180°.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

34. How do you find the area of a sector of a circle?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A fraction whose denominator is 100 i.e. 17% = 17/100
Their sum is 90°.
Area = (x°/360)(pr^2) where x is the central angle.

35. What is a ratio?

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36. Properties of zero 5
A^m/b^m = (a/b)^m
For any number b: b = -b if and only if b = 0.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

37. What is the formula for the surface area of a cube?
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.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
At least one of the factors is 0.
A = 6(l^2)

38. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = pr^2
An integer greater than one that is not prime.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

39. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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 ratio of corresponding sides of similar triangles.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A fraction whose denominator is 100 i.e. 17% = 17/100

40. Important binomial 3
1 is the smallest positive odd integer.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
In the expression x^b - x is the base and b is the exponent.
A = (1/2)bh.

41. What is the formula for the volume of a rectangular solid?
V = lwh
An angle formed by extending the side of the polygon.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
360°

42. What is a multiple of an integer?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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 fraction whose denominator is 100 i.e. 17% = 17/100

43. What is an even and an odd number?
0 is the only number that is neither positive nor negative.
Even numbers are divisible by 2 and odd numbers are not.
V = l^3
V = lwh

44. 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 or A =d^2/2 where d is the diagonal
[(x1 + x2)/2] -[(y1 + y2)/2]
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

45. Law of exponents 2
B^m*b^n = b^m+n
Set y = 0 - and solve.
B^m/b^n = b^m-n
Shifted down 2 units.

46. What are the quotient and the remainder?

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47. How do you find the slope of a line?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
360°
M = (y2 - y1)/(x2 - x1)
For any number n: x^-n means 1/x^n.

48. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
360°
Shifted right 2 units.
360°
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

49. What is a percent?
V = pr^2h
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A fraction whose denominator is 100 i.e. 17% = 17/100
An angle formed by extending the side of the polygon.

50. Law of exponents 4
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
For any right triangle - a^2 + b^2 = c^2.
A = s^2 or A =d^2/2 where d is the diagonal
A^m*b^m = (ab)^m