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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 true about the areas of similar triangles?
Corresponding sides of similar triangles are in proportion.
A = [(s^2*v3)/4]
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Shifted down 2 units.

2. What are the properties of a parallelogram?
For any right triangle - a^2 + b^2 = c^2.
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

3. What is a negative exponent?
A fraction whose denominator is 100 i.e. 17% = 17/100
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For any number n: x^-n means 1/x^n.
The two pairs of opposite angles formed are equal to each other.

4. 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.
In the expression x^b - x is the base and b is the exponent.
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.

5. How do we write the equation of a line?
[(x1 + x2)/2] -[(y1 + y2)/2]
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For any right triangle - a^2 + b^2 = c^2.

6. What is the relationship between a radius of a circle and a line that is tangent to the circle?
A = [(s^2*v3)/4]
360°
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Divide - then multiply by 100.

7. Properties of zero 3
0 is a multiple of every integer.
Avg = sum of n numbers/n
At least one of the factors is 0.
(x + y)(x - y) = x^2 - y^2

8. What is the probability of an event that cannot occur? That must occur?
In the expression x^b - x is the base and b is the exponent.
Cannot is 0 - must is 1 - all others are in between.
A^m/b^m = (a/b)^m
Shifted right 2 units.

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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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.

10. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Divide - then multiply by 100.
Write the percent as a decimal - and multiply.
For any integer n: 1^n = 1.

11. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
V = pr^2h
A^m/b^m = (a/b)^m
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.

12. What is the sum of the measures of the n angles of a polygon with n sides?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
An integer greater than one that is not prime.
V = lwh
(n - 2)(180°)

13. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
For any number b: b = -b if and only if b = 0.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
M = (y2 - y1)/(x2 - x1)

14. Properties of zero 4
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Write the percent as a decimal - and multiply.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

15. Important binomial 1
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
An equation that states that two ratios are equivalent. 4/6 = 10/15
(x + y)(x - y) = x^2 - y^2
Corresponding sides of similar triangles are in proportion.

16. What is the volume of a cube?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Arc = (x°/360)(2pr) where x is the central angle.
V = l^3
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

17. What is a composite number?
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.
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.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

18. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
Area = (x°/360)(pr^2) where x is the central angle.
(x + y)(x - y) = x^2 - y^2
Shifted up 2 units.

19. What is a prime number?
Corresponding sides of similar triangles are in proportion.
A = s^2 or A =d^2/2 where d is the diagonal
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.
180°. If two or more angles form a straight angle - their sum is 180°.

20. What is a ratio?

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21. What is the sum of the measures of all angles around a point?
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.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
No matter how many angles there are - the sum around the point is 360°.

22. In a circle of radius r - what is the formula for the diameter?
D = 2r
Divide - then multiply by 100.
Area = (x°/360)(pr^2) where x is the central angle.
V = l^3

23. What does it mean if y is inversely proportional to x?
(n - 2)(180°)
M = (y2 - y1)/(x2 - x1)
Then the product xy is a constant.
All positive and negative whole numbers - and zero.

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

25. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
A^m*b^m = (ab)^m
P(e) = (# of favorable outcomes)/(# of possible outcomes)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

26. Properties of zero 1
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
0 is the only number that is neither positive nor negative.
Their sum is 180°.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

27. What is the formula for the volume of a rectangular solid?
A = [(s^2*v3)/4]
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
0 is a multiple of every integer.
V = lwh

28. What is an integer?
All positive and negative whole numbers - and zero.
A = [(s^2*v3)/4]
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Their sum is 180°.

29. What does it mean if y is directly proportional to x?
Shifted down 2 units.
Then the quotient y/x is a constant.
The set of all ordered pairs (x -y) such that y = f(x).
B^m/b^n = b^m-n

30. What are the quotient and the remainder?

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31. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^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°.
Their sum is 180°.

32. Properties of one 4
1 is the smallest positive odd integer.
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.
In the expression x^b - x is the base and b is the exponent.

33. What formula is used for an average?
How steep the line is. Horizontal line = 0 - vertical has no slope.
The product of their slopes is -1 (negative reciprocal).
Avg = sum of n numbers/n
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. What are the median and the mode of a set of data?
For any right triangle - a^2 + b^2 = c^2.
Their sum is 180°.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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.

35. Properties of zero 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
If a is negative and b is positive - then a < 0 < b.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

36. What is an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
Divide - then multiply by 100.
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.
360°

37. In a circle of radius r - what is the formula for the area?
A = pr^2
Their sum is 180°.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

38. What do we mean by the slope of the line?
A^m*b^m = (ab)^m
How steep the line is. Horizontal line = 0 - vertical has no slope.
Then the product xy is a constant.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

39. What is a proportion?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The product of their slopes is -1 (negative reciprocal).
Write the percent as a decimal - and multiply.
An equation that states that two ratios are equivalent. 4/6 = 10/15

40. What is true about the slopes of parallel lines?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Shifted right 2 units.
Equal slopes.

41. If you were given the graph of y = f(x) - what does f(a) represent?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A = 6(l^2)
0 is a multiple of every integer.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

42. What is the Pythagorean theorem?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any right triangle - a^2 + b^2 = c^2.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

43. What is an even and an odd number?
C = p2r
Cannot is 0 - must is 1 - all others are in between.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Even numbers are divisible by 2 and odd numbers are not.

44. What is a multiple of an integer?
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.
Is a right triangle with a ratio of sides x:xv3:2x.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

45. How do you find the y-intercept of a graph?
For any integer n: 1^n = 1.
For any right triangle - a^2 + b^2 = c^2.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Set x = 0 - and solve.

46. In a circle of radius r - what is the formula for the circumference?
A = pr^2
C = p2r
360°
The product of their slopes is -1 (negative reciprocal).

47. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
Shifted left 2 units.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
V = pr^2h

48. Law of exponents 4
A^m*b^m = (ab)^m
An integer greater than one that is not prime.
Their sum is 180°.
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.

49. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
How steep the line is. Horizontal line = 0 - vertical has no slope.
A^m*b^m = (ab)^m
An equation that states that two ratios are equivalent. 4/6 = 10/15

50. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2