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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 relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
In the expression x^b - x is the base and b is the exponent.
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.
D = 2r

2. Law of exponents 5
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
D = 2r
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A^m/b^m = (a/b)^m

3. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
Corresponding sides of similar triangles are in proportion.
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.
Then the quotient y/x is a constant.

4. Properties of zero 5
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any number b: b = -b if and only if b = 0.
Shifted down 2 units.

5. What is an exterior angle of a triangle?
A^m*b^m = (ab)^m
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
If a is negative and b is positive - then a < 0 < b.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

6. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
The ratio of corresponding sides of similar triangles.
A^m*b^m = (ab)^m
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

7. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Write the percent as a decimal - and multiply.
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.
Is a right triangle with a ratio of sides x:xv3:2x.
Shifted right 2 units.

8. What is an integer?
All positive and negative whole numbers - and zero.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
0 is a multiple of every integer.
A = pr^2

9. How do you calculate a weighted average?
M = (y2 - y1)/(x2 - x1)
Even numbers are divisible by 2 and odd numbers are not.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For any number n: x^-n means 1/x^n.

10. What is the ratio of similitude?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
The ratio of corresponding sides of similar triangles.
C = p2r
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

11. What is true about the measures of the four angles formed by two intersecting lines?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Set x = 0 - and solve.
A = lw
The two pairs of opposite angles formed are equal to each other.

12. If the product of two or more numbers is 0 - what do you know about the numbers?
The product of their slopes is -1 (negative reciprocal).
Is a right triangle with a ratio of sides x:xv3:2x.
A = bh
At least one of the factors is 0.

13. What is a negative exponent?
Is a right triangle with a ratio of sides x:xv3:2x.
A = 6(l^2)
For any number n: x^-n means 1/x^n.
Then the quotient y/x is a constant.

14. What is the Pythagorean theorem?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^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.
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.

15. What is a prime number?
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.
B^m*b^n = b^m+n
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.

16. How do we write the equation of a line?
An angle formed by extending the side of the polygon.
Is a right triangle with a ratio of sides x:xv3:2x.
A = [(s^2*v3)/4]
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

17. Properties of square roots
An integer greater than one that is not prime.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Shifted right 2 units.
Divide - then multiply by 100.

18. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
(n - 2)(180°)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(Circumference/diameter) of a circle - or approximately 3.14.

19. What is the formula for the area of a rectangle?
Write the percent as a decimal - and multiply.
A = lw
360°
V = pr^2h

20. 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.
Avg = sum of n numbers/n
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

21. How do you find a percent of a number?
A = 2(lw + lh + hw)
C = p2r
A^m*b^m = (ab)^m
Write the percent as a decimal - and multiply.

22. Properties of zero 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°.
How steep the line is. Horizontal line = 0 - vertical has no slope.
If a is negative and b is positive - then a < 0 < b.
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.

23. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
1 is the smallest positive odd integer.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
No matter how many angles there are - the sum around the point is 360°.

24. What is a function?
360°
The set of all ordered pairs (x -y) such that y = f(x).
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

25. Properties of zero 3
An angle formed by extending the side of the polygon.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
0 is a multiple of every integer.
180°. If two or more angles form a straight angle - their sum is 180°.

26. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted left 2 units.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

27. If you were given the graph of y = f(x) - what does f(a) represent?
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°.
Area = (x°/360)(pr^2) where x is the central angle.
At least one of the factors is 0.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

28. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The product of their slopes is -1 (negative reciprocal).
M = (y2 - y1)/(x2 - x1)
Shifted up 2 units.

29. What is true about the slopes of perpendicular lines?
A = s^2 or A =d^2/2 where d is the diagonal
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.

30. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Write the percent over 100 and reduce.
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.
360°

31. Law of exponents 4
A^m*b^m = (ab)^m
The product of their slopes is -1 (negative reciprocal).
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = [(s^2*v3)/4]

32. What formula is used for an average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Avg = sum of n numbers/n
B^m*b^n = b^m+n
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

33. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
They are both the same. A divisor or factor of an integer leaves no remainder.
Shifted down 2 units.

34. What is a ratio?

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35. In a circle of radius r - what is the formula for the diameter?
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°.
D = 2r
M = (y2 - y1)/(x2 - x1)
Arc = (x°/360)(2pr) where x is the central angle.

36. What is a multiple of an integer?
B^m*b^n = b^m+n
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.
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.
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.

37. What is a composite number?
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.
An integer greater than one that is not prime.
D = 2r

38. In a circle of radius r - what is the formula for the circumference?
C = p2r
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
360°
All positive and negative whole numbers - and zero.

39. For what values of a function is the function undefined?
A = 2(lw + lh + hw)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.
360°

40. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
B^m*b^n = b^m+n
B^m/b^n = b^m-n
How steep the line is. Horizontal line = 0 - vertical has no slope.

41. How do you calculate percent increases and decreases?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Equal slopes.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Write the percent over 100 and reduce.

42. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
360°
Shifted down 2 units.
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.
Corresponding sides of similar triangles are in proportion.

43. What are the median and the mode of a set of data?
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
For any number b: b = -b if and only if b = 0.
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.

44. What is the sum of the measures of the four angles in a quadrilateral?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A^m*b^m = (ab)^m
360°
Shifted up 2 units.

45. What is the volume of a cube?
Avg = sum of n numbers/n
For any number b: b = -b if and only if b = 0.
Set y = 0 - and solve.
V = l^3

46. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
The ratio of corresponding sides of similar triangles.
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.
Even numbers are divisible by 2 and odd numbers are not.
Shifted up 2 units.

47. Law of exponents 2
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
B^m/b^n = b^m-n
A^m*b^m = (ab)^m
At least one of the factors is 0.

48. What are the properties of a square?
An integer greater than one that is not prime.
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.
360°
A = bh

49. What is the formula for the volume of a rectangular solid?
V = lwh
For any right triangle - a^2 + b^2 = c^2.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^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°.

50. What do we mean by the slope of the line?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
1 is a divisor (or factor) of every integer.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = (1/2)bh.