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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. Properties of zero 1
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
0 is the only number that is neither positive nor negative.
A = pr^2
Set y = 0 - and solve.

2. In a circle of radius r - what is the formula for the diameter?
D = 2r
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 = 2(lw + lh + hw)

3. What is special formula for the area of an equilateral triangle?
B^m*b^n = b^m+n
A = [(s^2*v3)/4]
D = 2r
Then the quotient y/x is a constant.

4. What is a negative exponent?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For any number n: x^-n means 1/x^n.
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.

5. What is a ratio?

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6. What is an integer?
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
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
All positive and negative whole numbers - and zero.

7. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
They are both the same. A divisor or factor of an integer leaves no remainder.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A^m/b^m = (a/b)^m

8. Properties of one 2
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted down 2 units.
For any integer n: 1^n = 1.
Corresponding sides of similar triangles are in proportion.

9. What is the formula for the surface area of a rectangular solid?
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.
A = 2(lw + lh + hw)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

10. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
If a is negative and b is positive - then a < 0 < b.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

11. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Shifted up 2 units.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

12. What is the probability of an event that cannot occur? That must occur?
They are both the same. A divisor or factor of an integer leaves no remainder.
No matter how many angles there are - the sum around the point is 360°.
A = 6(l^2)
Cannot is 0 - must is 1 - all others are in between.

13. What is true about the measures of the four angles formed by two intersecting lines?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The two pairs of opposite angles formed are equal to each other.
Shifted down 2 units.
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.

14. What is the formula for the area of a triangle?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(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.
A = (1/2)bh.

15. Important binomial 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.
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)(x - y) = x^2 - y^2
Corresponding sides of similar triangles are in proportion.

16. Properties of zero 2
A^m/b^m = (a/b)^m
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.
If a is negative and b is positive - then a < 0 < b.

17. What is a multiple of an integer?
(b^m)^n = b^mn
All positive and negative whole numbers - and zero.
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 = s^2 or A =d^2/2 where d is the diagonal

18. What is the formula for the volume of a cylinder?
A = s^2 or A =d^2/2 where d is the diagonal
An integer greater than one that is not prime.
V = pr^2h
M = (y2 - y1)/(x2 - x1)

19. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
In the expression x^b - x is the base and b is the exponent.
B^m*b^n = b^m+n
1 is the smallest positive odd integer.

20. How do we write the equation of a line?
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.
Write the percent over 100 and reduce.
0 is a multiple of every integer.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

21. What are the properties of a parallelogram?
For any right triangle - a^2 + b^2 = c^2.
A = (1/2)bh.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

22. What is the triangle inequality?
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
An integer greater than one that is not prime.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

23. What is true about the areas of similar triangles?
For any integer n: 1^n = 1.
B^m/b^n = b^m-n
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

24. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Is a right triangle with a ratio of sides x:xv3:2x.
An integer greater than one that is not prime.
If a is negative and b is positive - then a < 0 < b.
360°

25. What is the sum of the measures of the four angles in a quadrilateral?
No matter how many angles there are - the sum around the point is 360°.
360°
In the expression x^b - x is the base and b is the exponent.
The two pairs of opposite angles formed are equal to each other.

26. How you convert a fraction or a decimal to a percent?
Shifted up 2 units.
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.
Divide - then multiply by 100.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

27. Properties of zero 5
If a is negative and b is positive - then a < 0 < b.
In the expression x^b - x is the base and b is the exponent.
Set y = 0 - and solve.
For any number b: b = -b if and only if b = 0.

28. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Set x = 0 - and solve.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

29. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Set x = 0 - and solve.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

30. What is the ratio of similitude?
A = (1/2)bh.
The ratio of corresponding sides of similar triangles.
360°
Then the quotient y/x is a constant.

31. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
Corresponding sides of similar triangles are in proportion.
V = pr^2h
A^m*b^m = (ab)^m

32. In a circle of radius r - what is the formula for the circumference?
Shifted up 2 units.
The set of all ordered pairs (x -y) such that y = f(x).
C = p2r
Then the product xy is a constant.

33. What is true about the measures of the three angles in a triangle?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Shifted left 2 units.
Their sum is 180°.
Shifted up 2 units.

34. Important binomial 3
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
V = pr^2h
C = p2r
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

35. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Corresponding sides of similar triangles are in proportion.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = s^2 or A =d^2/2 where d is the diagonal

36. How do you calculate percent increases and decreases?
A = lw
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any right triangle - a^2 + b^2 = c^2.
Shifted down 2 units.

37. What is the formula for the surface area of a cube?
(b^m)^n = b^mn
Set x = 0 - and solve.
A = 2(lw + lh + hw)
A = 6(l^2)

38. What are the important properties of 30-60-90 triangle?
For any integer n: 1^n = 1.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Is a right triangle with a ratio of sides x:xv3:2x.
B^m*b^n = b^m+n

39. How do you find the area of a sector of a circle?
For any number a: a * 1 = a and a / 1 = a.
A = pr^2
Area = (x°/360)(pr^2) where x is the central angle.
A = [(s^2*v3)/4]

40. What are the properties of a rectangle?
Write the percent over 100 and reduce.
For any number b: b = -b if and only if b = 0.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Arc = (x°/360)(2pr) where x is the central angle.

41. Properties of zero 4
B^m*b^n = b^m+n
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
V = l^3

42. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
A = 2(lw + lh + hw)
Arc = (x°/360)(2pr) where x is the central angle.
360°

43. Properties of one 3
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Equal slopes.
1 is the smallest positive odd integer.
1 is a divisor (or factor) of every integer.

44. What is a prime number?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
No matter how many angles there are - the sum around the point is 360°.
The two pairs of opposite angles formed are equal to each other.
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.

45. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = bh
V = l^3

46. Properties of one 4
How steep the line is. Horizontal line = 0 - vertical has no slope.
The ratio of corresponding sides of similar triangles.
1 is the smallest positive odd integer.
All positive and negative whole numbers - and zero.

47. In a circle of radius r - what is the formula for the area?
A = pr^2
Their sum is 90°.
D = 2r
A^m*b^m = (ab)^m

48. What is a proportion?
V = lwh
An angle formed by extending the side of the polygon.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

49. Properties of one 1
Their sum is 180°.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any number a: a * 1 = a and a / 1 = a.
(Circumference/diameter) of a circle - or approximately 3.14.

50. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
An angle formed by extending the side of the polygon.
360°
Then the quotient y/x is a constant.