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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 a composite number?
An integer greater than one that is not prime.
Is a right triangle with a ratio of sides x:xv3:2x.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For any number n: x^-n means 1/x^n.

2. Important binomial 3
Area = (x°/360)(pr^2) where x is the central angle.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

3. Properties of zero 3
The two pairs of opposite angles formed are equal to each other.
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.
0 is a multiple of every integer.

4. How do you calculate percent increases and decreases?
V = l^3
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.
Set y = 0 - and solve.

5. Properties of square roots
0 is a multiple of every integer.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(Circumference/diameter) of a circle - or approximately 3.14.
B^m/b^n = b^m-n

6. 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.
Write the percent over 100 and reduce.
A = [(s^2*v3)/4]
Equal slopes.

7. What is the distance formula?
360°
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
V = pr^2h

8. Law of exponents 2
A^m*b^m = (ab)^m
An angle formed by extending the side of the polygon.
B^m/b^n = b^m-n
For any number b: b = -b if and only if b = 0.

9. What is the area of a square?
V = l^3
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = s^2 or A =d^2/2 where d is the diagonal

10. What is true about the areas of similar triangles?
360°
Corresponding sides of similar triangles are in proportion.
360°
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

11. Important binomial 1
A = s^2 or A =d^2/2 where d is the diagonal
360°
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(x + y)(x - y) = x^2 - y^2

12. Properties of one 3
Shifted down 2 units.
A = 6(l^2)
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
1 is a divisor (or factor) of every integer.

13. What is the formula for the volume of a cylinder?
V = pr^2h
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The two pairs of opposite angles formed are equal to each other.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

14. What is the sum of the measures of the n angles of a polygon with n sides?
D = 2r
Shifted left 2 units.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(n - 2)(180°)

15. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
(x + y)(x - y) = x^2 - y^2
Cannot is 0 - must is 1 - all others are in between.
A = (1/2)bh.

16. What is a ratio?

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17. What is the midpoint formula?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
At least one of the factors is 0.
[(x1 + x2)/2] -[(y1 + y2)/2]

18. What is the triangle inequality?
180°. If two or more angles form a straight angle - their sum is 180°.
If a is negative and b is positive - then a < 0 < b.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.

19. For what values of a function is the function undefined?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Then the product xy is a constant.
V = lwh

20. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
B^m*b^n = b^m+n
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A = [(s^2*v3)/4]

21. What is an even and an odd number?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
C = p2r
Even numbers are divisible by 2 and odd numbers are not.
Shifted up 2 units.

22. What is the formula for the volume of a rectangular solid?
1 is a divisor (or factor) of every integer.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
At least one of the factors is 0.
V = lwh

23. What formula is used for an average?
Avg = sum of n numbers/n
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*v3)/4]
A = (1/2)bh.

24. In a circle of radius r - what is the formula for the diameter?
(n - 2)(180°)
Area = (x°/360)(pr^2) where x is the central angle.
D = 2r
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

25. In a circle of radius r - what is the formula for the area?
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.
A = pr^2
A^m*b^m = (ab)^m
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

26. What is the volume of a cube?
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.
0 is the only number that is neither positive nor negative.
V = l^3
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

27. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
C = p2r
All positive and negative whole numbers - and zero.
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.

28. How do you find the y-intercept of a graph?
Then the product xy is a constant.
360°
Set x = 0 - and solve.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

29. What is the Pythagorean theorem?
Then the quotient y/x is a constant.
0 is a multiple of every integer.
For any right triangle - a^2 + b^2 = c^2.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

30. What is special formula for the area of an equilateral triangle?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The set of all ordered pairs (x -y) such that y = f(x).
Their sum is 180°.
A = [(s^2*v3)/4]

31. What are the sum - difference - products - and quotient of two numbers?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

32. What is true about the slopes of perpendicular lines?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
(n - 2)(180°)
The product of their slopes is -1 (negative reciprocal).
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

33. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
(x + y)(x - y) = x^2 - y^2
A^m/b^m = (a/b)^m
Avg = sum of n numbers/n

34. Properties of one 2
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For any integer n: 1^n = 1.
Set y = 0 - and solve.
Shifted left 2 units.

35. What is the measure of a straight angle?
Set x = 0 - and solve.
(x + y)(x - y) = x^2 - y^2
Shifted left 2 units.
180°. If two or more angles form a straight angle - their sum is 180°.

36. What is an exponent?
(Circumference/diameter) of a circle - or approximately 3.14.
In the expression x^b - x is the base and b is the exponent.
0 is a multiple of every integer.
They are both the same. A divisor or factor of an integer leaves no remainder.

37. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Set y = 0 - and solve.
Shifted left 2 units.

38. If you were given the graph of y = f(x) - what does f(a) represent?
B^m/b^n = b^m-n
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
0 is the only number that is neither positive nor negative.

39. Properties of one 4
1 is a divisor (or factor) of every integer.
1 is the smallest positive odd integer.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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.

40. How do you convert a percent to a fraction or a decimal?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Shifted down 2 units.
Write the percent over 100 and reduce.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

41. Law of exponents 4
For any right triangle - a^2 + b^2 = c^2.
A^m*b^m = (ab)^m
M = (y2 - y1)/(x2 - x1)
Set y = 0 - and solve.

42. Law of exponents 1
A = 6(l^2)
A = lw
(Circumference/diameter) of a circle - or approximately 3.14.
B^m*b^n = b^m+n

43. How do you find the probability that an event will occur?
Arc = (x°/360)(2pr) where x is the central angle.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
If a is negative and b is positive - then a < 0 < b.

44. Law of exponents 5
A^m/b^m = (a/b)^m
How steep the line is. Horizontal line = 0 - vertical has no slope.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Equal slopes.

45. What is true about the measures of the three angles in a triangle?
Divide - then multiply by 100.
Their sum is 180°.
For any number b: b = -b if and only if b = 0.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

46. How do you find the length of an arc of a circle?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Arc = (x°/360)(2pr) where x is the central angle.
The ratio of corresponding sides of similar triangles.
No matter how many angles there are - the sum around the point is 360°.

47. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted right 2 units.
Set x = 0 - and solve.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

48. What is a fractional exponent?
All positive and negative whole numbers - and zero.
Then the product xy is a constant.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.

49. What is the square root of a number?
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 = 6(l^2)
The ratio of corresponding sides of similar triangles.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

50. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = pr^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.