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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 an even and an odd number?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Even numbers are divisible by 2 and odd numbers are not.
The set of all ordered pairs (x -y) such that y = f(x).
For any number n: x^-n means 1/x^n.

2. 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 = bh
For any number n: x^-n means 1/x^n.
C = p2r

3. What is a ratio?

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4. For what values of a function is the function undefined?
M = (y2 - y1)/(x2 - x1)
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.
0 is a multiple of every integer.

5. In a circle of radius r - what is the formula for the circumference?
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.
C = p2r
360°
A^m*b^m = (ab)^m

6. If you were given the graph of y = f(x) - what does f(a) represent?
[(x1 + x2)/2] -[(y1 + y2)/2]
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
The product of their slopes is -1 (negative reciprocal).
Shifted up 2 units.

7. What are the quotient and the remainder?

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8. What is true about the areas of similar triangles?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
An angle formed by extending the side of the polygon.

9. What formula is used for an average?
Then the product xy is a constant.
A^m*b^m = (ab)^m
Cannot is 0 - must is 1 - all others are in between.
Avg = sum of n numbers/n

10. What important property do similar triangles have?
For any number b: b = -b if and only if b = 0.
B^m*b^n = b^m+n
Even numbers are divisible by 2 and odd numbers are not.
Corresponding sides of similar triangles are in proportion.

11. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
[(x1 + x2)/2] -[(y1 + y2)/2]
Their sum is 90°.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

12. Properties of one 3
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.
At least one of the factors is 0.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
1 is a divisor (or factor) of every integer.

13. What are the important properties of 30-60-90 triangle?
A = 2(lw + lh + hw)
Is a right triangle with a ratio of sides x:xv3:2x.
For any right triangle - a^2 + b^2 = c^2.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

14. What is the area of a square?
0 is the only number that is neither positive nor negative.
B^m/b^n = b^m-n
A = s^2 or A =d^2/2 where d is the diagonal
How steep the line is. Horizontal line = 0 - vertical has no slope.

15. What is the graph of a function?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
They are both the same. A divisor or factor of an integer leaves no remainder.
The set of all ordered pairs (x -y) such that y = f(x).
An integer greater than one that is not prime.

16. What is the formula for the volume of a rectangular solid?
An integer greater than one that is not prime.
V = lwh
0 is a multiple of every integer.
Set y = 0 - and solve.

17. What is p?
No matter how many angles there are - the sum around the point is 360°.
(Circumference/diameter) of a circle - or approximately 3.14.
B^m/b^n = b^m-n
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°.

18. What are similar triangles?
Shifted down 2 units.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
D = 2r

19. Properties of zero 1
Equal slopes.
180°. If two or more angles form a straight angle - their sum is 180°.
0 is the only number that is neither positive nor negative.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

20. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
A = [(s^2*v3)/4]
No matter how many angles there are - the sum around the point is 360°.
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°.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

21. Law of exponents 3
(b^m)^n = b^mn
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = (1/2)bh.
Then the product xy is a constant.

22. Important binomial 2
D = 2r
(Circumference/diameter) of a circle - or approximately 3.14.
For any number b: b = -b if and only if b = 0.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

23. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
For any number n: x^-n means 1/x^n.
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Shifted right 2 units.

24. How do you find the length of an arc of a circle?
A^m/b^m = (a/b)^m
Arc = (x°/360)(2pr) where x is the central angle.
How steep the line is. Horizontal line = 0 - vertical has no slope.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

25. Properties of zero 5
For any number b: b = -b if and only if b = 0.
Area = (x°/360)(pr^2) where x is the central angle.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

26. Properties of one 4
V = lwh
Then the quotient y/x is a constant.
For any number a: a * 1 = a and a / 1 = a.
1 is the smallest positive odd integer.

27. What is the formula for the area of a triangle?
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = (1/2)bh.
A^m*b^m = (ab)^m
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.

28. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
180°. If two or more angles form a straight angle - their sum is 180°.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
360°

29. What are the properties of a rectangle?
A = s^2 or A =d^2/2 where d is the diagonal
B^m*b^n = b^m+n
Cannot is 0 - must is 1 - all others are in between.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

30. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

31. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Avg = sum of n numbers/n
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
If a is negative and b is positive - then a < 0 < b.

32. Important binomial 3
360°
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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.

33. How do you find the y-intercept of a graph?
Write the percent as a decimal - and multiply.
Set x = 0 - and solve.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A fraction whose denominator is 100 i.e. 17% = 17/100

34. What is the formula for the surface area of a cube?
A = 6(l^2)
A = (1/2)bh.
Avg = sum of n numbers/n
Shifted right 2 units.

35. What is the formula for the volume of a cylinder?
Shifted left 2 units.
1 is a divisor (or factor) of every integer.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
V = pr^2h

36. Law of exponents 4
A = (1/2)bh.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A^m*b^m = (ab)^m

37. How do you find the probability that an event will occur?
Area = (x°/360)(pr^2) where x is the central angle.
The two pairs of opposite angles formed are equal to each other.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For any right triangle - a^2 + b^2 = c^2.

38. What is the sum of the measures of all angles around a point?
A = pr^2
(n - 2)(180°)
No matter how many angles there are - the sum around the point is 360°.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

39. How do you calculate a weighted average?
The two pairs of opposite angles formed are equal to each other.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Set x = 0 - and solve.
The product of their slopes is -1 (negative reciprocal).

40. Law of exponents 5
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.
1 is a divisor (or factor) of every integer.

41. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
For any right triangle - a^2 + b^2 = c^2.
Then the quotient y/x is a constant.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

42. Properties of zero 3
Divide - then multiply by 100.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
0 is a multiple of every integer.
A = lw

43. What is a composite number?
An integer greater than one that is not prime.
D = 2r
For any number a: a * 1 = a and a / 1 = a.
For any number b: b = -b if and only if b = 0.

44. What is a multiple of an integer?
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.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
An equation that states that two ratios are equivalent. 4/6 = 10/15

45. What is an exterior angle of a polygon?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
(x + y)(x - y) = x^2 - y^2
An angle formed by extending the side of the polygon.
Shifted up 2 units.

46. What is true about the measures of the four angles formed by two intersecting lines?
360°
The two pairs of opposite angles formed are equal to each other.
A^m*b^m = (ab)^m
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

47. What is an integer?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Shifted left 2 units.
All positive and negative whole numbers - and zero.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

48. Properties of one 1
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Write the percent as a decimal - and multiply.
For any number a: a * 1 = a and a / 1 = a.

49. In a circle of radius r - what is the formula for the diameter?
A = 2(lw + lh + hw)
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Then the quotient y/x is a constant.
D = 2r

50. What is a fractional exponent?
Even numbers are divisible by 2 and odd numbers are not.
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.
Write the percent over 100 and reduce.