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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 5
For any number b: b = -b if and only if b = 0.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The ratio of corresponding sides of similar triangles.

2. What are the quotient and the remainder?

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3. What is true about the measures of the two acute angles in a right triangle?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
V = lwh
For any number a: a * 1 = a and a / 1 = a.
Their sum is 90°.

4. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A^m/b^m = (a/b)^m
Avg = sum of n numbers/n
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

5. Properties of zero 1
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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.
0 is the only number that is neither positive nor negative.

6. Law of exponents 2
For any number b: b = -b if and only if b = 0.
Even numbers are divisible by 2 and odd numbers are not.
V = lwh
B^m/b^n = b^m-n

7. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Divide - then multiply by 100.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = pr^2

8. How do you find the slope of a line?
A = 6(l^2)
A^m*b^m = (ab)^m
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
M = (y2 - y1)/(x2 - x1)

9. Properties of one 4
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
1 is the smallest positive odd integer.
Their sum is 180°.

10. What are the properties of a square?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Avg = sum of n numbers/n

11. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any number b: b = -b if and only if b = 0.
Shifted up 2 units.
Equal slopes.

12. In a circle of radius r - what is the formula for the circumference?
(b^m)^n = b^mn
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.
C = p2r
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

13. What are the important properties of a 45-45 - 90 triangle?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.

14. What is the sum of the measures of the four angles in a quadrilateral?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
360°
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
(Circumference/diameter) of a circle - or approximately 3.14.

15. In a circle of radius r - what is the formula for the area?
Shifted down 2 units.
A = pr^2
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
(x + y)(x - y) = x^2 - y^2

16. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
360°
In the expression x^b - x is the base and b is the exponent.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Shifted left 2 units.

17. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Area = (x°/360)(pr^2) where x is the central angle.
360°
Their sum is 90°.
A = s^2 or A =d^2/2 where d is the diagonal

18. What is the sum of the measures of the n angles of a polygon with n sides?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(n - 2)(180°)

19. What is a composite number?
The set of all ordered pairs (x -y) such that y = f(x).
An integer greater than one that is not prime.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

20. In a circle of radius r - what is the formula for the diameter?
For any number a: a * 1 = a and a / 1 = a.
D = 2r
For any integer n: 1^n = 1.
They are both the same. A divisor or factor of an integer leaves no remainder.

21. What is true about the areas of similar triangles?
A = bh
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
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.

22. How do you find a percent of a number?
Then the quotient y/x is a constant.
Write the percent as a decimal - and multiply.
The ratio of corresponding sides of similar triangles.
360°

23. Important binomial 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.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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.

24. How do you calculate a weighted average?
C = p2r
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Area = (x°/360)(pr^2) where x is the central angle.

25. Properties of zero 4
1 is the smallest positive odd integer.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Shifted down 2 units.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

26. What is the graph of a function?
In the expression x^b - x is the base and b is the exponent.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
V = l^3
The set of all ordered pairs (x -y) such that y = f(x).

27. What is a negative exponent?
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.
Shifted right 2 units.
For any number n: x^-n means 1/x^n.

28. What are the important properties of 30-60-90 triangle?
Shifted left 2 units.
B^m*b^n = b^m+n
Is a right triangle with a ratio of sides x:xv3:2x.
A = s^2 or A =d^2/2 where d is the diagonal

29. Properties of one 2
Is a right triangle with a ratio of sides x:xv3:2x.
An integer greater than one that is not prime.
For any integer n: 1^n = 1.
B^m/b^n = b^m-n

30. What is true about the measures of the three angles in a triangle?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
0 is a multiple of every integer.
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.

31. What is a percent?
The two pairs of opposite angles formed are equal to each other.
No matter how many angles there are - the sum around the point is 360°.
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted up 2 units.

32. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
Even numbers are divisible by 2 and odd numbers are not.
Cannot is 0 - must is 1 - all others are in between.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

33. What are the properties of a rectangle?
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.
Equal slopes.
They are both the same. A divisor or factor of an integer leaves no remainder.

34. Law of exponents 4
B^m*b^n = b^m+n
A^m*b^m = (ab)^m
For any number b: b = -b if and only if b = 0.
An angle formed by extending the side of the polygon.

35. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted up 2 units.
Shifted down 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.
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.

36. What do we mean by the slope of the line?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
How steep the line is. Horizontal line = 0 - vertical has no slope.
An integer greater than one that is not prime.

37. What is an exterior angle of a polygon?
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.
A = (1/2)bh.
Is a right triangle with a ratio of sides x:xv3:2x.
An angle formed by extending the side of the polygon.

38. What are the median and the mode of a set of data?
A = bh
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

39. 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.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

40. What is the formula for the area of a rectangle?
V = l^3
A = lw
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.
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.

41. What is the formula for the volume of a rectangular solid?
Set y = 0 - and solve.
V = lwh
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

42. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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°.
A = [(s^2*v3)/4]
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Set y = 0 - and solve.

43. Properties of zero 2
P(e) = (# of favorable outcomes)/(# of possible outcomes)
If a is negative and b is positive - then a < 0 < b.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

44. What is the measure of a straight angle?
Area = (x°/360)(pr^2) where x is the central angle.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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.

45. For what values of a function is the function undefined?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.
Equal slopes.

46. What is the distance formula?
No matter how many angles there are - the sum around the point is 360°.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = bh
If a is negative and b is positive - then a < 0 < b.

47. Properties of one 1
V = l^3
1 is a divisor (or factor) of every integer.
Area = (x°/360)(pr^2) where x is the central angle.
For any number a: a * 1 = a and a / 1 = a.

48. How do you calculate percent increases and decreases?
For any number a: a * 1 = a and a / 1 = a.
The two pairs of opposite angles formed are equal to each other.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
C = p2r

49. What is an integer?
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°.
Shifted down 2 units.
All positive and negative whole numbers - and zero.
1 is a divisor (or factor) of every integer.

50. What are the sum - difference - products - and quotient of two numbers?
The ratio of corresponding sides of similar triangles.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any number n: x^-n means 1/x^n.
A = bh