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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 prime number?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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.
Write the percent over 100 and reduce.

2. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
Cannot is 0 - must is 1 - all others are in between.
V = pr^2h
A^m/b^m = (a/b)^m

3. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
(Circumference/diameter) of a circle - or approximately 3.14.
A^m*b^m = (ab)^m
No matter how many angles there are - the sum around the point is 360°.
Shifted up 2 units.

4. If the product of two or more numbers is 0 - what do you know about the numbers?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
At least one of the factors is 0.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
B^m/b^n = b^m-n

5. What is true about the measures of the two acute angles in a right triangle?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Their sum is 90°.
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.

6. Important binomial 3
Their sum is 90°.
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.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
360°

7. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
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.
Is a right triangle with a ratio of sides x:xv3:2x.
Set x = 0 - and solve.
360°

8. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
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°.
Write the percent over 100 and reduce.
V = pr^2h

9. For what values of a function is the function undefined?
Then the product xy is a constant.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
[(x1 + x2)/2] -[(y1 + y2)/2]
Arc = (x°/360)(2pr) where x is the central angle.

10. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
An angle formed by extending the side of the polygon.
Divide - then multiply by 100.
180°. If two or more angles form a straight angle - their sum is 180°.

11. What do we mean by the slope of the line?
Their sum is 90°.
For any integer n: 1^n = 1.
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.
How steep the line is. Horizontal line = 0 - vertical has no slope.

12. What is a function?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A fraction whose denominator is 100 i.e. 17% = 17/100
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

13. Properties of one 1
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any number b: b = -b if and only if b = 0.
For any number a: a * 1 = a and a / 1 = a.
The two pairs of opposite angles formed are equal to each other.

14. How do we write the equation of a line?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Set y = 0 - and solve.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

15. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
Shifted left 2 units.
A = [(s^2*v3)/4]
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

16. What is the sum of the measures of the n angles of a polygon with n sides?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Arc = (x°/360)(2pr) where x is the central angle.
A^m*b^m = (ab)^m
(n - 2)(180°)

17. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Then the quotient y/x is a constant.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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 left 2 units.

18. Law of exponents 2
Their sum is 90°.
B^m/b^n = b^m-n
1 is the smallest positive odd integer.
M = (y2 - y1)/(x2 - x1)

19. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
Shifted right 2 units.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior 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.

20. In a circle of radius r - what is the formula for the circumference?
0 is a multiple of every 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°.
A = lw
C = p2r

21. What is the formula for the surface area of a cube?
A = 6(l^2)
An angle formed by extending the side of the polygon.
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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

22. Properties of square roots
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For any right triangle - a^2 + b^2 = c^2.
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.

23. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For any number a: a * 1 = a and a / 1 = a.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = 6(l^2)

24. What is the formula for the volume of a cylinder?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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.
V = pr^2h
A = pr^2

25. What is the formula for the volume of a rectangular solid?
No matter how many angles there are - the sum around the point is 360°.
C = p2r
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
V = lwh

26. If you were given the graph of y = f(x) - what does f(a) represent?
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
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

27. Properties of one 3
The two pairs of opposite angles formed are equal to each other.
Their sum is 90°.
1 is a divisor (or factor) of every integer.
A^m*b^m = (ab)^m

28. How do you calculate percent increases and decreases?
B^m/b^n = b^m-n
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.
Avg = sum of n numbers/n

29. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
The ratio of corresponding sides of similar triangles.
Avg = sum of n numbers/n
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

30. What does it mean if y is directly proportional to x?
At least one of the factors is 0.
Then the quotient y/x is a constant.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

31. Properties of zero 5
A = (1/2)bh.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Shifted right 2 units.
For any number b: b = -b if and only if b = 0.

32. Properties of zero 3
1 is a divisor (or factor) of every integer.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
0 is a multiple of every integer.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

33. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
An angle formed by extending the side of the polygon.
(x + y)(x - y) = x^2 - y^2

34. How do you find the length of an arc of a circle?
A = bh
D = 2r
An integer greater than one that is not prime.
Arc = (x°/360)(2pr) where x is the central angle.

35. What is an integer?
Even numbers are divisible by 2 and odd numbers are not.
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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
All positive and negative whole numbers - and zero.

36. What is an exterior angle of a polygon?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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°.
An angle formed by extending the side of the polygon.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

37. What is true about the slopes of parallel lines?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Equal slopes.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Is a right triangle with a ratio of sides x:xv3:2x.

38. What is a Venn diagram?
An angle formed by extending the side of the polygon.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Shifted down 2 units.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

39. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
For any integer n: 1^n = 1.
Shifted left 2 units.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

40. Law of exponents 1
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
Shifted up 2 units.
B^m/b^n = b^m-n

41. What is a percent?
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 fraction whose denominator is 100 i.e. 17% = 17/100
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
1 is the smallest positive odd integer.

42. What are the sum - difference - products - and quotient of two numbers?
In the expression x^b - x is the base and b is the exponent.
[(x1 + x2)/2] -[(y1 + y2)/2]
Cannot is 0 - must is 1 - all others are in between.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

43. What is a composite number?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
No matter how many angles there are - the sum around the point is 360°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
An integer greater than one that is not prime.

44. What is the volume of a cube?
A^m*b^m = (ab)^m
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
V = l^3
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°.

45. What is a fractional exponent?
(x + y)(x - y) = x^2 - y^2
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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

46. In a circle of radius r - what is the formula for the diameter?
The ratio of corresponding sides of similar triangles.
D = 2r
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.

47. 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.
1 is the smallest positive odd integer.
Corresponding sides of similar triangles are in proportion.
(b^m)^n = b^mn

48. What is true about the slopes of perpendicular lines?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The product of their slopes is -1 (negative reciprocal).
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(b^m)^n = b^mn

49. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
All positive and negative whole numbers - and zero.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Area = (x°/360)(pr^2) where x is the central angle.

50. What is a proportion?
The two pairs of opposite angles formed are equal to each other.
Set y = 0 - and solve.
1 is a divisor (or factor) of every integer.
An equation that states that two ratios are equivalent. 4/6 = 10/15