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GRE Math: Facts

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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 negative exponent?
For any number n: x^-n means 1/x^n.
For any number a: a * 1 = a and a / 1 = a.
An integer greater than one that is not prime.
A = pr^2

2. What is a function?
Shifted right 2 units.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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.
The two pairs of opposite angles formed are equal to each other.

3. What are the important properties of 30-60-90 triangle?
180°. If two or more angles form a straight angle - their sum is 180°.
Is a right triangle with a ratio of sides x:xv3:2x.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

4. How do you find the length of an arc of a circle?
1 is the smallest positive odd integer.
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.
Arc = (x°/360)(2pr) where x is the central angle.

5. What is the distance formula?
Set y = 0 - and solve.
A = pr^2
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
All positive and negative whole numbers - and zero.

6. What is a divisor and a factor of an integer?
V = pr^2h
For any right triangle - a^2 + b^2 = c^2.
They are both the same. A divisor or factor of an integer leaves no remainder.
Equal slopes.

7. What is true about the slopes of parallel lines?
Set x = 0 - and solve.
Equal slopes.
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

8. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Set x = 0 - and solve.
For any number b: b = -b if and only if b = 0.
Then the quotient y/x is a constant.

9. How do we write the equation of a line?
Area = (x°/360)(pr^2) where x is the central angle.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Their sum is 180°.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

10. What is a composite number?
Then the quotient y/x is a constant.
0 is the only number that is neither positive nor negative.
An equation that states that two ratios are equivalent. 4/6 = 10/15
An integer greater than one that is not prime.

11. In a circle of radius r - what is the formula for the diameter?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
D = 2r
Then the quotient y/x is a constant.
V = pr^2h

12. Law of exponents 5
An integer greater than one that is not prime.
Shifted up 2 units.
A^m/b^m = (a/b)^m
P(e) = (# of favorable outcomes)/(# of possible outcomes)

13. What are the properties of a rectangle?
A = s^2 or A =d^2/2 where d is the diagonal
Shifted up 2 units.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

14. Properties of zero 1
0 is the only number that is neither positive nor negative.
How steep the line is. Horizontal line = 0 - vertical has no slope.
360°
C = p2r

15. Properties of square roots
Even numbers are divisible by 2 and odd numbers are not.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.

16. What is the probability of an event that cannot occur? That must occur?
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.
Cannot is 0 - must is 1 - all others are in between.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
V = lwh

17. What is an exterior angle of a triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
If a is negative and b is positive - then a < 0 < b.
(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.

18. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A = bh

19. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
The set of all ordered pairs (x -y) such that y = f(x).
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°.
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°.

20. What is the Pythagorean theorem?
0 is a multiple of every integer.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
For any right triangle - a^2 + b^2 = c^2.

21. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
B^m/b^n = b^m-n
Area = (x°/360)(pr^2) where x is the central angle.
(Circumference/diameter) of a circle - or approximately 3.14.
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.

22. In a circle of radius r - what is the formula for the area?
A^m*b^m = (ab)^m
If a is negative and b is positive - then a < 0 < b.
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 = pr^2

23. Law of exponents 4
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A^m*b^m = (ab)^m
For any integer n: 1^n = 1.
A = bh

24. What is the sum of the measures of the four angles in a quadrilateral?
360°
D = 2r
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

25. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
A^m/b^m = (a/b)^m
A = (1/2)bh.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Shifted left 2 units.

26. How do you find the x-intercept of a graph?
For any right triangle - a^2 + b^2 = c^2.
Set y = 0 - and solve.
1 is a divisor (or factor) of every integer.
B^m*b^n = b^m+n

27. 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.
An angle formed by extending the side of the polygon.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Then the product xy is a constant.

28. What are the properties of a parallelogram?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Set x = 0 - and solve.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
They are both the same. A divisor or factor of an integer leaves no remainder.

29. What is a prime number?
C = p2r
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.
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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

30. What is the formula for the area of a triangle?
An integer greater than one that is not prime.
A = (1/2)bh.
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^m*b^m = (ab)^m

31. What is a ratio?

32. What are the median and the mode of a set of data?
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 - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

33. What are the sum - difference - products - and quotient of two numbers?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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.
V = l^3

34. In a circle of radius r - what is the formula for the circumference?
An integer greater than one that is not prime.
An equation that states that two ratios are equivalent. 4/6 = 10/15
C = p2r
A = (1/2)bh.

35. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
At least one of the factors is 0.
Then the quotient y/x is a constant.

36. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = lw
A = 6(l^2)

37. Law of exponents 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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
B^m/b^n = b^m-n
(x + y)(x - y) = x^2 - y^2

38. Law of exponents 1
An equation that states that two ratios are equivalent. 4/6 = 10/15
They are both the same. A divisor or factor of an integer leaves no remainder.
For any number n: x^-n means 1/x^n.
B^m*b^n = b^m+n

39. What is special formula for the area of an equilateral triangle?
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.
Set x = 0 - and solve.
A = [(s^2*v3)/4]
Arc = (x°/360)(2pr) where x is the central angle.

40. Important binomial 1
360°
Write the percent as a decimal - and multiply.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
(x + y)(x - y) = x^2 - y^2

41. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
For any number a: a * 1 = a and a / 1 = a.
Shifted up 2 units.
(b^m)^n = b^mn
0 is a multiple of every integer.

42. What is true about the areas of similar triangles?
For any number b: b = -b if and only if b = 0.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Their sum is 90°.
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°.

43. 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.
B^m*b^n = b^m+n
At least one of the factors is 0.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

44. What is the formula for the area of a rectangle?
For any right triangle - a^2 + b^2 = c^2.
A = lw
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
360°

45. What are the quotient and the remainder?

46. What is the formula for the volume of a rectangular solid?
Corresponding sides of similar triangles are in proportion.
An integer greater than one that is not prime.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
V = lwh

47. What is the volume of a cube?
V = l^3
1 is a divisor (or factor) of every integer.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

48. What do we mean by the slope of the line?
A^m/b^m = (a/b)^m
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.
All positive and negative whole numbers - and zero.

49. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
V = lwh
P(e) = (# of favorable outcomes)/(# of possible outcomes)
360°
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

50. 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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Corresponding sides of similar triangles are in proportion.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.