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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 true about the measures of the four angles formed by two intersecting lines?
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.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
The two pairs of opposite angles formed are equal to each other.

2. What is the volume of a cube?
For any number n: x^-n means 1/x^n.
V = l^3
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted left 2 units.

3. In a circle of radius r - what is the formula for the area?
For any integer n: 1^n = 1.
V = l^3
A = pr^2
Corresponding sides of similar triangles are in proportion.

4. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

5. What is the formula for the surface area of a cube?
An equation that states that two ratios are equivalent. 4/6 = 10/15
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.
A = 6(l^2)

6. What are the properties of a square?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
B^m/b^n = b^m-n
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.

7. What are the important properties of a 45-45 - 90 triangle?
V = pr^2h
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A^m/b^m = (a/b)^m
Their sum is 180°.

8. What is a divisor and a factor of an integer?
360°
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
They are both the same. A divisor or factor of an integer leaves no remainder.
V = l^3

9. What are the properties of a rectangle?
V = lwh
Their sum is 90°.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A^m/b^m = (a/b)^m

10. For what values of a function is the function undefined?
B^m*b^n = b^m+n
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

11. What are the median and the mode of a set of data?
An angle formed by extending the side of the polygon.
[(x1 + x2)/2] -[(y1 + y2)/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.
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.

12. What are the properties of a parallelogram?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Arc = (x°/360)(2pr) where x is the central angle.
For any integer n: 1^n = 1.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

13. What is an integer?
(Circumference/diameter) of a circle - or approximately 3.14.
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.
Then the product xy is a constant.

14. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = 6(l^2)
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

15. How do you find the y-intercept of a graph?
A = [(s^2*v3)/4]
[(x1 + x2)/2] -[(y1 + y2)/2]
Set x = 0 - and solve.
For any integer n: 1^n = 1.

16. Important binomial 3
0 is a multiple of every integer.
Area = (x°/360)(pr^2) where x is the central angle.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Their sum is 180°.

17. Properties of one 2
The two pairs of opposite angles formed are equal to each other.
Shifted left 2 units.
The set of all ordered pairs (x -y) such that y = f(x).
For any integer n: 1^n = 1.

18. What is the graph of a function?
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.
Divide - then multiply by 100.
The set of all ordered pairs (x -y) such that y = f(x).

19. What is true about the slopes of parallel lines?
Equal slopes.
360°
All positive and negative whole numbers - and zero.
C = p2r

20. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
An angle formed by extending the side of the polygon.
360°
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.

21. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Shifted down 2 units.
Divide - then multiply by 100.
A^m*b^m = (ab)^m

22. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
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.
1 is the smallest positive odd integer.
The set of all ordered pairs (x -y) such that y = f(x).

23. If the product of two or more numbers is 0 - what do you know about the numbers?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
At least one of the factors is 0.
An angle formed by extending the side of the polygon.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

24. What is the formula for the area of a rectangle?
A = 2(lw + lh + hw)
A = lw
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
The set of all ordered pairs (x -y) such that y = f(x).

25. What is a multiple of an integer?
Their sum is 180°.
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

26. What are the important properties of 30-60-90 triangle?
V = pr^2h
B^m*b^n = b^m+n
Is a right triangle with a ratio of sides x:xv3:2x.
A = [(s^2*v3)/4]

27. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Write the percent over 100 and reduce.

28. 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°.
Their sum is 180°.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
(n - 2)(180°)

29. How do you find the x-intercept of a graph?
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 y = 0 - and solve.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

30. What is the triangle inequality?
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.
V = l^3

31. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
Shifted down 2 units.
Set y = 0 - and solve.
An equation that states that two ratios are equivalent. 4/6 = 10/15

32. What are similar triangles?
For any number b: b = -b if and only if b = 0.
A = bh
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

33. What is a fractional exponent?
M = (y2 - y1)/(x2 - x1)
D = 2r
An integer greater than one that is not prime.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

34. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Even numbers are divisible by 2 and odd numbers are not.

35. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
[(x1 + x2)/2] -[(y1 + y2)/2]

36. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Avg = sum of n numbers/n
A fraction whose denominator is 100 i.e. 17% = 17/100
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.
Shifted down 2 units.

37. Important binomial 2
The set of all ordered pairs (x -y) such that y = f(x).
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Write the percent over 100 and reduce.
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°.

38. What is a prime number?
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°.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
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.
360°

39. Properties of zero 1
(n - 2)(180°)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
0 is the only number that is neither positive nor negative.
(b^m)^n = b^mn

40. How do you find the probability that an event will occur?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

41. Properties of one 3
1 is a divisor (or factor) of every integer.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = s^2 or A =d^2/2 where d is the diagonal

42. 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.
Set y = 0 - and solve.
Shifted up 2 units.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

43. Law of exponents 1
Their sum is 90°.
Is a right triangle with a ratio of sides x:xv3:2x.
B^m*b^n = b^m+n
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.

44. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
Their sum is 180°.
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.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

45. What is the formula for the volume of a cylinder?
An integer greater than one that is not prime.
V = pr^2h
Then the quotient y/x is a constant.
V = l^3

46. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
They are both the same. A divisor or factor of an integer leaves no remainder.
1 is a divisor (or factor) of every integer.
V = pr^2h

47. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
No matter how many angles there are - the sum around the point is 360°.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

48. Properties of zero 3
Write the percent over 100 and reduce.
Then the quotient y/x is a constant.
Set x = 0 - and solve.
0 is a multiple of every integer.

49. What is true about the areas of similar triangles?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
V = l^3
Equal slopes.
1 is the smallest positive odd integer.

50. What is true about the measures of the three angles in a triangle?
1 is the smallest positive odd integer.
Their sum is 180°.
Write the percent over 100 and reduce.
A fraction whose denominator is 100 i.e. 17% = 17/100