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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 an exterior angle of a 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
A^m/b^m = (a/b)^m
(x + y)(x - y) = x^2 - y^2

2. What are the quotient and the remainder?

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3. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
360°
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.
Equal slopes.

4. What are the properties of a parallelogram?
Set y = 0 - and solve.
An integer greater than one that is not prime.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

5. What does it mean if y is directly proportional to x?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Then the quotient y/x is a constant.

6. What is an exterior angle of a polygon?
C = p2r
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
B^m*b^n = b^m+n
An angle formed by extending the side of the polygon.

7. What is the formula for the area of a parallelogram?
No matter how many angles there are - the sum around the point is 360°.
The set of all ordered pairs (x -y) such that y = f(x).
A = bh
In the expression x^b - x is the base and b is the exponent.

8. How do you calculate a weighted average?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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°.
0 is a multiple of every integer.

9. How do you find the y-intercept of a graph?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A^m/b^m = (a/b)^m
Set x = 0 - and solve.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

10. In a circle of radius r - what is the formula for the area?
360°
A = pr^2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

11. Important binomial 3
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(n - 2)(180°)
The product of their slopes is -1 (negative reciprocal).

12. What are the properties of a rectangle?
(Circumference/diameter) of a circle - or approximately 3.14.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

13. How you convert a fraction or a decimal to a percent?
Avg = sum of n numbers/n
Divide - then multiply by 100.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = 2(lw + lh + hw)

14. 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.
No matter how many angles there are - the sum around the point is 360°.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

15. Properties of zero 3
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.
0 is a multiple of every integer.
Then the product xy is a constant.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

16. What is a prime number?
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 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
Is a right triangle with a ratio of sides x:xv3:2x.

17. What formula is used for an average?
The product of their slopes is -1 (negative reciprocal).
Their sum is 180°.
Avg = sum of n numbers/n
A = s^2 or A =d^2/2 where d is the diagonal

18. What is p?
For any integer n: 1^n = 1.
V = l^3
Avg = sum of n numbers/n
(Circumference/diameter) of a circle - or approximately 3.14.

19. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
V = pr^2h
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. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
(n - 2)(180°)
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

21. Law of exponents 5
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A^m/b^m = (a/b)^m
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

22. What is a divisor and a factor of an integer?
They are both the same. A divisor or factor of an integer leaves no remainder.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For any right triangle - a^2 + b^2 = c^2.
The product of their slopes is -1 (negative reciprocal).

23. What is a composite number?
D = 2r
A = lw
An integer greater than one that is not prime.
360°

24. What is the sum of the measures of all angles around a point?
No matter how many angles there are - the sum around the point is 360°.
Their sum is 90°.
All positive and negative whole numbers - and zero.
B^m*b^n = b^m+n

25. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.
(Circumference/diameter) of a circle - or approximately 3.14.

26. What are the sum - difference - products - and quotient of two numbers?
V = lwh
A^m*b^m = (ab)^m
M = (y2 - y1)/(x2 - x1)
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

27. How do you calculate percent increases and decreases?
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.
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.

28. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
An integer greater than one that is not prime.
D = 2r
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

29. What is the distance formula?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
An integer greater than one that is not prime.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

30. What is a percent?
An equation that states that two ratios are equivalent. 4/6 = 10/15
The ratio of corresponding sides of similar triangles.
If a is negative and b is positive - then a < 0 < b.
A fraction whose denominator is 100 i.e. 17% = 17/100

31. Properties of zero 2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
If a is negative and b is positive - then a < 0 < b.
Set y = 0 - and solve.

32. Law of exponents 1
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
1 is the smallest positive odd integer.
B^m*b^n = b^m+n
A = pr^2

33. What is the area of a square?
A^m*b^m = (ab)^m
A = s^2 or A =d^2/2 where d is the diagonal
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.

34. What is the formula for the volume of a cylinder?
A = [(s^2*v3)/4]
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
V = pr^2h

35. For what values of a function is the function undefined?
All positive and negative whole numbers - and zero.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
360°
D = 2r

36. How do you find the probability that an event will occur?
For any integer n: 1^n = 1.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
An angle formed by extending the side of the polygon.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

37. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

38. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Shifted right 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

39. What is the volume of a cube?
Shifted up 2 units.
A = lw
V = l^3
A = [(s^2*v3)/4]

40. What are the properties of a square?
A fraction whose denominator is 100 i.e. 17% = 17/100
At least one of the factors is 0.
M = (y2 - y1)/(x2 - x1)
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 important property do similar triangles have?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Corresponding sides of similar triangles are in proportion.
An angle formed by extending the side of the polygon.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

42. What is an integer?
All positive and negative whole numbers - and zero.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Arc = (x°/360)(2pr) where x is the central angle.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

43. If you were given the graph of y = f(x) - what does f(a) represent?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
1 is a divisor (or factor) of every integer.
A fraction whose denominator is 100 i.e. 17% = 17/100
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 midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = [(s^2*v3)/4]
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.

45. What is the formula for the volume of a rectangular solid?
They are both the same. A divisor or factor of an integer leaves no remainder.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
V = lwh
The ratio of corresponding sides of similar triangles.

46. If the product of two or more numbers is 0 - what do you know about the numbers?
At least one of the factors is 0.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Cannot is 0 - must is 1 - all others are in between.
Set y = 0 - and solve.

47. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
If a is negative and b is positive - then a < 0 < b.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

48. Important binomial 2
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
No matter how many angles there are - the sum around the point is 360°.
Shifted up 2 units.

49. What is the sum of the measures of the four angles in a quadrilateral?
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.
V = pr^2h
360°
A = [(s^2*v3)/4]

50. Important binomial 1
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°.
(x + y)(x - y) = x^2 - y^2
For any number a: a * 1 = a and a / 1 = a.