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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.
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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?
Write the percent as a decimal - and multiply.
D = 2r
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.
1 is the smallest positive odd integer.

2. For what values of a function is the function undefined?
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.
D = 2r
[(x1 + x2)/2] -[(y1 + y2)/2]
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

3. What is a negative exponent?
Corresponding sides of similar triangles are in proportion.
For any number n: x^-n means 1/x^n.
For any number a: a * 1 = a and a / 1 = a.
Divide - then multiply by 100.

4. What is the square root of a number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = bh
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
D = 2r

5. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
(b^m)^n = b^mn
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
M = (y2 - y1)/(x2 - x1)

6. What is the formula for the volume of a cylinder?
For any right triangle - a^2 + b^2 = c^2.
For any number a: a * 1 = a and a / 1 = a.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
V = pr^2h

7. What are the median and the mode of a set of data?
Even numbers are divisible by 2 and odd numbers are not.
Their sum is 90°.
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.

8. How do you convert a percent to a fraction or a decimal?
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.
At least one of the factors is 0.
Write the percent over 100 and reduce.
Shifted down 2 units.

9. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
360°
The set of all ordered pairs (x -y) such that y = f(x).
Shifted left 2 units.

10. What is true about the measures of the four angles formed by two intersecting lines?
Is a right triangle with a ratio of sides x:xv3:2x.
180°. If two or more angles form a straight angle - their sum is 180°.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The two pairs of opposite angles formed are equal to each other.

11. Law of exponents 5
A = 2(lw + lh + hw)
A^m/b^m = (a/b)^m
No matter how many angles there are - the sum around the point is 360°.
Shifted left 2 units.

12. What is a composite number?
An integer greater than one that is not prime.
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.
At least one of the factors is 0.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

13. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A = [(s^2*v3)/4]
V = pr^2h
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

14. Properties of zero 2
The product of their slopes is -1 (negative reciprocal).
A = pr^2
M = (y2 - y1)/(x2 - x1)
If a is negative and b is positive - then a < 0 < b.

15. What is the distributive law?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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.

16. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
C = p2r
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.

17. What is true about the measures of the three angles in a triangle?
A = 2(lw + lh + hw)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
180°. If two or more angles form a straight angle - their sum is 180°.
Their sum is 180°.

18. How do you find the y-intercept of a graph?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Set x = 0 - and solve.
M = (y2 - y1)/(x2 - x1)
V = lwh

19. What are the important properties of 30-60-90 triangle?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Is a right triangle with a ratio of sides x:xv3:2x.
A = bh
How steep the line is. Horizontal line = 0 - vertical has no slope.

20. What is the Pythagorean theorem?
Area = (x°/360)(pr^2) where x is the central angle.
Shifted right 2 units.
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any right triangle - a^2 + b^2 = c^2.

21. What is the probability of an event that cannot occur? That must occur?
Even numbers are divisible by 2 and odd numbers are not.
Cannot is 0 - must is 1 - all others are in between.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = [(s^2*v3)/4]

22. What is the formula for the volume of a rectangular solid?
A = s^2 or A =d^2/2 where d is the diagonal
Shifted down 2 units.
V = lwh
For any number a: a * 1 = a and a / 1 = a.

23. What is the formula for the area of a parallelogram?
0 is a multiple of every integer.
Then the quotient y/x is a constant.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A = bh

24. In a circle of radius r - what is the formula for the diameter?
An equation that states that two ratios are equivalent. 4/6 = 10/15
D = 2r
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Even numbers are divisible by 2 and odd numbers are not.

25. Properties of one 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.
No matter how many angles there are - the sum around the point is 360°.
For any integer n: 1^n = 1.
Cannot is 0 - must is 1 - all others are in between.

26. What does it mean if y is directly proportional to x?
M = (y2 - y1)/(x2 - x1)
A^m/b^m = (a/b)^m
Shifted up 2 units.
Then the quotient y/x is a constant.

27. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
B^m/b^n = b^m-n
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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Shifted right 2 units.

28. 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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Then the quotient y/x is a constant.
Write the percent as a decimal - and multiply.

29. If you were given the graph of y = f(x) - what does f(a) represent?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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.
0 is a multiple of every integer.

30. Properties of zero 1
Then the quotient y/x is a constant.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
V = lwh
0 is the only number that is neither positive nor negative.

31. Properties of zero 4
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.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
180°. If two or more angles form a straight angle - their sum is 180°.

32. What important property do similar triangles have?
A = bh
Corresponding sides of similar triangles are in proportion.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

33. Properties of zero 5
Shifted down 2 units.
For any number b: b = -b if and only if b = 0.
0 is the only number that is neither positive nor negative.
Their sum is 180°.

34. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^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.
Their sum is 90°.
A = bh

35. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
0 is the only number that is neither positive nor negative.
Shifted down 2 units.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = bh

36. What is an exterior angle of a polygon?
A^m*b^m = (ab)^m
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.
V = pr^2h
An angle formed by extending the side of the polygon.

37. How do you find the length of an arc of a circle?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = lw
For any number b: b = -b if and only if b = 0.
Arc = (x°/360)(2pr) where x is the central angle.

38. How do you calculate percent increases and decreases?
Shifted down 2 units.
Set y = 0 - and solve.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Write the percent as a decimal - and multiply.

39. If the product of two or more numbers is 0 - what do you know about the numbers?
A = pr^2
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The set of all ordered pairs (x -y) such that y = f(x).
At least one of the factors is 0.

40. How do you find a percent of a number?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(b^m)^n = b^mn
A = bh
Write the percent as a decimal - and multiply.

41. What is the sum of the measures of the four angles in a quadrilateral?
For any right triangle - a^2 + b^2 = c^2.
In the expression x^b - x is the base and b is the exponent.
360°
Cannot is 0 - must is 1 - all others are in between.

42. Properties of one 4
How steep the line is. Horizontal line = 0 - vertical has no slope.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
An angle formed by extending the side of the polygon.
1 is the smallest positive odd integer.

43. What is true about the areas of similar triangles?
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°.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
1 is a divisor (or factor) of every integer.
Corresponding sides of similar triangles are in proportion.

44. What is a percent?
B^m/b^n = b^m-n
A fraction whose denominator is 100 i.e. 17% = 17/100
All positive and negative whole numbers - and zero.
Corresponding sides of similar triangles are in proportion.

45. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
The set of all ordered pairs (x -y) such that y = f(x).
An integer greater than one that is not prime.
Then the product xy is a constant.

46. Law of exponents 4
A^m*b^m = (ab)^m
No matter how many angles there are - the sum around the point is 360°.
Set x = 0 - and solve.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

47. How do you calculate a weighted average?
Shifted left 2 units.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = (1/2)bh.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

48. What formula is used for an average?
Shifted left 2 units.
Avg = sum of n numbers/n
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.

49. What is the area of a square?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = s^2 or A =d^2/2 where d is the diagonal
Shifted up 2 units.
A = bh

50. What are the important properties of a 45-45 - 90 triangle?
A^m/b^m = (a/b)^m
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
No matter how many angles there are - the sum around the point is 360°.
Shifted right 2 units.

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GRE Math: Facts

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