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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 an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
Then the product xy is a constant.
The ratio of corresponding sides of similar triangles.
In the expression x^b - x is the base and b is the exponent.

2. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
1 is a divisor (or factor) of every integer.
Set x = 0 - and solve.
In the expression x^b - x is the base and b is the exponent.

3. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
0 is a multiple of every integer.

4. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Even numbers are divisible by 2 and odd numbers are not.
Is a right triangle with a ratio of sides x:xv3:2x.
360°
(x + y)(x - y) = x^2 - y^2

5. Law of exponents 5
If a is negative and b is positive - then a < 0 < b.
In the expression x^b - x is the base and b is the exponent.
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

6. What is the midpoint formula?
For any number b: b = -b if and only if b = 0.
V = lwh
Their sum is 90°.
[(x1 + x2)/2] -[(y1 + y2)/2]

7. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
Shifted right 2 units.
In the expression x^b - x is the base and b is the exponent.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

8. What important property do similar triangles have?
V = lwh
A = 6(l^2)
Their sum is 90°.
Corresponding sides of similar triangles are in proportion.

9. What is an even and an odd number?
An integer greater than one that is not prime.
(Circumference/diameter) of a circle - or approximately 3.14.
Then the product xy is a constant.
Even numbers are divisible by 2 and odd numbers are not.

10. What are the sum - difference - products - and quotient of two numbers?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = lw

11. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Shifted down 2 units.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = [(s^2*v3)/4]

12. Properties of one 3
Corresponding sides of similar triangles are in proportion.
1 is a divisor (or factor) of every integer.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

13. What is the relationship between a radius of a circle and a line that is tangent to the circle?
B^m/b^n = b^m-n
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

14. What is true about the areas of similar triangles?
Corresponding sides of similar triangles are in proportion.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Set y = 0 - and solve.

15. Properties of one 4
1 is the smallest positive odd integer.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
At least one of the factors is 0.

16. How do you calculate percent increases and decreases?
A fraction whose denominator is 100 i.e. 17% = 17/100
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
360°
For any number a: a * 1 = a and a / 1 = a.

17. What is a negative exponent?
A = lw
For any number n: x^-n means 1/x^n.
Shifted down 2 units.
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.

18. How do you find the length of an arc of a circle?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Shifted right 2 units.
Arc = (x°/360)(2pr) where x is the central angle.

19. In a circle of radius r - what is the formula for the area?
A = pr^2
Their sum is 90°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

20. What are the properties of a parallelogram?
V = l^3
A = 2(lw + lh + hw)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
(x + y)(x - y) = x^2 - y^2

21. Law of exponents 1
The product of their slopes is -1 (negative reciprocal).
A = bh
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.

22. What is a ratio?

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23. What is the formula for the area of a parallelogram?
Is a right triangle with a ratio of sides x:xv3:2x.
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 fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = bh

24. What is an integer?
A fraction whose denominator is 100 i.e. 17% = 17/100
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
All positive and negative whole numbers - and zero.
360°

25. Properties of zero 4
All positive and negative whole numbers - and zero.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
The ratio of corresponding sides of similar triangles.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

26. Properties of square roots
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
[(x1 + x2)/2] -[(y1 + y2)/2]

27. What is true about the measures of the three angles in a triangle?
Shifted left 2 units.
Their sum is 180°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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.

28. Law of exponents 3
A fraction whose denominator is 100 i.e. 17% = 17/100
Write the percent as a decimal - and multiply.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(b^m)^n = b^mn

29. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
360°
A = pr^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

30. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
A = [(s^2*v3)/4]
At least one of the factors is 0.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

31. What does it mean if y is inversely proportional to x?
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
Then the product xy is a constant.
Then the quotient y/x is a constant.

32. What is the probability of an event that cannot occur? That must occur?
180°. If two or more angles form a straight angle - their sum is 180°.
Cannot is 0 - must is 1 - all others are in between.
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.

33. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
180°. If two or more angles form a straight angle - their sum is 180°.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Shifted right 2 units.
Shifted left 2 units.

34. Law of exponents 2
Corresponding sides of similar triangles are in proportion.
B^m/b^n = b^m-n
(n - 2)(180°)
Avg = sum of n numbers/n

35. Law of exponents 4
C = p2r
No matter how many angles there are - the sum around the point is 360°.
A^m*b^m = (ab)^m
For any number b: b = -b if and only if b = 0.

36. What is a prime number?
V = lwh
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A fraction whose denominator is 100 i.e. 17% = 17/100
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.

37. How do you find the slope of a line?
A = pr^2
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.
M = (y2 - y1)/(x2 - x1)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

38. What is a composite number?
V = l^3
In the expression x^b - x is the base and b is the exponent.
Shifted right 2 units.
An integer greater than one that is not prime.

39. What is a percent?
A^m/b^m = (a/b)^m
A fraction whose denominator is 100 i.e. 17% = 17/100
A = bh
The ratio of corresponding sides of similar triangles.

40. What is true about the slopes of perpendicular lines?
Write the percent over 100 and reduce.
The product of their slopes is -1 (negative reciprocal).
A = pr^2
Arc = (x°/360)(2pr) where x is the central angle.

41. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
The set of all ordered pairs (x -y) such that y = f(x).
Shifted up 2 units.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
For any integer n: 1^n = 1.

42. Important binomial 1
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(x + y)(x - y) = x^2 - y^2
C = p2r
Then the quotient y/x is a constant.

43. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A = (1/2)bh.
V = pr^2h
A fraction whose denominator is 100 i.e. 17% = 17/100

44. What do we mean by the slope of the line?
For any number b: b = -b if and only if b = 0.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = 2(lw + lh + hw)
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

45. What is the formula for the area of a triangle?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
[(x1 + x2)/2] -[(y1 + y2)/2]
A = (1/2)bh.
B^m/b^n = b^m-n

46. Important binomial 3
An angle formed by extending the side of the polygon.
360°
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(n - 2)(180°)

47. 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.
0 is a multiple of every integer.
Shifted down 2 units.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

48. What are the median and the mode of a set of data?
No matter how many angles there are - the sum around the point is 360°.
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = (1/2)bh.

49. What is true about the measures of the two acute angles in a right triangle?
A^m*b^m = (ab)^m
C = p2r
Their sum is 90°.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

50. If the product of two or more numbers is 0 - what do you know about the numbers?
Set x = 0 - and solve.
At least one of the factors is 0.
1 is a divisor (or factor) of every integer.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

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