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GRE Math: Facts

Subjects : gre, math

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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. Properties of zero 2
Shifted down 2 units.
1 is a divisor (or factor) of every integer.
If a is negative and b is positive - then a < 0 < b.
C = p2r

2. In a circle of radius r - what is the formula for the area?
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.
A = pr^2
Shifted up 2 units.
Write the percent over 100 and reduce.

3. What is the Pythagorean theorem?
(Circumference/diameter) of a circle - or approximately 3.14.
For any right triangle - a^2 + b^2 = c^2.
Divide - then multiply by 100.
For any number n: x^-n means 1/x^n.

4. What is the formula for the area of a parallelogram?
At least one of the factors is 0.
A = lw
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = bh

5. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Set y = 0 - and solve.
A = (1/2)bh.
V = lwh

6. What are the sum - difference - products - and quotient of two numbers?
They are both the same. A divisor or factor of an integer leaves no remainder.
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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
360°

7. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Set x = 0 - and solve.
Shifted left 2 units.
For any number b: b = -b if and only if b = 0.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

8. What is an exterior angle of a polygon?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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°.
They are both the same. A divisor or factor of an integer leaves no remainder.
An angle formed by extending the side of the polygon.

9. What are the important properties of 30-60-90 triangle?
B^m/b^n = b^m-n
Arc = (x°/360)(2pr) where x is the central angle.
Is a right triangle with a ratio of sides x:xv3:2x.
They are both the same. A divisor or factor of an integer leaves no remainder.

10. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
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°.
Shifted up 2 units.
A = s^2 or A =d^2/2 where d is the diagonal
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

11. What is the probability of an event that cannot occur? That must occur?
A^m/b^m = (a/b)^m
(n - 2)(180°)
Cannot is 0 - must is 1 - all others are in between.
A = [(s^2*v3)/4]

12. What is the sum of the measures of the n angles of a polygon with n sides?
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°.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(n - 2)(180°)
(b^m)^n = b^mn

13. What do we mean by the slope of the line?
A = s^2 or A =d^2/2 where d is the diagonal
0 is a multiple of every integer.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Shifted left 2 units.

14. What is a proportion?
(x + y)(x - y) = x^2 - y^2
For any number b: b = -b if and only if b = 0.
An equation that states that two ratios are equivalent. 4/6 = 10/15
360°

15. How do you find the area of a sector of a circle?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
0 is the only number that is neither positive nor negative.
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.
Area = (x°/360)(pr^2) where x is the central angle.

16. What are the properties of a square?
A = (1/2)bh.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(n - 2)(180°)
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.

17. Properties of zero 5
Divide - then multiply by 100.
[(x1 + x2)/2] -[(y1 + y2)/2]
For any number b: b = -b if and only if b = 0.
How steep the line is. Horizontal line = 0 - vertical has no slope.

18. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
All positive and negative whole numbers - and zero.
360°
0 is the only number that is neither positive nor negative.

19. What is the sum of the measures of all angles around a point?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
No matter how many angles there are - the sum around the point is 360°.
0 is the only number that is neither positive nor negative.
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.

20. How do you convert a percent to a fraction or a decimal?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
C = p2r
Write the percent over 100 and reduce.
Shifted left 2 units.

21. Properties of zero 1
An integer greater than one that is not prime.
180°. If two or more angles form a straight angle - their sum is 180°.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
0 is the only number that is neither positive nor negative.

22. How do you find the probability that an event will occur?
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)
0 is the only number that is neither positive nor negative.
Then the quotient y/x is a constant.

23. Properties of one 3
They are both the same. A divisor or factor of an integer leaves no remainder.
(b^m)^n = b^mn
1 is a divisor (or factor) of every integer.
A fraction whose denominator is 100 i.e. 17% = 17/100

24. Important binomial 2
No matter how many angles there are - the sum around the point is 360°.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Then the quotient y/x is a constant.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

25. If you were given the graph of y = f(x) - what does f(a) represent?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = bh
An equation that states that two ratios are equivalent. 4/6 = 10/15

26. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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 whose denominator is 100 i.e. 17% = 17/100
V = pr^2h
A = pr^2

27. How do you find the y-intercept of a graph?
A = 2(lw + lh + hw)
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.
Set x = 0 - and solve.

28. Law of exponents 4
Set y = 0 - and solve.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A^m*b^m = (ab)^m
Divide - then multiply by 100.

29. Properties of one 1
The ratio of corresponding sides of similar triangles.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any number a: a * 1 = a and a / 1 = a.
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.

30. What are the properties of a rectangle?
Area = (x°/360)(pr^2) where x is the central angle.
Even numbers are divisible by 2 and odd numbers are not.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
360°

31. What is the formula for the surface area of a rectangular solid?
A^m/b^m = (a/b)^m
A = lw
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = 2(lw + lh + hw)

32. What is the formula for the surface area of a cube?
A = 6(l^2)
360°
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = lw

33. What is a prime number?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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.
Shifted right 2 units.

34. How do we write the equation of a line?
Their sum is 90°.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
They are both the same. A divisor or factor of an integer leaves no remainder.
If a is negative and b is positive - then a < 0 < b.

35. What is the volume of a cube?
Cannot is 0 - must is 1 - all others are in between.
Divide - then multiply by 100.
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 = l^3

36. How do you find a percent of a number?
A = (1/2)bh.
Write the percent as a decimal - and multiply.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Arc = (x°/360)(2pr) where x is the central angle.

37. What is the graph of a function?
If a is negative and b is positive - then a < 0 < b.
For any right triangle - a^2 + b^2 = c^2.
B^m*b^n = b^m+n
The set of all ordered pairs (x -y) such that y = f(x).

38. Properties of zero 3
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
0 is a multiple of every integer.
B^m/b^n = b^m-n
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

39. What is an exponent?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
0 is the only number that is neither positive nor negative.
Their sum is 90°.
In the expression x^b - x is the base and b is the exponent.

40. What is the relationship between a radius of a circle and a line that is tangent to the circle?
A^m/b^m = (a/b)^m
An integer greater than one that is not prime.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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.

41. How do you find the slope of a line?
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.
If a is negative and b is positive - then a < 0 < b.
M = (y2 - y1)/(x2 - x1)
A = [(s^2*v3)/4]

42. How you convert a fraction or a decimal to a percent?
360°
(Circumference/diameter) of a circle - or approximately 3.14.
Divide - then multiply by 100.
For any number b: b = -b if and only if b = 0.

43. What are the properties of a parallelogram?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
If a is negative and b is positive - then a < 0 < b.
A = 6(l^2)

44. What is p?
Shifted right 2 units.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A = 6(l^2)
(Circumference/diameter) of a circle - or approximately 3.14.

45. How do you find the length of an arc of a circle?
V = lwh
At least one of the factors is 0.
Then the quotient y/x is a constant.
Arc = (x°/360)(2pr) where x is the central angle.

46. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^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.
Set x = 0 - and solve.
A = 6(l^2)

47. What is true about the measures of the four angles formed by two intersecting lines?
Shifted right 2 units.
An equation that states that two ratios are equivalent. 4/6 = 10/15
The two pairs of opposite angles formed are equal to each other.
Shifted down 2 units.

48. What is the sum of the measures of the four angles in a quadrilateral?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
360°
1 is the smallest positive odd integer.
0 is the only number that is neither positive nor negative.

49. What is the midpoint formula?
An equation that states that two ratios are equivalent. 4/6 = 10/15
A fraction whose denominator is 100 i.e. 17% = 17/100
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
[(x1 + x2)/2] -[(y1 + y2)/2]

50. What is a multiple of an integer?
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.
Their sum is 180°.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

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