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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. Important binomial 1
Shifted right 2 units.
All positive and negative whole numbers - and zero.
(x + y)(x - y) = x^2 - y^2
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

2. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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°.
A = (1/2)bh.
A = pr^2

3. Properties of zero 5
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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.
For any number b: b = -b if and only if b = 0.

4. Important binomial 3
Area = (x°/360)(pr^2) where x is the central angle.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(n - 2)(180°)
A = 6(l^2)

5. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Their sum is 180°.
Corresponding sides of similar triangles are in proportion.
A = bh

6. What is an even and an odd number?
For any number a: a * 1 = a and a / 1 = a.
Even numbers are divisible by 2 and odd numbers are not.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = 2(lw + lh + hw)

7. How do you find the slope of a line?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any number n: x^-n means 1/x^n.
M = (y2 - y1)/(x2 - x1)
An equation that states that two ratios are equivalent. 4/6 = 10/15

8. What are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.

9. Law of exponents 5
An equation that states that two ratios are equivalent. 4/6 = 10/15
A^m/b^m = (a/b)^m
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.
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.

10. What is the area of a square?
A = 6(l^2)
The set of all ordered pairs (x -y) such that y = f(x).
Is a right triangle with a ratio of sides x:xv3:2x.
A = s^2 or A =d^2/2 where d is the diagonal

11. 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.
Equal slopes.
A^m/b^m = (a/b)^m
For any integer n: 1^n = 1.

12. What is a ratio?

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13. How do you find the area of a sector of a circle?
A = s^2 or A =d^2/2 where d is the diagonal
Area = (x°/360)(pr^2) where x is the central angle.
(b^m)^n = b^mn
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

14. What is true about the slopes of parallel lines?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Equal slopes.
(n - 2)(180°)
C = p2r

15. How do you convert a percent to a fraction or a decimal?
Shifted right 2 units.
Corresponding sides of similar triangles are in proportion.
Write the percent over 100 and reduce.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

16. What is true about the measures of the four angles formed by two intersecting lines?
The two pairs of opposite angles formed are equal to each other.
A = 6(l^2)
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.
Arc = (x°/360)(2pr) where x is the central angle.

17. Properties of zero 2
A^m*b^m = (ab)^m
If a is negative and b is positive - then a < 0 < b.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Shifted down 2 units.

18. If the product of two or more numbers is 0 - what do you know about the numbers?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
At least one of the factors is 0.
Then the product xy is a constant.

19. What does it mean if y is directly proportional to x?
A = 6(l^2)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Then the quotient y/x is a constant.
Cannot is 0 - must is 1 - all others are in between.

20. What is a percent?
C = p2r
Area = (x°/360)(pr^2) where x is the central angle.
A fraction whose denominator is 100 i.e. 17% = 17/100
Write the percent as a decimal - and multiply.

21. How you convert a fraction or a decimal to a percent?
An equation that states that two ratios are equivalent. 4/6 = 10/15
How steep the line is. Horizontal line = 0 - vertical has no slope.
Divide - then multiply by 100.
Their sum is 180°.

22. What is a multiple of an integer?
B^m/b^n = b^m-n
Avg = sum of n numbers/n
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.

23. What is the midpoint formula?
All positive and negative whole numbers - and zero.
Shifted left 2 units.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
[(x1 + x2)/2] -[(y1 + y2)/2]

24. What is the sum of the measures of the n angles of a polygon with n sides?
The set of all ordered pairs (x -y) such that y = f(x).
A^m*b^m = (ab)^m
D = 2r
(n - 2)(180°)

25. Properties of zero 4
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.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Shifted right 2 units.

26. What is the formula for the volume of a cylinder?
V = pr^2h
For any number a: a * 1 = a and a / 1 = a.
A = 6(l^2)
They are both the same. A divisor or factor of an integer leaves no remainder.

27. What does it mean if y is inversely proportional to x?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Then the product xy is a constant.
360°
A = (1/2)bh.

28. Properties of one 4
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Shifted up 2 units.
Area = (x°/360)(pr^2) where x is the central angle.
1 is the smallest positive odd integer.

29. Important binomial 2
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Shifted down 2 units.
Write the percent over 100 and reduce.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

30. What is the relationship between a radius of a circle and a line that is tangent to the circle?
0 is the only number that is neither positive nor negative.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = [(s^2*v3)/4]
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

31. 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.
Shifted down 2 units.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
For any right triangle - a^2 + b^2 = c^2.

32. Law of exponents 2
[(x1 + x2)/2] -[(y1 + y2)/2]
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
B^m/b^n = b^m-n
If a is negative and b is positive - then a < 0 < b.

33. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
For any number b: b = -b if and only if b = 0.
A = 6(l^2)
Shifted up 2 units.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

34. Properties of zero 3
A = 6(l^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.
0 is a multiple of every integer.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

35. What is p?
0 is the only number that is neither positive nor negative.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Set x = 0 - and solve.
(Circumference/diameter) of a circle - or approximately 3.14.

36. In a circle of radius r - what is the formula for the diameter?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
If a is negative and b is positive - then a < 0 < b.
D = 2r
A = bh

37. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
If a is negative and b is positive - then a < 0 < b.
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.
Set y = 0 - and solve.

38. What is the distributive law?
Corresponding sides of similar triangles are in proportion.
A = 6(l^2)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

39. What is the formula for the area of a rectangle?
A = lw
An integer greater than one that is not prime.
For any integer n: 1^n = 1.
V = lwh

40. What is a function?
Shifted right 2 units.
The ratio of corresponding sides of similar triangles.
360°
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

41. What is the Pythagorean theorem?
Then the product xy is a constant.
Even numbers are divisible by 2 and odd numbers are not.
For any right triangle - a^2 + b^2 = c^2.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

42. If you were given the graph of y = f(x) - what does f(a) represent?
1 is the smallest positive odd integer.
A = [(s^2*v3)/4]
Then the quotient y/x is a constant.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

43. What are similar triangles?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(n - 2)(180°)
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°.
Divide - then multiply by 100.

44. What is the formula for the area of a triangle?
How steep the line is. Horizontal line = 0 - vertical has no slope.
The set of all ordered pairs (x -y) such that y = f(x).
360°
A = (1/2)bh.

45. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
For any number b: b = -b if and only if b = 0.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

46. What important property do similar triangles have?
V = lwh
Corresponding sides of similar triangles are in proportion.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A^m*b^m = (ab)^m

47. Properties of zero 1
0 is the only number that is neither positive nor negative.
Equal slopes.
How steep the line is. Horizontal line = 0 - vertical has no slope.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

48. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
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.
A = 2(lw + lh + hw)

49. How do you find the x-intercept of a graph?
No matter how many angles there are - the sum around the point is 360°.
D = 2r
Their sum is 90°.
Set y = 0 - and solve.

50. What is true about the slopes of perpendicular lines?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
An angle formed by extending the side of the polygon.
The product of their slopes is -1 (negative reciprocal).
360°

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