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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 are the properties of a parallelogram?
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Is a right triangle with a ratio of sides x:xv3:2x.

2. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
(x + y)(x - y) = x^2 - y^2
A = 2(lw + lh + hw)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

3. What is the relationship between a radius of a circle and a line that is tangent to the circle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Shifted up 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Set y = 0 - and solve.

4. What are the important properties of a 45-45 - 90 triangle?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Write the percent over 100 and reduce.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Their sum is 180°.

5. What is p?
180°. If two or more angles form a straight angle - their sum is 180°.
D = 2r
(Circumference/diameter) of a circle - or approximately 3.14.
Equal slopes.

6. What are similar triangles?
For any integer n: 1^n = 1.
Write the percent over 100 and reduce.
V = l^3
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

7. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
If a is negative and b is positive - then a < 0 < b.

8. How do you find the x-intercept of a graph?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Then the quotient y/x is a constant.
Set y = 0 - and solve.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

9. Properties of zero 5
A^m*b^m = (ab)^m
For any number b: b = -b if and only if b = 0.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

10. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
They are both the same. A divisor or factor of an integer leaves no remainder.
1 is a divisor (or factor) of every integer.
For any number a: a * 1 = a and a / 1 = a.

11. What is the distributive law?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Avg = sum of n numbers/n
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
For any number n: x^-n means 1/x^n.

12. What is a prime number?
A = lw
0 is the only number that is neither positive nor negative.
360°
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.

13. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
Shifted right 2 units.
Cannot is 0 - must is 1 - all others are in between.
In the expression x^b - x is the base and b is the exponent.

14. In a circle of radius r - what is the formula for the area?
A = pr^2
Avg = sum of n numbers/n
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.
Then the product xy is a constant.

15. What is an exterior angle of a triangle?
A = 6(l^2)
Set y = 0 - and solve.
A = [(s^2*v3)/4]
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

16. What is the midpoint formula?
Area = (x°/360)(pr^2) where x is the central angle.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.
[(x1 + x2)/2] -[(y1 + y2)/2]

17. How do you calculate a weighted average?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Even numbers are divisible by 2 and odd numbers are not.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
M = (y2 - y1)/(x2 - x1)

18. If you were given the graph of y = f(x) - what does f(a) represent?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
180°. If two or more angles form a straight angle - their sum is 180°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
An angle formed by extending the side of the polygon.

19. What is the formula for the volume of a cylinder?
V = pr^2h
A = 6(l^2)
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
For any integer n: 1^n = 1.

20. Law of exponents 5
Shifted up 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.
A^m/b^m = (a/b)^m
A = 2(lw + lh + hw)

21. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
The product of their slopes is -1 (negative reciprocal).
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

22. What is an even and an odd number?
An integer greater than one that is not prime.
Shifted down 2 units.
Even numbers are divisible by 2 and odd numbers are not.
A = 2(lw + lh + hw)

23. In a circle of radius r - what is the formula for the diameter?
D = 2r
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.
A = 2(lw + lh + hw)
For any number b: b = -b if and only if b = 0.

24. What is true about the measures of the three angles in a triangle?
For any number b: b = -b if and only if b = 0.
A = (1/2)bh.
Their sum is 180°.
Write the percent over 100 and reduce.

25. How do you find a percent of a number?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
M = (y2 - y1)/(x2 - x1)
Write the percent as a decimal - and multiply.
The set of all ordered pairs (x -y) such that y = f(x).

26. What is a multiple of an integer?
(Circumference/diameter) of a circle - or approximately 3.14.
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.
Write the percent as a decimal - and multiply.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

27. What is the distance formula?
V = l^3
1 is a divisor (or factor) of every integer.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
The set of all ordered pairs (x -y) such that y = f(x).

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.
Shifted right 2 units.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

29. Law of exponents 2
Equal slopes.
They are both the same. A divisor or factor of an integer leaves no remainder.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
B^m/b^n = b^m-n

30. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
An angle formed by extending the side of the polygon.
D = 2r
Corresponding sides of similar triangles are in proportion.

31. For what values of a function is the function undefined?
(Circumference/diameter) of a circle - or approximately 3.14.
Then the product xy is a constant.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
The ratio of corresponding sides of similar triangles.

32. What is an exponent?
Their sum is 180°.
In the expression x^b - x is the base and b is the exponent.
B^m*b^n = b^m+n
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

33. What is the formula for the surface area of a cube?
1 is a divisor (or factor) of every integer.
A = 6(l^2)
Then the quotient y/x is a constant.
An equation that states that two ratios are equivalent. 4/6 = 10/15

34. What is a negative exponent?
A^m*b^m = (ab)^m
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For any integer n: 1^n = 1.
For any number n: x^-n means 1/x^n.

35. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
0 is the only number that is neither positive nor negative.
Equal slopes.
(Circumference/diameter) of a circle - or approximately 3.14.

36. What are the quotient and the remainder?

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37. Properties of zero 4
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Set y = 0 - and solve.

38. How do you calculate percent increases and decreases?
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
V = l^3

39. What is the formula for the area of a rectangle?
A = lw
At least one of the factors is 0.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Avg = sum of n numbers/n

40. Important binomial 3
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
A fraction whose denominator is 100 i.e. 17% = 17/100
The ratio of corresponding sides of similar triangles.

41. What is a composite number?
A fraction whose denominator is 100 i.e. 17% = 17/100
360°
An integer greater than one that is not prime.
(n - 2)(180°)

42. What is a percent?
Set y = 0 - and solve.
A fraction whose denominator is 100 i.e. 17% = 17/100
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.

43. What is true about the measures of the four angles formed by two intersecting lines?
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.
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.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

44. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = 2(lw + lh + hw)
Is a right triangle with a ratio of sides x:xv3:2x.
An angle formed by extending the side of the polygon.

45. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

46. Properties of zero 1
0 is the only number that is neither positive nor negative.
A = s^2 or A =d^2/2 where d is the diagonal
How steep the line is. Horizontal line = 0 - vertical has no slope.
D = 2r

47. What does it mean if y is directly proportional to x?
The product of their slopes is -1 (negative reciprocal).
Shifted left 2 units.
Then the quotient y/x is a constant.
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.

48. What is an integer?
[(x1 + x2)/2] -[(y1 + y2)/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.
All positive and negative whole numbers - and zero.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

49. What is the formula for the area of a triangle?
180°. If two or more angles form a straight angle - their sum is 180°.
A = (1/2)bh.
An equation that states that two ratios are equivalent. 4/6 = 10/15
V = pr^2h

50. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Cannot is 0 - must is 1 - all others are in between.
Shifted right 2 units.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
An angle formed by extending the side of the polygon.