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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 formula is used for an average?
V = l^3
B^m/b^n = b^m-n
Avg = sum of n numbers/n
A = lw

2. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
0 is the only number that is neither positive nor negative.
For any integer n: 1^n = 1.

3. Properties of one 2
Is a right triangle with a ratio of sides x:xv3:2x.
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.
In the expression x^b - x is the base and b is the exponent.
For any integer n: 1^n = 1.

4. What is a ratio?

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5. What is the formula for the area of a parallelogram?
Shifted left 2 units.
C = p2r
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = bh

6. What is the formula for the surface area of a rectangular solid?
Their sum is 180°.
In the expression x^b - x is the base and b is the exponent.
A = 2(lw + lh + hw)
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

7. What is a negative exponent?
D = 2r
For any number n: x^-n means 1/x^n.
V = lwh
Their sum is 90°.

8. What is the formula for the surface area of a cube?
180°. If two or more angles form a straight angle - their sum is 180°.
A = lw
Their sum is 180°.
A = 6(l^2)

9. What is the formula for the area of a triangle?
A = (1/2)bh.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
The ratio of corresponding sides of similar triangles.

10. What is a fractional exponent?
A = (1/2)bh.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = lw
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

11. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Shifted left 2 units.
0 is a multiple of every integer.
(x + y)(x - y) = x^2 - y^2

12. What is a divisor and a factor of an integer?
A = bh
360°
They are both the same. A divisor or factor of an integer leaves no remainder.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

13. Properties of zero 3
The two pairs of opposite angles formed are equal to each other.
0 is a multiple of every integer.
A = [(s^2*v3)/4]
For any number n: x^-n means 1/x^n.

14. How do you calculate a weighted average?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Their sum is 180°.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
The set of all ordered pairs (x -y) such that y = f(x).

15. Properties of zero 4
0 is the only number that is neither positive nor negative.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Avg = sum of n numbers/n
For any integer n: 1^n = 1.

16. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
An integer greater than one that is not prime.
Shifted right 2 units.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
B^m/b^n = b^m-n

17. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
V = lwh
The set of all ordered pairs (x -y) such that y = f(x).
The ratio of corresponding sides of similar triangles.
Shifted down 2 units.

18. What is the sum of the measures of all angles around a point?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
In the expression x^b - x is the base and b is the exponent.
For any number a: a * 1 = a and a / 1 = a.
No matter how many angles there are - the sum around the point is 360°.

19. Law of exponents 1
A = s^2 or A =d^2/2 where d is the diagonal
B^m*b^n = b^m+n
At least one of the factors is 0.
For any right triangle - a^2 + b^2 = c^2.

20. How do you find the area of a sector of a circle?
360°
Area = (x°/360)(pr^2) where x is the central angle.
Divide - then multiply by 100.
For any integer n: 1^n = 1.

21. What is the area of a square?
(x + y)(x - y) = x^2 - y^2
Divide - then multiply by 100.
A = pr^2
A = s^2 or A =d^2/2 where d is the diagonal

22. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
B^m/b^n = b^m-n
A = (1/2)bh.
0 is the only number that is neither positive nor negative.

23. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
In the expression x^b - x is the base and b is the exponent.
Shifted up 2 units.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

24. What is a prime number?
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.
An angle formed by extending the side of the polygon.
1 is a divisor (or factor) of every integer.
180°. If two or more angles form a straight angle - their sum is 180°.

25. What is a function?
360°
1 is a divisor (or factor) of every integer.
M = (y2 - y1)/(x2 - x1)
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

26. What is the formula for the volume of a cylinder?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Write the percent over 100 and reduce.
V = pr^2h
1 is a divisor (or factor) of every integer.

27. In a circle of radius r - what is the formula for the circumference?
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.
C = p2r
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.

28. What is the square root of a number?
A = s^2 or A =d^2/2 where d is the diagonal
V = lwh
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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

29. How do you find the y-intercept of a graph?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Their sum is 90°.
Set x = 0 - and solve.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

30. What is an even and an odd number?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
V = lwh
Even numbers are divisible by 2 and odd numbers are not.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

31. Law of exponents 4
A^m*b^m = (ab)^m
0 is the only number that is neither positive nor negative.
A = 6(l^2)
A = pr^2

32. Properties of zero 5
A^m/b^m = (a/b)^m
Even numbers are divisible by 2 and odd numbers are not.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any number b: b = -b if and only if b = 0.

33. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
All positive and negative whole numbers - and zero.
Shifted left 2 units.
Avg = sum of n numbers/n

34. What is the triangle inequality?
For any number n: x^-n means 1/x^n.
Equal slopes.
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 a is negative and b is positive - then a < 0 < b.

35. What is the Pythagorean theorem?
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
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any right triangle - a^2 + b^2 = c^2.

36. 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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Arc = (x°/360)(2pr) where x is the central angle.
A fraction whose denominator is 100 i.e. 17% = 17/100

37. 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.
They are both the same. A divisor or factor of an integer leaves no remainder.
Their sum is 90°.
(Circumference/diameter) of a circle - or approximately 3.14.

38. What is a percent?
The set of all ordered pairs (x -y) such that y = f(x).
Set x = 0 - and solve.
Set y = 0 - and solve.
A fraction whose denominator is 100 i.e. 17% = 17/100

39. What is true about the measures of the four angles formed by two intersecting lines?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The two pairs of opposite angles formed are equal to each other.
A = pr^2
D = 2r

40. Properties of one 3
1 is a divisor (or factor) of every integer.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
0 is the only number that is neither positive nor negative.

41. What is an exponent?
(n - 2)(180°)
A = [(s^2*v3)/4]
In the expression x^b - x is the base and b is the exponent.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

42. What is an exterior angle of a polygon?
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.
(n - 2)(180°)
V = l^3

43. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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°.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

44. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Arc = (x°/360)(2pr) where x is the central angle.
A = 6(l^2)
Then the quotient y/x is a constant.
360°

45. Properties of zero 1
0 is the only number that is neither positive nor negative.
1 is the smallest positive odd integer.
(Circumference/diameter) of a circle - or approximately 3.14.
Their sum is 180°.

46. What is true about the areas of similar triangles?
A = lw
The two pairs of opposite angles formed are equal to each other.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Their sum is 180°.

47. What are the properties of a rectangle?
Arc = (x°/360)(2pr) where x is the central angle.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

48. What is true about the slopes of parallel lines?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Write the percent over 100 and reduce.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Equal slopes.

49. What is true about the measures of the two acute angles in a right triangle?
M = (y2 - y1)/(x2 - x1)
Set x = 0 - and solve.
Equal slopes.
Their sum is 90°.

50. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
360°
For any number n: x^-n means 1/x^n.
V = lwh