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GRE Math: Facts

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. 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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = (1/2)bh.
V = pr^2h

2. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For any right triangle - a^2 + b^2 = c^2.

3. How do you convert a percent to a fraction or a decimal?
V = l^3
Even numbers are divisible by 2 and odd numbers are not.
Write the percent over 100 and reduce.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

4. How do you find the y-intercept of a graph?
[(x1 + x2)/2] -[(y1 + y2)/2]
Divide - then multiply by 100.
They are both the same. A divisor or factor of an integer leaves no remainder.
Set x = 0 - and solve.

5. What is a ratio?

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6. What are the median and the mode of a set of data?
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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
The product of their slopes is -1 (negative reciprocal).

7. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
(Circumference/diameter) of a circle - or approximately 3.14.
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.
In the expression x^b - x is the base and b is the exponent.

8. What is the sum of the measures of all angles around a point?
0 is the only number that is neither positive nor negative.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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°.
No matter how many angles there are - the sum around the point is 360°.

9. Properties of zero 1
0 is the only number that is neither positive nor negative.
360°
Their sum is 180°.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

10. What is an even and an odd number?
The two pairs of opposite angles formed are equal to each other.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Even numbers are divisible by 2 and odd numbers are not.
An integer greater than one that is not prime.

11. What is the formula for the area of a rectangle?
A = lw
Shifted down 2 units.
A = 2(lw + lh + hw)
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

12. How do you calculate a weighted average?
V = l^3
Shifted right 2 units.
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.

13. What is the formula for the volume of a cylinder?
A^m/b^m = (a/b)^m
Then the quotient y/x is a constant.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
V = pr^2h

14. How you convert a fraction or a decimal to a percent?
A = 6(l^2)
Shifted up 2 units.
Divide - then multiply by 100.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

15. What is true about the slopes of parallel lines?
Corresponding sides of similar triangles are in proportion.
Their sum is 180°.
Equal slopes.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

16. 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.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted left 2 units.

17. What is a function?
For any right triangle - a^2 + b^2 = c^2.
(Circumference/diameter) of a circle - or approximately 3.14.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

18. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
C = p2r
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.
0 is the only number that is neither positive nor negative.
Shifted left 2 units.

19. What is the sum of the measures of the n angles of a polygon with n sides?
For any right triangle - a^2 + b^2 = c^2.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(n - 2)(180°)
If a is negative and b is positive - then a < 0 < b.

20. What is the Pythagorean theorem?
The set of all ordered pairs (x -y) such that y = f(x).
(n - 2)(180°)
Write the percent over 100 and reduce.
For any right triangle - a^2 + b^2 = c^2.

21. Properties of one 4
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.
All positive and negative whole numbers - and zero.
1 is the smallest positive odd integer.
The two pairs of opposite angles formed are equal to each other.

22. Properties of zero 3
0 is a multiple of every integer.
At least one of the factors is 0.
Shifted left 2 units.
(Circumference/diameter) of a circle - or approximately 3.14.

23. Law of exponents 5
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A^m/b^m = (a/b)^m
A = s^2 or A =d^2/2 where d is the diagonal
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

24. What is the formula for the surface area of a cube?
A = 6(l^2)
A = lw
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Set y = 0 - and solve.

25. Properties of one 3
A^m*b^m = (ab)^m
1 is a divisor (or factor) of every integer.
A = [(s^2*v3)/4]
Write the percent as a decimal - and multiply.

26. What are the properties of a square?
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 = bh
All positive and negative whole numbers - and zero.
Even numbers are divisible by 2 and odd numbers are not.

27. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
In the expression x^b - x is the base and b is the exponent.
[(x1 + x2)/2] -[(y1 + y2)/2]
For any integer n: 1^n = 1.
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°.

28. What is the probability of an event that cannot occur? That must occur?
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.
Cannot is 0 - must is 1 - all others are in between.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

29. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Then the product xy is a constant.
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.
The product of their slopes is -1 (negative reciprocal).

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

31. How do you find the length of an arc of a circle?
(Circumference/diameter) of a circle - or approximately 3.14.
Corresponding sides of similar triangles are in proportion.
Arc = (x°/360)(2pr) where x is the central angle.
A = 2(lw + lh + hw)

32. What is the volume of a cube?
(Circumference/diameter) of a circle - or approximately 3.14.
V = l^3
The ratio of corresponding sides of similar triangles.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

33. What is the measure of a straight angle?
For any number n: x^-n means 1/x^n.
180°. If two or more angles form a straight angle - their sum is 180°.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

34. What are the quotient and the remainder?

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35. What is a percent?
How steep the line is. Horizontal line = 0 - vertical has no slope.
An angle formed by extending the side of the polygon.
A fraction whose denominator is 100 i.e. 17% = 17/100
360°

36. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
Even numbers are divisible by 2 and odd numbers are not.
B^m*b^n = b^m+n
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

37. What is a composite number?
Even numbers are divisible by 2 and odd numbers are not.
Is a right triangle with a ratio of sides x:xv3:2x.
An integer greater than one that is not prime.
Shifted right 2 units.

38. What is the formula for the area of a parallelogram?
If a is negative and b is positive - then a < 0 < b.
V = lwh
Equal slopes.
A = bh

39. What is an exterior angle of a polygon?
B^m*b^n = b^m+n
Shifted right 2 units.
Then the quotient y/x is a constant.
An angle formed by extending the side of the polygon.

40. What is a prime number?
A = s^2 or A =d^2/2 where d is the diagonal
(x + y)(x - y) = x^2 - y^2
The ratio of corresponding sides of similar triangles.
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.

41. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
[(x1 + x2)/2] -[(y1 + y2)/2]
An integer greater than one that is not prime.
Even numbers are divisible by 2 and odd numbers are not.

42. What is the area of a square?
No matter how many angles there are - the sum around the point is 360°.
They are both the same. A divisor or factor of an integer leaves no remainder.
A = s^2 or A =d^2/2 where d is the diagonal
Equal slopes.

43. 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.
180°. If two or more angles form a straight angle - their sum is 180°.
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.

44. Law of exponents 4
The two pairs of opposite angles formed are equal to each other.
A^m*b^m = (ab)^m
V = pr^2h
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

45. What is an integer?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
All positive and negative whole numbers - and zero.
360°
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

46. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Their sum is 90°.
1 is a divisor (or factor) of every integer.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

47. What is the square root of a number?
They are both the same. A divisor or factor of an integer leaves no remainder.
V = pr^2h
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A^m/b^m = (a/b)^m

48. Important binomial 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.
Shifted down 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The set of all ordered pairs (x -y) such that y = f(x).

49. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
Write the percent as a decimal - and multiply.
A = (1/2)bh.
For any number b: b = -b if and only if b = 0.

50. What is true about the measures of the three angles in a triangle?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
At least one of the factors is 0.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Their sum is 180°.