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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. What is the sum of the measures of the four angles in a quadrilateral?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For any right triangle - a^2 + b^2 = c^2.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
360°

2. How do you convert a percent to a fraction or a decimal?
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.
Write the percent over 100 and reduce.
Cannot is 0 - must is 1 - all others are in between.

3. What is the formula for the area of a rectangle?
1 is a divisor (or factor) of every integer.
A = bh
Divide - then multiply by 100.
A = lw

4. What does it mean if y is inversely proportional to x?
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.
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.
No matter how many angles there are - the sum around the point is 360°.

5. What are the properties of a square?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Their sum is 90°.
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.

6. What are the quotient and the remainder?

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7. How do we write the equation of a line?
V = pr^2h
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
The two pairs of opposite angles formed are equal to each other.
The product of their slopes is -1 (negative reciprocal).

8. What is a divisor and a factor of an integer?
They are both the same. A divisor or factor of an integer leaves no remainder.
(b^m)^n = b^mn
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.
For any number a: a * 1 = a and a / 1 = a.

9. Properties of zero 3
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
0 is a multiple of every integer.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any number a: a * 1 = a and a / 1 = a.

10. If the product of two or more numbers is 0 - what do you know about the numbers?
1 is a divisor (or factor) of every integer.
An equation that states that two ratios are equivalent. 4/6 = 10/15
At least one of the factors is 0.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

11. How do you find the x-intercept of a graph?
Shifted left 2 units.
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.
Set y = 0 - and solve.

12. 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.
B^m/b^n = b^m-n
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
[(x1 + x2)/2] -[(y1 + y2)/2]

13. What is the distance formula?
The product of their slopes is -1 (negative reciprocal).
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = lw

14. Law of exponents 3
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A fraction whose denominator is 100 i.e. 17% = 17/100
(b^m)^n = b^mn
0 is a multiple of every integer.

15. What is a fractional exponent?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
An equation that states that two ratios are equivalent. 4/6 = 10/15
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
(n - 2)(180°)

16. What is true about the slopes of perpendicular lines?
Avg = sum of n numbers/n
The product of their slopes is -1 (negative reciprocal).
V = l^3
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

17. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
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.
Shifted up 2 units.
A = 6(l^2)
In the expression x^b - x is the base and b is the exponent.

18. What formula is used for an average?
Avg = sum of n numbers/n
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 two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

19. What is the sum of the measures of all angles around a point?
How steep the line is. Horizontal line = 0 - vertical has no slope.
0 is a multiple of every integer.
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.
No matter how many angles there are - the sum around the point is 360°.

20. What is true about the measures of the four angles formed by two intersecting lines?
Even numbers are divisible by 2 and odd numbers are not.
For any number n: x^-n means 1/x^n.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
The two pairs of opposite angles formed are equal to each other.

21. Properties of zero 2
1 is the smallest positive odd integer.
If a is negative and b is positive - then a < 0 < b.
(x + y)(x - y) = x^2 - y^2
They are both the same. A divisor or factor of an integer leaves no remainder.

22. Properties of zero 5
For any number b: b = -b if and only if b = 0.
Even numbers are divisible by 2 and odd numbers are not.
If a is negative and b is positive - then a < 0 < b.
The ratio of corresponding sides of similar triangles.

23. What is the formula for the area of a parallelogram?
Area = (x°/360)(pr^2) where x is the central angle.
Arc = (x°/360)(2pr) where x is the central angle.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = bh

24. Properties of one 4
Shifted down 2 units.
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.
The two pairs of opposite angles formed are equal to each other.
1 is the smallest positive odd integer.

25. What is the volume of a cube?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
V = l^3
A = 2(lw + lh + hw)
For any number n: x^-n means 1/x^n.

26. What is the measure of a straight angle?
V = pr^2h
Shifted right 2 units.
Write the percent over 100 and reduce.
180°. If two or more angles form a straight angle - their sum is 180°.

27. What is an even and an odd number?
A = bh
Avg = sum of n numbers/n
[(x1 + x2)/2] -[(y1 + y2)/2]
Even numbers are divisible by 2 and odd numbers are not.

28. What is a prime number?
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°.
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 fraction whose denominator is 100 i.e. 17% = 17/100
A = 2(lw + lh + hw)

29. What is the formula for the surface area of a cube?
Shifted right 2 units.
A = 6(l^2)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(n - 2)(180°)

30. How do you find the y-intercept of a graph?
Set y = 0 - and solve.
Shifted down 2 units.
Set x = 0 - and solve.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

31. What is a composite number?
An integer greater than one that is not prime.
At least one of the factors is 0.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = lw

32. What does it mean if y is directly proportional to x?
M = (y2 - y1)/(x2 - x1)
Then the quotient y/x is a constant.
A^m*b^m = (ab)^m
Write the percent as a decimal - and multiply.

33. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A fraction whose denominator is 100 i.e. 17% = 17/100
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

34. Law of exponents 2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
B^m/b^n = b^m-n
Shifted right 2 units.

35. What is the distributive law?
Set x = 0 - and solve.
A fraction whose denominator is 100 i.e. 17% = 17/100
(n - 2)(180°)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

36. Properties of square roots
A = (1/2)bh.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
All positive and negative whole numbers - and zero.
180°. If two or more angles form a straight angle - their sum is 180°.

37. In a circle of radius r - what is the formula for the area?
Write the percent as a decimal - and multiply.
A = pr^2
(x + y)(x - y) = x^2 - y^2
V = l^3

38. What is the formula for the volume of a cylinder?
V = pr^2h
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.

39. What is the formula for the surface area of a rectangular solid?
(b^m)^n = b^mn
B^m*b^n = b^m+n
A = 2(lw + lh + hw)
Corresponding sides of similar triangles are in proportion.

40. What is the midpoint formula?
Shifted left 2 units.
They are both the same. A divisor or factor of an integer leaves no remainder.
[(x1 + x2)/2] -[(y1 + y2)/2]
Then the product xy is a constant.

41. What is the graph of a function?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
No matter how many angles there are - the sum around the point is 360°.
For any number n: x^-n means 1/x^n.
The set of all ordered pairs (x -y) such that y = f(x).

42. What is the Pythagorean theorem?
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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For any right triangle - a^2 + b^2 = c^2.
Shifted down 2 units.

43. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
0 is a multiple of every integer.
Corresponding sides of similar triangles are in proportion.
Shifted down 2 units.

44. What is a ratio?

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45. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
At least one of the factors is 0.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
(x + y)(x - y) = x^2 - y^2
Shifted down 2 units.

46. What is p?
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°.
(Circumference/diameter) of a circle - or approximately 3.14.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
(x + y)(x - y) = x^2 - y^2

47. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Equal slopes.

48. For what values of a function is the function undefined?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = s^2 or A =d^2/2 where d is the diagonal
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A fraction whose denominator is 100 i.e. 17% = 17/100

49. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
They are both the same. A divisor or factor of an integer leaves no remainder.
A^m/b^m = (a/b)^m
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°.
V = l^3

50. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
Set x = 0 - and solve.
They are both the same. A divisor or factor of an integer leaves no remainder.
The product of their slopes is -1 (negative reciprocal).