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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 is the distance formula?
The two pairs of opposite angles formed are equal to each other.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

2. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
(n - 2)(180°)
Their sum is 180°.

3. What is the triangle inequality?
Avg = sum of n numbers/n
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.
An integer greater than one that is not prime.
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.

4. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
V = pr^2h
Divide - then multiply by 100.
V = lwh

5. How do you calculate percent increases and decreases?
Write the percent over 100 and reduce.
A^m*b^m = (ab)^m
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

6. What is an exponent?
[(x1 + x2)/2] -[(y1 + y2)/2]
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
360°
In the expression x^b - x is the base and b is the exponent.

7. What is special formula for the area of an equilateral triangle?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = lw
A = [(s^2*v3)/4]
How steep the line is. Horizontal line = 0 - vertical has no slope.

8. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The set of all ordered pairs (x -y) such that y = f(x).
A = lw

9. How you convert a fraction or a decimal to a percent?
Cannot is 0 - must is 1 - all others are in between.
C = p2r
The two pairs of opposite angles formed are equal to each other.
Divide - then multiply by 100.

10. What are the median and the mode of a set of data?
Write the percent as a decimal - and multiply.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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°.
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.

11. In a circle of radius r - what is the formula for the area?
Shifted left 2 units.
A = pr^2
The ratio of corresponding sides of similar triangles.
How steep the line is. Horizontal line = 0 - vertical has no slope.

12. What is an even and an odd number?
Shifted left 2 units.
Even numbers are divisible by 2 and odd numbers are not.
180°. If two or more angles form a straight angle - their sum is 180°.
An integer greater than one that is not prime.

13. What is an exterior angle of a triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A^m*b^m = (ab)^m
A = lw
The two pairs of opposite angles formed are equal to each other.

14. Law of exponents 5
B^m/b^n = b^m-n
(Circumference/diameter) of a circle - or approximately 3.14.
A^m/b^m = (a/b)^m
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.

15. What is a ratio?

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16. What is an integer?
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 = (1/2)bh.
All positive and negative whole numbers - and zero.
The two pairs of opposite angles formed are equal to each other.

17. How do you find the probability that an event will occur?
C = p2r
A = s^2 or A =d^2/2 where d is the diagonal
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Cannot is 0 - must is 1 - all others are in between.

18. What is a multiple of an integer?
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.
They are both the same. A divisor or factor of an integer leaves no remainder.
1 is the smallest positive odd integer.
D = 2r

19. How do you find the y-intercept of a graph?
If a is negative and b is positive - then a < 0 < b.
A = 2(lw + lh + hw)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Set x = 0 - and solve.

20. Important binomial 1
(x + y)(x - y) = x^2 - y^2
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A fraction whose denominator is 100 i.e. 17% = 17/100

21. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
For any number a: a * 1 = a and a / 1 = a.
A = [(s^2*v3)/4]
Shifted down 2 units.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

22. Properties of one 3
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
1 is a divisor (or factor) of every integer.
180°. If two or more angles form a straight angle - their sum is 180°.
At least one of the factors is 0.

23. What is a percent?
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 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
Then the product xy is a constant.

24. For what values of a function is the function undefined?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
B^m/b^n = b^m-n
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Equal slopes.

25. Properties of one 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.
A = lw
For any integer n: 1^n = 1.
A = (1/2)bh.

26. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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°.
Then the quotient y/x is a constant.
Their sum is 180°.
Cannot is 0 - must is 1 - all others are in between.

27. What is a composite number?
[(x1 + x2)/2] -[(y1 + y2)/2]
An integer greater than one that is not prime.
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.
Then the quotient y/x is a constant.

28. What is a function?
For any right triangle - a^2 + b^2 = c^2.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
C = p2r

29. Law of exponents 3
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any integer n: 1^n = 1.
V = l^3
(b^m)^n = b^mn

30. 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.
In the expression x^b - x is the base and b is the exponent.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

31. What is true about the slopes of parallel lines?
A = lw
1 is the smallest positive odd integer.
Equal slopes.
Divide - then multiply by 100.

32. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
In the expression x^b - x is the base and b is the exponent.
A^m*b^m = (ab)^m
1 is the smallest positive odd integer.

33. What is a fractional exponent?
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 and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Corresponding sides of similar triangles are in proportion.
No matter how many angles there are - the sum around the point is 360°.

34. What does it mean if y is inversely proportional to x?
A = [(s^2*v3)/4]
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Then the product xy is a constant.
In the expression x^b - x is the base and b is the exponent.

35. Properties of one 1
In the expression x^b - x is the base and b is the exponent.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For any number a: a * 1 = a and a / 1 = a.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

36. What is the sum of the measures of all angles around a point?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
An angle formed by extending the side of the polygon.
No matter how many angles there are - the sum around the point is 360°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

37. What is true about the slopes of perpendicular lines?
(x + y)(x - y) = x^2 - y^2
P(e) = (# of favorable outcomes)/(# of possible outcomes)
The product of their slopes is -1 (negative reciprocal).
1 is the smallest positive odd integer.

38. What is the formula for the surface area of a rectangular solid?
A = lw
A = 6(l^2)
A = 2(lw + lh + hw)
D = 2r

39. What do we mean by the slope of the line?
Write the percent over 100 and reduce.
(n - 2)(180°)
How steep the line is. Horizontal line = 0 - vertical has no slope.
Their sum is 90°.

40. What is the probability of an event that cannot occur? That must occur?
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.
In the expression x^b - x is the base and b is the exponent.
Cannot is 0 - must is 1 - all others are in between.
Shifted up 2 units.

41. Properties of one 4
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
1 is the smallest positive odd integer.
(n - 2)(180°)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

42. Properties of zero 1
0 is a multiple of every integer.
The two pairs of opposite angles formed are equal to each other.
0 is the only number that is neither positive nor negative.
If a is negative and b is positive - then a < 0 < b.

43. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
The set of all ordered pairs (x -y) such that y = f(x).
All positive and negative whole numbers - and zero.
A^m*b^m = (ab)^m
Shifted up 2 units.

44. Law of exponents 4
A^m*b^m = (ab)^m
Area = (x°/360)(pr^2) where x is the central angle.
Arc = (x°/360)(2pr) where x is the central angle.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

45. 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.
All positive and negative whole numbers - and zero.
A = lw
For any right triangle - a^2 + b^2 = c^2.

46. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
0 is a multiple of every integer.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

47. What are the quotient and the remainder?

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48. Properties of zero 5
Cannot is 0 - must is 1 - all others are in between.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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.

49. What is true about the measures of the four angles formed by two intersecting lines?
Set y = 0 - and solve.
The two pairs of opposite angles formed are equal to each other.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Write the percent as a decimal - and multiply.

50. What is the graph of a function?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Equal slopes.
The set of all ordered pairs (x -y) such that y = f(x).
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.