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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. Important binomial 1
Equal slopes.
(x + y)(x - y) = x^2 - y^2
For any integer n: 1^n = 1.
An integer greater than one that is not prime.

2. What is true about the measures of the four angles formed by two intersecting lines?
The two pairs of opposite angles formed are equal to each other.
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°.
Their sum is 180°.
The ratio of corresponding sides of similar triangles.

3. How do you find the y-intercept of a graph?
How steep the line is. Horizontal line = 0 - vertical has no slope.
An angle formed by extending the side of the polygon.
Set x = 0 - and solve.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

4. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = (1/2)bh.
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.

5. How do you find the length of an arc of a circle?
Shifted left 2 units.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For any number n: x^-n means 1/x^n.
Arc = (x°/360)(2pr) where x is the central angle.

6. What is the relationship between a radius of a circle and a line that is tangent to the circle?
(Circumference/diameter) of a circle - or approximately 3.14.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Area = (x°/360)(pr^2) where x is the central angle.
How steep the line is. Horizontal line = 0 - vertical has no slope.

7. Properties of zero 4
Their sum is 180°.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
V = lwh
(x + y)(x - y) = x^2 - y^2

8. If you were given the graph of y = f(x) - what does f(a) represent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Equal slopes.
D = 2r
Arc = (x°/360)(2pr) where x is the central angle.

9. Important binomial 3
360°
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
0 is the only number that is neither positive nor negative.

10. In a circle of radius r - what is the formula for the circumference?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
C = p2r
Their sum is 90°.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

11. Law of exponents 1
The set of all ordered pairs (x -y) such that y = f(x).
A = bh
B^m*b^n = b^m+n
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

12. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
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.
Write the percent over 100 and reduce.

13. What are the sum - difference - products - and quotient of two numbers?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = s^2 or A =d^2/2 where d is the diagonal
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

14. Properties of one 1
How steep the line is. Horizontal line = 0 - vertical has no slope.
Write the percent as a decimal - and multiply.
For any number a: a * 1 = a and a / 1 = a.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

15. What is the midpoint formula?
A = [(s^2*v3)/4]
[(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.
For any number n: x^-n means 1/x^n.

16. What important property do similar triangles have?
A^m/b^m = (a/b)^m
Corresponding sides of similar triangles are in proportion.
V = pr^2h
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

17. What is the formula for the area of a triangle?
Set y = 0 - and solve.
For any right triangle - a^2 + b^2 = c^2.
A = (1/2)bh.
Shifted down 2 units.

18. What is a fractional exponent?
Their sum is 180°.
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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

19. What is a percent?
360°
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A fraction whose denominator is 100 i.e. 17% = 17/100
0 is the only number that is neither positive nor negative.

20. What is a Venn diagram?
A = 6(l^2)
A = s^2 or A =d^2/2 where d is the diagonal
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

21. Law of exponents 4
180°. If two or more angles form a straight angle - their sum is 180°.
A^m*b^m = (ab)^m
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

22. What is p?
Area = (x°/360)(pr^2) where x is the central angle.
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.
(Circumference/diameter) of a circle - or approximately 3.14.
Shifted down 2 units.

23. How do you calculate percent increases and decreases?
Write the percent as a decimal - and multiply.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
At least one of the factors is 0.

24. Properties of one 2
Shifted right 2 units.
At least one of the factors is 0.
For any integer n: 1^n = 1.
Then the quotient y/x is a constant.

25. What is true about the areas of similar triangles?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
The ratio of corresponding sides of similar triangles.

26. What is the formula for the area of a rectangle?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = s^2 or A =d^2/2 where d is the diagonal
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = lw

27. What is a composite number?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
An integer greater than one that is not prime.
0 is a multiple of every integer.
Their sum is 90°.

28. What are the properties of a rectangle?
Shifted down 2 units.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
How steep the line is. Horizontal line = 0 - vertical has no slope.
The product of their slopes is -1 (negative reciprocal).

29. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
For any number n: x^-n means 1/x^n.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

30. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
(Circumference/diameter) of a circle - or approximately 3.14.
A = (1/2)bh.
A = 6(l^2)

31. 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.
Their sum is 180°.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted right 2 units.

32. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
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.
360°
Write the percent as a decimal - and multiply.

33. In a circle of radius r - what is the formula for the diameter?
D = 2r
Even numbers are divisible by 2 and odd numbers are not.
If a is negative and b is positive - then a < 0 < b.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

34. What is true about the slopes of parallel lines?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
If a is negative and b is positive - then a < 0 < b.
Equal slopes.
A^m*b^m = (ab)^m

35. What is the formula for the surface area of a cube?
0 is a multiple of every integer.
A = 6(l^2)
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
The product of their slopes is -1 (negative reciprocal).

36. What is an integer?
The ratio of corresponding sides of similar triangles.
All positive and negative whole numbers - and zero.
Their sum is 90°.
0 is the only number that is neither positive nor negative.

37. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
C = p2r
(b^m)^n = b^mn
Shifted left 2 units.
Even numbers are divisible by 2 and odd numbers are not.

38. 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.
The product of their slopes is -1 (negative reciprocal).
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Avg = sum of n numbers/n

39. What is a function?
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.
How steep the line is. Horizontal line = 0 - vertical has no slope.
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

40. What are similar triangles?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Area = (x°/360)(pr^2) where x is the central angle.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

41. What does it mean if y is inversely proportional to x?
A = pr^2
(x + y)(x - y) = x^2 - y^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.
Then the product xy is a constant.

42. What is the square root of a number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Is a right triangle with a ratio of sides x:xv3:2x.
Write the percent as a decimal - and multiply.
For any number a: a * 1 = a and a / 1 = a.

43. If the product of two or more numbers is 0 - what do you know about the numbers?
Their sum is 90°.
At least one of the factors is 0.
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.
M = (y2 - y1)/(x2 - x1)

44. What are the quotient and the remainder?

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45. What is the graph of a function?
V = l^3
The set of all ordered pairs (x -y) such that y = f(x).
All positive and negative whole numbers - and zero.
If a is negative and b is positive - then a < 0 < b.

46. What are the median and the mode of a set of data?
1 is the smallest positive odd integer.
The two pairs of opposite angles formed are equal to each other.
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.
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.

47. Properties of zero 5
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
For any number b: b = -b if and only if b = 0.
A fraction whose denominator is 100 i.e. 17% = 17/100
Their sum is 180°.

48. In a circle of radius r - what is the formula for the area?
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 = [(s^2*v3)/4]
A = pr^2
Then the quotient y/x is a constant.

49. What is a ratio?

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50. How do you find the probability that an event will occur?
The set of all ordered pairs (x -y) such that y = f(x).
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.
M = (y2 - y1)/(x2 - x1)
P(e) = (# of favorable outcomes)/(# of possible outcomes)