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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. How do you find the length of an arc of a circle?
Their sum is 90°.
Arc = (x°/360)(2pr) where x is the central angle.
A fraction whose denominator is 100 i.e. 17% = 17/100
A = pr^2

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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

3. What does it mean if y is directly proportional to x?
All positive and negative whole numbers - and zero.
Then the quotient y/x is a constant.
0 is the only number that is neither positive nor negative.
Arc = (x°/360)(2pr) where x is the central angle.

4. What is a composite number?
An integer greater than one that is not prime.
For any right triangle - a^2 + b^2 = c^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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

5. What is the distributive law?
A = pr^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted right 2 units.
C = p2r

6. How do you find the x-intercept of a graph?
For any number a: a * 1 = a and a / 1 = a.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A^m/b^m = (a/b)^m
Set y = 0 - and solve.

7. 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.
Shifted right 2 units.
(x + y)(x - y) = x^2 - y^2
All positive and negative whole numbers - and zero.

8. What is special formula for the area of an equilateral triangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For any number b: b = -b if and only if b = 0.
A = [(s^2*v3)/4]
P(e) = (# of favorable outcomes)/(# of possible outcomes)

9. What is the formula for the volume of a cylinder?
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.
V = pr^2h
1 is a divisor (or factor) of every integer.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

10. What is the formula for the area of a rectangle?
A = lw
[(x1 + x2)/2] -[(y1 + y2)/2]
C = p2r
An angle formed by extending the side of the polygon.

11. What are the properties of a square?
Shifted up 2 units.
Their sum is 90°.
(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.

12. What is the formula for the surface area of a cube?
Set y = 0 - and solve.
A = 6(l^2)
An integer greater than one that is not prime.
1 is a divisor (or factor) of every integer.

13. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

14. How do you find the area of a sector of a circle?
The ratio of corresponding sides of similar triangles.
Area = (x°/360)(pr^2) where x is the central angle.
Write the percent as a decimal - and multiply.
An angle formed by extending the side of the polygon.

15. Properties of one 3
A = bh
1 is a divisor (or factor) of every integer.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
All positive and negative whole numbers - and zero.

16. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
A = lw
V = lwh
The set of all ordered pairs (x -y) such that y = f(x).
Shifted left 2 units.

17. Important binomial 3
The set of all ordered pairs (x -y) such that y = f(x).
360°
Shifted down 2 units.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

18. Properties of one 2
For any integer n: 1^n = 1.
No matter how many angles there are - the sum around the point is 360°.
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.

19. What is a ratio?

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20. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
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
They are both the same. A divisor or factor of an integer leaves no remainder.

21. What is a multiple of an integer?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
V = lwh
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 left 2 units.

22. What is a negative exponent?
A = (1/2)bh.
For any number n: x^-n means 1/x^n.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
An integer greater than one that is not prime.

23. Law of exponents 2
A = [(s^2*v3)/4]
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
For any number n: x^-n means 1/x^n.

24. How do you calculate a weighted average?
Equal slopes.
Shifted left 2 units.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

25. Properties of one 4
180°. If two or more angles form a straight angle - their sum is 180°.
1 is the smallest positive odd integer.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
0 is a multiple of every integer.

26. What are the important properties of 30-60-90 triangle?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Is a right triangle with a ratio of sides x:xv3:2x.
A = (1/2)bh.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

27. What are the median and the mode of a set of data?
Shifted down 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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

28. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
A fraction whose denominator is 100 i.e. 17% = 17/100
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted up 2 units.

29. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
A = bh
A = [(s^2*v3)/4]
Set x = 0 - and solve.

30. What is the probability of an event that cannot occur? That must occur?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Cannot is 0 - must is 1 - all others are in between.

31. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
The product of their slopes is -1 (negative reciprocal).
V = pr^2h
A = [(s^2*v3)/4]

32. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
An integer greater than one that is not prime.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Shifted down 2 units.

33. What are the quotient and the remainder?

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34. In a circle of radius r - what is the formula for the area?
A = pr^2
No matter how many angles there are - the sum around the point is 360°.
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 and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

35. What is true about the areas of similar triangles?
(Circumference/diameter) of a circle - or approximately 3.14.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = 6(l^2)
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

36. Law of exponents 4
An angle formed by extending the side of the polygon.
360°
A^m*b^m = (ab)^m
(n - 2)(180°)

37. What is the sum of the measures of all angles around a point?
Write the percent as a decimal - and multiply.
Then the product xy is a constant.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
No matter how many angles there are - the sum around the point is 360°.

38. What important property do similar triangles have?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
M = (y2 - y1)/(x2 - x1)
C = p2r
Corresponding sides of similar triangles are in proportion.

39. Properties of zero 4
Shifted up 2 units.
All positive and negative whole numbers - and zero.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

40. Law of exponents 3
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any number b: b = -b if and only if b = 0.
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.
(b^m)^n = b^mn

41. Properties of zero 3
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
0 is a multiple of every integer.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Arc = (x°/360)(2pr) where x is the central angle.

42. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = pr^2
P(e) = (# of favorable outcomes)/(# of possible outcomes)

43. If you were given the graph of y = f(x) - what does f(a) represent?
360°
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
For any number b: b = -b if and only if b = 0.
B^m*b^n = b^m+n

44. What is the area of a square?
A = pr^2
Shifted right 2 units.
A = s^2 or A =d^2/2 where d is the diagonal
Cannot is 0 - must is 1 - all others are in between.

45. What is true about the measures of the three angles in a triangle?
1 is a divisor (or factor) of every integer.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Their sum is 180°.

46. What is the distance formula?
A = (1/2)bh.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
In the expression x^b - x is the base and b is the exponent.
For any right triangle - a^2 + b^2 = c^2.

47. What do we mean by the slope of the line?
Cannot is 0 - must is 1 - all others are in between.
How steep the line is. Horizontal line = 0 - vertical has no slope.
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°

48. Law of exponents 5
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.
Write the percent over 100 and reduce.
A^m/b^m = (a/b)^m
A = 6(l^2)

49. What is the formula for the volume of a rectangular solid?
Shifted right 2 units.
V = lwh
If a is negative and b is positive - then a < 0 < b.
The two pairs of opposite angles formed are equal to each other.

50. What are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
C = p2r
Shifted left 2 units.
Then the quotient y/x is a constant.