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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 you convert a fraction or a decimal to a percent?
A = pr^2
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Divide - then multiply by 100.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

2. Law of exponents 3
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.
(b^m)^n = b^mn
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

3. What is an exterior angle of a triangle?
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.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

4. In a circle of radius r - what is the formula for the circumference?
Corresponding sides of similar triangles are in proportion.
A^m*b^m = (ab)^m
C = p2r
A = lw

5. Properties of one 4
1 is the smallest positive odd integer.
A = lw
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
The set of all ordered pairs (x -y) such that y = f(x).

6. What are the important properties of 30-60-90 triangle?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = 2(lw + lh + hw)
Is a right triangle with a ratio of sides x:xv3:2x.

7. What is an integer?
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.
All positive and negative whole numbers - and zero.
The ratio of corresponding sides of similar triangles.
For any number n: x^-n means 1/x^n.

8. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
1 is the smallest positive odd integer.
A = [(s^2*v3)/4]
C = p2r

9. How do you convert a percent to a fraction or a decimal?
They are both the same. A divisor or factor of an integer leaves no remainder.
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.
Write the percent over 100 and reduce.
Avg = sum of n numbers/n

10. What is the sum of the measures of the four angles in a quadrilateral?
Shifted down 2 units.
Write the percent as a decimal - and multiply.
360°
(b^m)^n = b^mn

11. Important binomial 1
360°
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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
(x + y)(x - y) = x^2 - y^2

12. What are the properties of a rectangle?
(Circumference/diameter) of a circle - or approximately 3.14.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = bh
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

13. What are the properties of a parallelogram?
A^m*b^m = (ab)^m
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For any number a: a * 1 = a and a / 1 = a.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

14. What is special formula for the area of an equilateral triangle?
A fraction whose denominator is 100 i.e. 17% = 17/100
V = l^3
A = [(s^2*v3)/4]
(x + y)(x - y) = x^2 - y^2

15. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
A = lw
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Set y = 0 - and solve.

16. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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.
Divide - then multiply by 100.
V = lwh

17. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
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.
360°
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

18. What are the properties of a square?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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.
M = (y2 - y1)/(x2 - x1)

19. What is the formula for the volume of a rectangular solid?
[(x1 + x2)/2] -[(y1 + y2)/2]
V = lwh
180°. If two or more angles form a straight angle - their sum is 180°.
A = bh

20. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
360°
B^m*b^n = b^m+n

21. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
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.
A = pr^2
B^m*b^n = b^m+n

22. Important binomial 3
[(x1 + x2)/2] -[(y1 + y2)/2]
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(n - 2)(180°)
A^m/b^m = (a/b)^m

23. What are similar triangles?
Divide - then multiply by 100.
Set y = 0 - and solve.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
360°

24. For what values of a function is the function undefined?
Their sum is 180°.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

25. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted down 2 units.
At least one of the factors is 0.
360°

26. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Is a right triangle with a ratio of sides x:xv3:2x.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
No matter how many angles there are - the sum around the point is 360°.

27. What is true about the slopes of parallel lines?
Is a right triangle with a ratio of sides x:xv3:2x.
(Circumference/diameter) of a circle - or approximately 3.14.
Equal slopes.
A = lw

28. What is a negative exponent?
They are both the same. A divisor or factor of an integer leaves no remainder.
If a is negative and b is positive - then a < 0 < b.
Their sum is 180°.
For any number n: x^-n means 1/x^n.

29. What is true about the slopes of perpendicular lines?
Set y = 0 - and solve.
Area = (x°/360)(pr^2) where x is the central angle.
The product of their slopes is -1 (negative reciprocal).
Shifted up 2 units.

30. What are the median and the mode of a set of data?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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 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 = [(s^2*v3)/4]

31. What is the square root of a number?
Then the quotient y/x is a constant.
Shifted right 2 units.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
V = lwh

32. Properties of zero 4
For any integer n: 1^n = 1.
If a is negative and b is positive - then a < 0 < b.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

33. What is true about the measures of the two acute angles in a right triangle?
A = 6(l^2)
Their sum is 90°.
Divide - then multiply by 100.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

34. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
The product of their slopes is -1 (negative reciprocal).
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = pr^2

35. How do you find the probability that an event will occur?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
The ratio of corresponding sides of similar triangles.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

36. How do you find the slope of a line?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Their sum is 90°.
M = (y2 - y1)/(x2 - x1)
The product of their slopes is -1 (negative reciprocal).

37. What does it mean if y is inversely proportional to x?
An angle formed by extending the side of the polygon.
Corresponding sides of similar triangles are in proportion.
Then the product xy is a constant.
A = lw

38. What is a composite number?
Avg = sum of n numbers/n
An integer greater than one that is not prime.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Shifted up 2 units.

39. What is true about the measures of the four angles formed by two intersecting lines?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The two pairs of opposite angles formed are equal to each other.
Area = (x°/360)(pr^2) where x is the central angle.
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°.

40. What is a prime number?
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.
The ratio of corresponding sides of similar triangles.
0 is a multiple of every integer.
A fraction whose denominator is 100 i.e. 17% = 17/100

41. What are the quotient and the remainder?

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42. How do you find the area of a sector of a circle?
A = pr^2
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Area = (x°/360)(pr^2) where x is the central angle.
B^m*b^n = b^m+n

43. What is the formula for the surface area of a cube?
A^m/b^m = (a/b)^m
360°
A = 6(l^2)
No matter how many angles there are - the sum around the point is 360°.

44. What does it mean if y is directly proportional to x?
No matter how many angles there are - the sum around the point is 360°.
B^m*b^n = b^m+n
A = [(s^2*v3)/4]
Then the quotient y/x is a constant.

45. What is an exponent?
Write the percent as a decimal - and multiply.
In the expression x^b - x is the base and b is the exponent.
360°
M = (y2 - y1)/(x2 - x1)

46. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Then the product xy is a constant.
A^m*b^m = (ab)^m

47. What is the sum of the measures of all angles around a point?
For any integer n: 1^n = 1.
No matter how many angles there are - the sum around the point is 360°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
At least one of the factors is 0.

48. What is the formula for the area of a triangle?
Write the percent as a decimal - and multiply.
A = (1/2)bh.
B^m/b^n = b^m-n
A = bh

49. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
A^m*b^m = (ab)^m
Is a right triangle with a ratio of sides x:xv3:2x.
Shifted left 2 units.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

50. What is the volume of a cube?
V = l^3
Their sum is 180°.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
1 is the smallest positive odd integer.