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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. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Set x = 0 - and solve.
360°
P(e) = (# of favorable outcomes)/(# of possible outcomes)

2. What is a composite number?
An integer greater than one that is not prime.
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For any number n: x^-n means 1/x^n.

3. What is the probability of an event that cannot occur? That must occur?
M = (y2 - y1)/(x2 - x1)
Cannot is 0 - must is 1 - all others are in between.
Equal slopes.
How steep the line is. Horizontal line = 0 - vertical has no slope.

4. For what values of a function is the function undefined?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

5. What is the formula for the area of a parallelogram?
For any integer n: 1^n = 1.
A = bh
V = lwh
A^m/b^m = (a/b)^m

6. Law of exponents 3
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
The ratio of corresponding sides of similar triangles.
(b^m)^n = b^mn
Area = (x°/360)(pr^2) where x is the central angle.

7. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
(Circumference/diameter) of a circle - or approximately 3.14.
A = 6(l^2)
Shifted right 2 units.
For any number a: a * 1 = a and a / 1 = a.

8. What is a multiple of an integer?
An integer greater than one that is not prime.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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 ratio of corresponding sides of similar triangles.

9. What is an exponent?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
At least one of the factors is 0.
In the expression x^b - x is the base and b is the exponent.
B^m/b^n = b^m-n

10. What is the formula for the surface area of a cube?
Their sum is 180°.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = 6(l^2)

11. In a circle of radius r - what is the formula for the diameter?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Shifted right 2 units.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
D = 2r

12. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
[(x1 + x2)/2] -[(y1 + y2)/2]
(x + y)(x - y) = x^2 - y^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.

13. What is true about the areas of similar triangles?
Avg = sum of n numbers/n
A fraction whose denominator is 100 i.e. 17% = 17/100
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

14. What is true about the slopes of perpendicular lines?
Divide - then multiply by 100.
Set x = 0 - and solve.
Shifted up 2 units.
The product of their slopes is -1 (negative reciprocal).

15. What is the Pythagorean theorem?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For any right triangle - a^2 + b^2 = c^2.
(Circumference/diameter) of a circle - or approximately 3.14.

16. Properties of one 2
B^m*b^n = b^m+n
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Write the percent over 100 and reduce.
For any integer n: 1^n = 1.

17. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
A = (1/2)bh.
Divide - then multiply by 100.
Shifted left 2 units.

18. What is an exterior angle of a polygon?
1 is the smallest positive odd integer.
An angle formed by extending the side of the polygon.
Set y = 0 - and solve.
A^m/b^m = (a/b)^m

19. What is the formula for the area of a rectangle?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.
A = lw
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.

20. What is an integer?
A fraction whose denominator is 100 i.e. 17% = 17/100
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
All positive and negative whole numbers - and zero.

21. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Avg = sum of n numbers/n
Equal slopes.
Shifted up 2 units.
V = lwh

22. What is the volume of a cube?
Shifted right 2 units.
V = l^3
Avg = sum of n numbers/n
How steep the line is. Horizontal line = 0 - vertical has no slope.

23. How do you find the x-intercept of a graph?
A = bh
Even numbers are divisible by 2 and odd numbers are not.
Set y = 0 - and solve.
(n - 2)(180°)

24. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
At least one of the factors is 0.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

25. What is an even and an odd number?
Arc = (x°/360)(2pr) where x is the central angle.
In the expression x^b - x is the base and b is the exponent.
Their sum is 90°.
Even numbers are divisible by 2 and odd numbers are not.

26. What is the relationship between a radius of a circle and a line that is tangent to the circle?
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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

27. If the product of two or more numbers is 0 - what do you know about the numbers?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(b^m)^n = b^mn
At least one of the factors is 0.

28. What is true about the measures of the four angles formed by two intersecting lines?
A = s^2 or A =d^2/2 where d is the diagonal
The two pairs of opposite angles formed are equal to each other.
A^m*b^m = (ab)^m
D = 2r

29. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
In the expression x^b - x is the base and b is the exponent.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.
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°.

30. Important binomial 2
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Is a right triangle with a ratio of sides x:xv3:2x.

31. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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°.
(x + y)(x - y) = x^2 - y^2
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.

32. What is a negative exponent?
B^m/b^n = b^m-n
A = 2(lw + lh + hw)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any number n: x^-n means 1/x^n.

33. Properties of one 4
Even numbers are divisible by 2 and odd numbers are not.
C = p2r
A = 2(lw + lh + hw)
1 is the smallest positive odd integer.

34. What is the formula for the volume of a rectangular solid?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^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.
V = lwh
Then the product xy is a constant.

35. What are the quotient and the remainder?

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36. What is the formula for the area of a triangle?
A = (1/2)bh.
A = 6(l^2)
Equal slopes.
360°

37. What are the sum - difference - products - and quotient of two numbers?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = 6(l^2)
Is a right triangle with a ratio of sides x:xv3:2x.

38. Law of exponents 5
Avg = sum of n numbers/n
Cannot is 0 - must is 1 - all others are in between.
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^m/b^m = (a/b)^m

39. What is the triangle inequality?
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.
A = 2(lw + lh + hw)
A = 6(l^2)
Shifted left 2 units.

40. What are the properties of a rectangle?
For any number n: x^-n means 1/x^n.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = s^2 or A =d^2/2 where d is the diagonal

41. What does it mean if y is directly proportional to x?
(b^m)^n = b^mn
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Then the quotient y/x is a constant.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

42. What is the measure of a straight angle?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = (1/2)bh.
180°. If two or more angles form a straight angle - their sum is 180°.

43. Properties of zero 2
Write the percent as a decimal - and multiply.
Corresponding sides of similar triangles are in proportion.
If a is negative and b is positive - then a < 0 < b.
They are both the same. A divisor or factor of an integer leaves no remainder.

44. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
For any right triangle - a^2 + b^2 = c^2.
0 is a multiple of every integer.
Divide - then multiply by 100.

45. What is the formula for the volume of a cylinder?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Avg = sum of n numbers/n
Then the product xy is a constant.
V = pr^2h

46. Properties of zero 1
A = [(s^2*v3)/4]
The ratio of corresponding sides of similar triangles.
A = 2(lw + lh + hw)
0 is the only number that is neither positive nor negative.

47. What are the properties of a parallelogram?
1 is a divisor (or factor) of every integer.
Then the product xy is a constant.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

48. Important binomial 3
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
V = l^3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

49. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
A^m*b^m = (ab)^m
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
360°

50. How do you convert a percent to a fraction or a decimal?
1 is the smallest positive odd integer.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Then the quotient y/x is a constant.
Write the percent over 100 and reduce.