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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 volume of a cube?
Divide - then multiply by 100.
V = l^3
Then the product xy is a constant.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

2. What is a percent?
B^m*b^n = b^m+n
The set of all ordered pairs (x -y) such that y = f(x).
A fraction whose denominator is 100 i.e. 17% = 17/100
0 is the only number that is neither positive nor negative.

3. What is true about the measures of the three angles in a triangle?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Their sum is 180°.
Shifted right 2 units.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

4. What is the Pythagorean theorem?
A = s^2 or A =d^2/2 where d is the diagonal
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For any right triangle - a^2 + b^2 = c^2.

5. What formula is used for an average?
M = (y2 - y1)/(x2 - x1)
Avg = sum of n numbers/n
A = (1/2)bh.
Their sum is 180°.

6. What are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
B^m/b^n = b^m-n
Equal slopes.
Corresponding sides of similar triangles are in proportion.

7. What is the formula for the volume of a cylinder?
V = pr^2h
A = [(s^2*v3)/4]
In the expression x^b - x is the base and b is the exponent.
Area = (x°/360)(pr^2) where x is the central angle.

8. What is the area of a square?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = s^2 or A =d^2/2 where d is the diagonal
A = 6(l^2)

9. What are the properties of a parallelogram?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

10. If you were given the graph of y = f(x) - what does f(a) represent?
Their sum is 90°.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Cannot is 0 - must is 1 - all others are in between.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

11. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
Avg = sum of n numbers/n
A = lw
Write the percent over 100 and reduce.

12. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
(b^m)^n = b^mn
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.

13. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
360°
B^m*b^n = b^m+n
C = p2r

14. In a circle of radius r - what is the formula for the diameter?
D = 2r
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Their sum is 90°.
An integer greater than one that is not prime.

15. What is the formula for the surface area of a rectangular solid?
0 is a multiple of every integer.
V = pr^2h
Shifted down 2 units.
A = 2(lw + lh + hw)

16. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
An angle formed by extending the side of the polygon.
A = (1/2)bh.
A^m*b^m = (ab)^m

17. In a circle of radius r - what is the formula for the area?
Shifted right 2 units.
A fraction whose denominator is 100 i.e. 17% = 17/100
A = pr^2
Set y = 0 - and solve.

18. Properties of one 4
1 is the smallest positive odd integer.
Set y = 0 - and solve.
Then the product xy is a constant.
At least one of the factors is 0.

19. Important binomial 1
(x + y)(x - y) = x^2 - y^2
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = s^2 or A =d^2/2 where d is the diagonal
Then the quotient y/x is a constant.

20. How do we write the equation of a line?
If a is negative and b is positive - then a < 0 < b.
The set of all ordered pairs (x -y) such that y = f(x).
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(n - 2)(180°)

21. Law of exponents 3
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.
(b^m)^n = b^mn
Shifted down 2 units.
Area = (x°/360)(pr^2) where x is the central angle.

22. What is an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
A = s^2 or A =d^2/2 where d is the diagonal
Then the product xy is a constant.
180°. If two or more angles form a straight angle - their sum is 180°.

23. 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.
Shifted left 2 units.
B^m*b^n = b^m+n
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.

24. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Arc = (x°/360)(2pr) where x is the central angle.
A fraction whose denominator is 100 i.e. 17% = 17/100

25. What is true about the slopes of perpendicular lines?
V = l^3
The product of their slopes is -1 (negative reciprocal).
(Circumference/diameter) of a circle - or approximately 3.14.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

26. What are similar triangles?
A^m*b^m = (ab)^m
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For any integer n: 1^n = 1.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

27. What are the median and the mode of a set of data?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(b^m)^n = b^mn
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.
1 is the smallest positive odd integer.

28. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Shifted down 2 units.
360°
Set x = 0 - and solve.

29. What is a composite number?
Divide - then multiply by 100.
They are both the same. A divisor or factor of an integer leaves no remainder.
An integer greater than one that is not prime.
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
D = 2r
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

31. What is a function?
360°
Then the product xy is a constant.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
An angle formed by extending the side of the polygon.

32. What is an integer?
All positive and negative whole numbers - and zero.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Even numbers are divisible by 2 and odd numbers are not.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

33. What is a fractional exponent?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
180°. If two or more angles form a straight angle - their sum is 180°.
Then the quotient y/x is a constant.
(n - 2)(180°)

34. What is the formula for the area of a rectangle?
Shifted up 2 units.
Their sum is 90°.
V = l^3
A = lw

35. How do you find the probability that an event will occur?
0 is the only number that is neither positive nor negative.
V = lwh
All positive and negative whole numbers - and zero.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

36. Properties of zero 5
For any number b: b = -b if and only if b = 0.
All positive and negative whole numbers - and zero.
360°
Write the percent as a decimal - and multiply.

37. In a circle of radius r - what is the formula for the circumference?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Divide - then multiply by 100.
C = p2r
Arc = (x°/360)(2pr) where x is the central angle.

38. What is true about the slopes of parallel lines?
[(x1 + x2)/2] -[(y1 + y2)/2]
1 is the smallest positive odd integer.
Equal slopes.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

39. What is a proportion?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
No matter how many angles there are - the sum around the point is 360°.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Then the product xy is a constant.

40. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Their sum 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.
A^m/b^m = (a/b)^m
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.

41. If the product of two or more numbers is 0 - what do you know about the numbers?
At least one of the factors is 0.
M = (y2 - y1)/(x2 - x1)
Shifted left 2 units.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

42. What are the quotient and the remainder?

43. Properties of square roots
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

44. What is a ratio?

45. What is the relationship between a radius of a circle and a line that is tangent to the circle?
B^m/b^n = b^m-n
The product of their slopes is -1 (negative reciprocal).
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
V = l^3

46. What is an even and an odd number?
A = bh
Even numbers are divisible by 2 and odd numbers are not.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
The product of their slopes is -1 (negative reciprocal).

47. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Their sum is 90°.
V = pr^2h

48. Law of exponents 1
B^m*b^n = b^m+n
Arc = (x°/360)(2pr) where x is the central angle.
For any right triangle - a^2 + b^2 = c^2.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

49. What is the formula for the area of a parallelogram?
Avg = sum of n numbers/n
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = bh
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

50. What is p?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
(Circumference/diameter) of a circle - or approximately 3.14.
The product of their slopes is -1 (negative reciprocal).
At least one of the factors is 0.