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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.
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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 x-intercept of a graph?
(b^m)^n = b^mn
If a is negative and b is positive - then a < 0 < b.
Set y = 0 - and solve.
Corresponding sides of similar triangles are in proportion.

2. What is the area of a square?
Corresponding sides of similar triangles are in proportion.
For any right triangle - a^2 + b^2 = c^2.
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

3. What is a function?
V = pr^2h
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 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.
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.

4. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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°.
A = [(s^2*v3)/4]
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.

5. Properties of one 1
In the expression x^b - x is the base and b is the exponent.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
180°. If two or more angles form a straight angle - their sum is 180°.
For any number a: a * 1 = a and a / 1 = a.

6. Law of exponents 5
For any number n: x^-n means 1/x^n.
Then the quotient y/x is a constant.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A^m/b^m = (a/b)^m

7. Law of exponents 4
For any number a: a * 1 = a and a / 1 = a.
A^m*b^m = (ab)^m
Divide - then multiply by 100.
360°

8. What is true about the measures of the three angles in a triangle?
Set x = 0 - and solve.
Their sum is 180°.
Even numbers are divisible by 2 and odd numbers are not.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

9. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
D = 2r
V = pr^2h
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

10. What is a negative exponent?
For any number n: x^-n means 1/x^n.
Cannot is 0 - must is 1 - all others are in between.
All positive and negative whole numbers - and zero.
For any number b: b = -b if and only if b = 0.

11. 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.
Their sum is 90°.
For any number n: x^-n means 1/x^n.
[(x1 + x2)/2] -[(y1 + y2)/2]

12. What are the sum - difference - products - and quotient of two numbers?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Divide - then multiply by 100.
0 is the only number that is neither positive nor negative.

13. In a circle of radius r - what is the formula for the diameter?
Set x = 0 - and solve.
Their sum is 180°.
D = 2r
C = p2r

14. What is the probability of an event that cannot occur? That must occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Cannot is 0 - must is 1 - all others are in between.
An integer greater than one that is not prime.
How steep the line is. Horizontal line = 0 - vertical has no slope.

15. Properties of zero 5
(Circumference/diameter) of a circle - or approximately 3.14.
For any number b: b = -b if and only if b = 0.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
How steep the line is. Horizontal line = 0 - vertical has no slope.

16. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
Then the quotient y/x is a constant.
0 is the only number that is neither positive nor negative.
For any number n: x^-n means 1/x^n.

17. Properties of zero 3
0 is a multiple of every integer.
A = 6(l^2)
A = 2(lw + lh + hw)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

18. What is a composite number?
An integer greater than one that is not prime.
The set of all ordered pairs (x -y) such that y = f(x).
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°.
Write the percent over 100 and reduce.

19. What are the median and the mode of a set of data?
All positive and negative whole numbers - and zero.
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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

20. What is the formula for the volume of a cylinder?
V = pr^2h
For any integer n: 1^n = 1.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
0 is a multiple of every integer.

21. What is an exterior angle of a triangle?
The product of their slopes is -1 (negative reciprocal).
Avg = sum of n numbers/n
C = p2r
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

22. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Cannot is 0 - must is 1 - all others are in between.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = bh
Equal slopes.

23. How do you find the slope of a line?
Set x = 0 - and solve.
V = l^3
M = (y2 - y1)/(x2 - x1)
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.

24. What is a ratio?

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25. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
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 left 2 units.
V = l^3

26. What is the formula for the volume of a rectangular solid?
A = bh
V = lwh
Their sum is 90°.
360°

27. What is the sum of the measures of the n angles of a polygon with n sides?
In the expression x^b - x is the base and b is the exponent.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
(n - 2)(180°)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

28. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
Equal slopes.
For any number n: x^-n means 1/x^n.
For any number a: a * 1 = a and a / 1 = a.

29. What is p?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any number a: a * 1 = a and a / 1 = a.
A = bh
(Circumference/diameter) of a circle - or approximately 3.14.

30. What formula is used for an average?
M = (y2 - y1)/(x2 - x1)
B^m*b^n = b^m+n
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Avg = sum of n numbers/n

31. Properties of zero 1
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
An angle formed by extending the side of the polygon.
0 is the only number that is neither positive nor negative.
Arc = (x°/360)(2pr) where x is the central angle.

32. What is a fractional exponent?
360°
Area = (x°/360)(pr^2) where x is the central angle.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

33. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.
V = l^3

34. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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°.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

35. What is the formula for the area of a parallelogram?
Cannot is 0 - must is 1 - all others are in between.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A = bh
All positive and negative whole numbers - and zero.

36. What is the formula for the surface area of a cube?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Shifted left 2 units.
Avg = sum of n numbers/n
A = 6(l^2)

37. If the product of two or more numbers is 0 - what do you know about the numbers?
Area = (x°/360)(pr^2) where x is the central angle.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
0 is the only number that is neither positive nor negative.
At least one of the factors is 0.

38. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
For any integer n: 1^n = 1.
Shifted up 2 units.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For any number a: a * 1 = a and a / 1 = a.

39. Properties of one 3
B^m*b^n = b^m+n
C = p2r
1 is a divisor (or factor) of every integer.
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.

40. What are the quotient and the remainder?

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41. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
A = pr^2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.

42. Properties of zero 2
Shifted down 2 units.
A = pr^2
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
If a is negative and b is positive - then a < 0 < b.

43. How do you convert a percent to a fraction or a decimal?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Write the percent over 100 and reduce.
Their sum is 90°.
V = pr^2h

44. What is a multiple of an integer?
(b^m)^n = b^mn
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 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.
At least one of the factors is 0.

45. What is a percent?
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^m*b^m = (ab)^m
A fraction whose denominator is 100 i.e. 17% = 17/100
(n - 2)(180°)

46. What does it mean if y is inversely proportional to x?
Divide - then multiply by 100.
Their sum is 180°.
(x + y)(x - y) = x^2 - y^2
Then the product xy is a constant.

47. What is an exterior angle of a polygon?
Corresponding sides of similar triangles are in proportion.
The two pairs of opposite angles formed are equal to each other.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
An angle formed by extending the side of the polygon.

48. What is a divisor and a factor of an integer?
Their sum is 180°.
They are both the same. A divisor or factor of an integer leaves no remainder.
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°.
An angle formed by extending the side of the polygon.

49. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
For any right triangle - a^2 + b^2 = c^2.
A^m/b^m = (a/b)^m
Avg = sum of n numbers/n
360°

50. What is the volume of a cube?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
V = l^3
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

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