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GRE Math: Facts

Subjects : gre, math

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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. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
The ratio of corresponding sides of similar triangles.
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.
360°

2. What is the triangle inequality?
All positive and negative whole numbers - and zero.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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.
B^m/b^n = b^m-n

3. What is the sum of the measures of the n angles of a polygon with n sides?
Then the quotient y/x is a constant.
The set of all ordered pairs (x -y) such that y = f(x).
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(n - 2)(180°)

4. What is the relationship between a radius of a circle and a line that is tangent to the circle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
D = 2r
How steep the line is. Horizontal line = 0 - vertical has no slope.

5. What is a divisor and a factor of an integer?
Even numbers are divisible by 2 and odd numbers are not.
They are both the same. A divisor or factor of an integer leaves no remainder.
Corresponding sides of similar triangles are in proportion.
How steep the line is. Horizontal line = 0 - vertical has no slope.

6. What are the median and the mode of a set of data?
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 = 6(l^2)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

7. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
C = p2r
An integer greater than one that is not prime.
All positive and negative whole numbers - and zero.

8. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Shifted right 2 units.
0 is the only number that is neither positive nor negative.

9. How do you find the length of an arc of a circle?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Arc = (x°/360)(2pr) where x is the central angle.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A fraction whose denominator is 100 i.e. 17% = 17/100

10. What does it mean if y is inversely proportional to x?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Then the product xy is a constant.
A = pr^2
Area = (x°/360)(pr^2) where x is the central angle.

11. What is a prime number?
1 is the smallest positive odd 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.
(b^m)^n = b^mn
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.

12. What is the formula for the volume of a rectangular solid?
For any integer n: 1^n = 1.
V = lwh
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Shifted right 2 units.

13. Law of exponents 3
(b^m)^n = b^mn
M = (y2 - y1)/(x2 - x1)
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
They are both the same. A divisor or factor of an integer leaves no remainder.

14. What is the midpoint formula?
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.
For any integer n: 1^n = 1.
[(x1 + x2)/2] -[(y1 + y2)/2]
Area = (x°/360)(pr^2) where x is the central angle.

15. Properties of square roots
C = p2r
(n - 2)(180°)
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A^m*b^m = (ab)^m

16. What do we mean by the slope of the line?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Cannot is 0 - must is 1 - all others are in between.
How steep the line is. Horizontal line = 0 - vertical has no slope.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

17. What is the formula for the area of a triangle?
For any number n: x^-n means 1/x^n.
A = lw
A = (1/2)bh.
For any number b: b = -b if and only if b = 0.

18. Important binomial 3
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°.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
1 is the smallest positive odd integer.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

19. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
The product of their slopes is -1 (negative reciprocal).
A = pr^2
No matter how many angles there are - the sum around the point is 360°.

20. What is an exponent?
D = 2r
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
In the expression x^b - x is the base and b is the exponent.
For any number n: x^-n means 1/x^n.

21. What is the formula for the surface area of a cube?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = 6(l^2)
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

22. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
An angle formed by extending the side of the polygon.
The ratio of corresponding sides of similar triangles.
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°.

23. What is an integer?
Shifted up 2 units.
All positive and negative whole numbers - and zero.
Write the percent over 100 and reduce.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

24. Properties of zero 3
0 is a multiple of every integer.
[(x1 + x2)/2] -[(y1 + y2)/2]
Is a right triangle with a ratio of sides x:xv3:2x.
If a is negative and b is positive - then a < 0 < b.

25. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
All positive and negative whole numbers - and zero.
(n - 2)(180°)
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

26. What is the distributive law?
Area = (x°/360)(pr^2) where x is the central angle.
Equal slopes.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

27. What are the properties of a square?
The product of their slopes is -1 (negative reciprocal).
A fraction whose denominator is 100 i.e. 17% = 17/100
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

28. How do you calculate a weighted average?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Shifted left 2 units.
Then the quotient y/x is a constant.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

29. What is the area of a square?
0 is the only number that is neither positive nor negative.
Their sum is 90°.
A = s^2 or A =d^2/2 where d is the diagonal
A = lw

30. In a circle of radius r - what is the formula for the area?
M = (y2 - y1)/(x2 - x1)
A = pr^2
Then the product xy is a constant.
0 is the only number that is neither positive nor negative.

31. What are the properties of a parallelogram?
Is a right triangle with a ratio of sides x:xv3:2x.
Equal slopes.
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

32. What is the square root of a number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
D = 2r
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

33. What is a proportion?
A = [(s^2*v3)/4]
For any integer n: 1^n = 1.
An integer greater than one that is not prime.
An equation that states that two ratios are equivalent. 4/6 = 10/15

34. For what values of a function is the function undefined?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Arc = (x°/360)(2pr) where x is the central angle.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any right triangle - a^2 + b^2 = c^2.

35. Properties of zero 1
1 is a divisor (or factor) of every integer.
A = 6(l^2)
0 is the only number that is neither positive nor negative.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

36. What is the formula for the area of a parallelogram?
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 = l^3
A = bh
Write the percent as a decimal - and multiply.

37. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
The ratio of corresponding sides of similar triangles.
A = (1/2)bh.
How steep the line is. Horizontal line = 0 - vertical has no slope.

38. What is true about the measures of the three angles in a triangle?
180°. If two or more angles form a straight angle - their sum is 180°.
Their sum is 180°.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Area = (x°/360)(pr^2) where x is the central angle.

39. Properties of zero 5
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
B^m*b^n = b^m+n
Their sum is 90°.
For any number b: b = -b if and only if b = 0.

40. What is true about the slopes of perpendicular lines?
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).
Divide - then multiply by 100.
Even numbers are divisible by 2 and odd numbers are not.

41. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
For any right triangle - a^2 + b^2 = c^2.
Their sum is 90°.
A^m/b^m = (a/b)^m

42. What is a fractional exponent?
A = (1/2)bh.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Area = (x°/360)(pr^2) where x is the central angle.
At least one of the factors is 0.

43. What are similar triangles?
For any right triangle - a^2 + b^2 = c^2.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Then the product xy is a constant.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

44. In a circle of radius r - what is the formula for the circumference?
Set y = 0 - and solve.
360°
Their sum is 90°.
C = p2r

45. What is a composite number?
For any number n: x^-n means 1/x^n.
0 is the only number that is neither positive nor negative.
An integer greater than one that is not prime.
Shifted down 2 units.

46. What is true about the areas of similar triangles?
The set of all ordered pairs (x -y) such that y = f(x).
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.
C = p2r
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

47. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
For any integer n: 1^n = 1.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
An equation that states that two ratios are equivalent. 4/6 = 10/15

48. What is a function?
1 is the smallest positive odd integer.
(x + y)(x - y) = x^2 - y^2
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

49. If you were given the graph of y = f(x) - what does f(a) represent?
Write the percent as a decimal - and multiply.
Cannot is 0 - must is 1 - all others are in between.
Set y = 0 - and solve.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

50. What are the sum - difference - products - and quotient of two numbers?
360°
D = 2r
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

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