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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. If you were given the graph of y = f(x) - what does f(a) represent?
The set of all ordered pairs (x -y) such that y = f(x).
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

2. What is the formula for the surface area of a cube?
C = p2r
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
(x + y)(x - y) = x^2 - y^2
A = 6(l^2)

3. How do you calculate a weighted average?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Their sum is 180°.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Their sum is 90°.

4. Law of exponents 5
1 is the smallest positive odd integer.
A^m/b^m = (a/b)^m
A = (1/2)bh.
B^m*b^n = b^m+n

5. What is a function?
(b^m)^n = b^mn
V = pr^2h
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

6. What is special formula for the area of an equilateral triangle?
Write the percent over 100 and reduce.
A = [(s^2*v3)/4]
B^m*b^n = b^m+n
Cannot is 0 - must is 1 - all others are in between.

7. Properties of one 1
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any number a: a * 1 = a and a / 1 = a.
Corresponding sides of similar triangles are in proportion.
360°

8. What are the properties of a rectangle?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(Circumference/diameter) of a circle - or approximately 3.14.
A = pr^2

9. Properties of zero 2
(Circumference/diameter) of a circle - or approximately 3.14.
(b^m)^n = b^mn
If a is negative and b is positive - then a < 0 < b.
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.

10. Law of exponents 2
B^m/b^n = b^m-n
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.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
An equation that states that two ratios are equivalent. 4/6 = 10/15

11. Law of exponents 4
Shifted up 2 units.
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.
A = 6(l^2)
A^m*b^m = (ab)^m

12. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

13. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
1 is the smallest positive odd integer.
V = l^3
No matter how many angles there are - the sum around the point is 360°.

14. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
1 is the smallest positive odd integer.
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.
V = lwh
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

15. How do you find the area of a sector of a circle?
M = (y2 - y1)/(x2 - x1)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
[(x1 + x2)/2] -[(y1 + y2)/2]
Area = (x°/360)(pr^2) where x is the central angle.

16. How do you find a percent of a number?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Divide - then multiply by 100.
Write the percent as a decimal - and multiply.

17. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
A = 2(lw + lh + hw)
They are both the same. A divisor or factor of an integer leaves no remainder.
The ratio of corresponding sides of similar triangles.

18. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
Set x = 0 - and solve.
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.
For any number a: a * 1 = a and a / 1 = a.

19. Properties of one 4
1 is the smallest positive odd integer.
An equation that states that two ratios are equivalent. 4/6 = 10/15
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = 2(lw + lh + hw)

20. What is an exponent?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The two pairs of opposite angles formed are equal to each other.
In the expression x^b - x is the base and b is the exponent.
If a is negative and b is positive - then a < 0 < b.

21. What is the sum of the measures of all angles around a point?
No matter how many angles there are - the sum around the point is 360°.
(n - 2)(180°)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
B^m/b^n = b^m-n

22. Properties of zero 4
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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).
Arc = (x°/360)(2pr) where x is the central angle.

23. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
V = lwh
Their sum is 180°.

24. What is the Pythagorean theorem?
(b^m)^n = b^mn
A fraction whose denominator is 100 i.e. 17% = 17/100
For any right triangle - a^2 + b^2 = c^2.
A = 2(lw + lh + hw)

25. In a circle of radius r - what is the formula for the area?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = 2(lw + lh + hw)
A = pr^2

26. What are the properties of a parallelogram?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Avg = sum of n numbers/n

27. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
C = p2r
Write the percent as a decimal - and multiply.
Shifted right 2 units.
Set x = 0 - and solve.

28. 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°.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = lw

29. What is true about the slopes of parallel lines?
Equal slopes.
No matter how many angles there are - the sum around the point is 360°.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Divide - then multiply by 100.

30. What is a ratio?

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31. Law of exponents 1
For any number b: b = -b if and only if b = 0.
Even numbers are divisible by 2 and odd numbers are not.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
B^m*b^n = b^m+n

32. What are the important properties of 30-60-90 triangle?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Is a right triangle with a ratio of sides x:xv3:2x.
A = bh
A^m*b^m = (ab)^m

33. What are the quotient and the remainder?

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34. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
V = l^3
A = lw
For any number n: x^-n means 1/x^n.

35. Important binomial 2
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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
Shifted up 2 units.

36. What are the median and the mode of a set of data?
0 is the only number that is neither positive nor negative.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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 = pr^2

37. What is a multiple of an integer?
A = bh
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 = 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.

38. What is the square root of a number?
Cannot is 0 - must is 1 - all others are in between.
Equal slopes.
Write the percent over 100 and reduce.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

39. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Their sum is 90°.
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

40. What are the important properties of a 45-45 - 90 triangle?
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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Then the quotient y/x is a constant.
The product of their slopes is -1 (negative reciprocal).

41. What is p?
At least one of the factors is 0.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
(Circumference/diameter) of a circle - or approximately 3.14.
(x + y)(x - y) = x^2 - y^2

42. 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.
The two pairs of opposite angles formed are equal to each other.
They are both the same. A divisor or factor of an integer leaves no remainder.
(Circumference/diameter) of a circle - or approximately 3.14.

43. In a circle of radius r - what is the formula for the diameter?
Divide - then multiply by 100.
D = 2r
Set y = 0 - and solve.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

44. What is a percent?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For any right triangle - a^2 + b^2 = c^2.
A fraction whose denominator is 100 i.e. 17% = 17/100
C = p2r

45. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
An angle formed by extending the side of the polygon.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Cannot is 0 - must is 1 - all others are in between.

46. What is the formula for the area of a parallelogram?
A = bh
An integer greater than one that is not prime.
A = pr^2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

47. How do we write the equation of a line?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
They are both the same. A divisor or factor of an integer leaves no remainder.
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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

48. What is the measure of a straight angle?
If a is negative and b is positive - then a < 0 < b.
(b^m)^n = b^mn
The product of their slopes is -1 (negative reciprocal).
180°. If two or more angles form a straight angle - their sum is 180°.

49. 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.
For any number n: x^-n means 1/x^n.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(b^m)^n = b^mn

50. Properties of one 3
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
1 is a divisor (or factor) of every integer.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Then the product xy is a constant.