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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 the product of two or more numbers is 0 - what do you know about the numbers?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
How steep the line is. Horizontal line = 0 - vertical has no slope.
At least one of the factors is 0.
(Circumference/diameter) of a circle - or approximately 3.14.

2. What is a fractional exponent?
Equal slopes.
(x + y)(x - y) = x^2 - y^2
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

3. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Shifted up 2 units.
Even numbers are divisible by 2 and odd numbers are not.

4. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
Write the percent as a decimal - and multiply.
For any integer n: 1^n = 1.
The product of their slopes is -1 (negative reciprocal).

5. Important binomial 2
The two pairs of opposite angles formed are equal to each other.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Set y = 0 - and solve.
B^m/b^n = b^m-n

6. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Area = (x°/360)(pr^2) where x is the central angle.
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°.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

7. What is an even and an odd number?
180°. If two or more angles form a straight angle - their sum is 180°.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = bh
Even numbers are divisible by 2 and odd numbers are not.

8. 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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
B^m*b^n = b^m+n
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

9. In a circle of radius r - what is the formula for the area?
Arc = (x°/360)(2pr) where x is the central angle.
A = pr^2
360°
Even numbers are divisible by 2 and odd numbers are not.

10. What is a multiple of an integer?
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.
Arc = (x°/360)(2pr) where x is the central angle.
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.
Shifted down 2 units.

11. Law of exponents 3
A^m*b^m = (ab)^m
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any right triangle - a^2 + b^2 = c^2.
(b^m)^n = b^mn

12. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
C = p2r
For any integer n: 1^n = 1.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

13. Properties of one 2
(b^m)^n = b^mn
[(x1 + x2)/2] -[(y1 + y2)/2]
For any integer n: 1^n = 1.
Cannot is 0 - must is 1 - all others are in between.

14. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
0 is the only number that is neither positive nor negative.
Then the product xy is a constant.
How steep the line is. Horizontal line = 0 - vertical has no slope.

15. What are the properties of a square?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted right 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 fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

16. What is the volume of a cube?
V = l^3
For any number b: b = -b if and only if b = 0.
Arc = (x°/360)(2pr) where x is the central angle.
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.

17. Properties of zero 5
360°
For any number b: b = -b if and only if b = 0.
In the expression x^b - x is the base and b is the exponent.
The product of their slopes is -1 (negative reciprocal).

18. Law of exponents 4
A^m*b^m = (ab)^m
1 is the smallest positive odd integer.
They are both the same. A divisor or factor of an integer leaves no remainder.
Area = (x°/360)(pr^2) where x is the central angle.

19. How do you calculate percent increases and decreases?
Corresponding sides of similar triangles are in proportion.
A = (1/2)bh.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = pr^2

20. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
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 right triangle - a^2 + b^2 = c^2.
All positive and negative whole numbers - and zero.

21. How do we write the equation of a line?
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°.
The ratio of corresponding sides of similar triangles.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Avg = sum of n numbers/n

22. What are the important properties of 30-60-90 triangle?
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 = (ab)^m
Is a right triangle with a ratio of sides x:xv3:2x.
The set of all ordered pairs (x -y) such that y = f(x).

23. What is true about the slopes of parallel lines?
Equal slopes.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Their sum is 90°.
V = l^3

24. What is a negative exponent?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The set of all ordered pairs (x -y) such that y = f(x).
Shifted left 2 units.
For any number n: x^-n means 1/x^n.

25. What is the square root of a number?
Corresponding sides of similar triangles are in proportion.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Is a right triangle with a ratio of sides x:xv3:2x.
Their sum is 180°.

26. What is the graph of a function?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = 2(lw + lh + hw)
The set of all ordered pairs (x -y) such that y = f(x).

27. What is a function?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An angle formed by extending the side of the polygon.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

28. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Shifted down 2 units.
Avg = sum of n numbers/n

29. How do you find the length of an arc of a circle?
(b^m)^n = b^mn
V = l^3
They are both the same. A divisor or factor of an integer leaves no remainder.
Arc = (x°/360)(2pr) where x is the central angle.

30. What is the distance formula?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
All positive and negative whole numbers - and zero.
1 is the smallest positive odd integer.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

31. What is a ratio?

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32. What is true about the measures of the four angles formed by two intersecting lines?
The two pairs of opposite angles formed are equal to each other.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A fraction whose denominator is 100 i.e. 17% = 17/100

33. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
For any number a: a * 1 = a and a / 1 = a.
Write the percent over 100 and reduce.
[(x1 + x2)/2] -[(y1 + y2)/2]

34. What is true about the measures of the three angles in a triangle?
Shifted up 2 units.
Is a right triangle with a ratio of sides x:xv3:2x.
Their sum is 180°.
A^m*b^m = (ab)^m

35. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Shifted down 2 units.
Divide - then multiply by 100.

36. Law of exponents 1
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
All positive and negative whole numbers - and zero.
B^m*b^n = b^m+n
Shifted up 2 units.

37. How do you find the x-intercept of a graph?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
C = p2r
A = 6(l^2)
Set y = 0 - and solve.

38. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Cannot is 0 - must is 1 - all others are in between.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
M = (y2 - y1)/(x2 - x1)

39. What is the formula for the area of a parallelogram?
Set y = 0 - and solve.
A = bh
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
B^m/b^n = b^m-n

40. What is the sum of the measures of the n angles of a polygon with n sides?
For any integer n: 1^n = 1.
For any number a: a * 1 = a and a / 1 = a.
(n - 2)(180°)
P(e) = (# of favorable outcomes)/(# of possible outcomes)

41. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
Write the percent over 100 and reduce.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
360°

42. 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.
For any number a: a * 1 = a and a / 1 = a.
V = l^3
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

43. What are the quotient and the remainder?

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44. Law of exponents 2
B^m/b^n = b^m-n
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
0 is a multiple of every integer.
An angle formed by extending the side of the polygon.

45. What is the probability of an event that cannot occur? That must occur?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Set x = 0 - and solve.
Cannot is 0 - must is 1 - all others are in between.
Shifted right 2 units.

46. What is an exterior angle of a triangle?
1 is a divisor (or factor) of every integer.
The set of all ordered pairs (x -y) such that y = f(x).
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

47. What are similar triangles?
1 is a divisor (or factor) of every integer.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(b^m)^n = b^mn
V = l^3

48. What is the Pythagorean theorem?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
V = lwh
For any right triangle - a^2 + b^2 = c^2.
Shifted up 2 units.

49. What is the formula for the surface area of a cube?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Equal slopes.
A = 6(l^2)
Area = (x°/360)(pr^2) where x is the central angle.

50. What is a composite number?
360°
Their sum is 180°.
An integer greater than one that is not prime.
(b^m)^n = b^mn