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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?
Set y = 0 - and solve.
At least one of the factors is 0.
[(x1 + x2)/2] -[(y1 + y2)/2]
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

2. What is the distance formula?
Set x = 0 - and solve.
A = (1/2)bh.
A = 6(l^2)
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

3. What is the midpoint formula?
M = (y2 - y1)/(x2 - x1)
Divide - then multiply by 100.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
[(x1 + x2)/2] -[(y1 + y2)/2]

4. What is true about the measures of the three angles in a triangle?
(b^m)^n = b^mn
Their sum is 90°.
Their sum is 180°.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

5. What is p?
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/b^n = b^m-n
(Circumference/diameter) of a circle - or approximately 3.14.
Arc = (x°/360)(2pr) where x is the central angle.

6. What is true about the slopes of parallel lines?
For any number a: a * 1 = a and a / 1 = a.
Equal slopes.
Write the percent over 100 and reduce.
Shifted up 2 units.

7. 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.
An angle formed by extending the side of the polygon.
V = lwh
For any integer n: 1^n = 1.

8. What do we mean by the slope of the line?
An integer greater than one that is not prime.
How steep the line is. Horizontal line = 0 - vertical has no slope.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
(b^m)^n = b^mn

9. What is true about the measures of the two acute angles in a right triangle?
[(x1 + x2)/2] -[(y1 + y2)/2]
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Their sum is 90°.
In the expression x^b - x is the base and b is the exponent.

10. What is the formula for the area of a triangle?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Set x = 0 - and solve.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = (1/2)bh.

11. Important binomial 1
For any integer n: 1^n = 1.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
(x + y)(x - y) = x^2 - y^2
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

12. What is the graph of a function?
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.
The set of all ordered pairs (x -y) such that y = f(x).
Write the percent as a decimal - and multiply.
Shifted up 2 units.

13. What is true about the areas of similar triangles?
At least one of the factors is 0.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any number b: b = -b if and only if b = 0.

14. Properties of zero 5
Then the quotient y/x is a constant.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any number b: b = -b if and only if b = 0.
V = lwh

15. What are the important properties of 30-60-90 triangle?
For any right triangle - a^2 + b^2 = c^2.
A = pr^2
At least one of the factors is 0.
Is a right triangle with a ratio of sides x:xv3:2x.

16. What is the formula for the volume of a cylinder?
Write the percent as a decimal - and multiply.
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.
V = pr^2h

17. What is the sum of the measures of the n angles of a polygon with n sides?
The set of all ordered pairs (x -y) such that y = f(x).
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(n - 2)(180°)
A = 2(lw + lh + hw)

18. What is a negative exponent?
V = l^3
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.
For any number n: x^-n means 1/x^n.
Shifted down 2 units.

19. What is the formula for the area of a parallelogram?
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = bh
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Shifted up 2 units.

20. What is a multiple of an integer?
Write the percent as a decimal - and multiply.
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.
M = (y2 - y1)/(x2 - x1)
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

21. 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.
A^m/b^m = (a/b)^m
(b^m)^n = b^mn

22. In a circle of radius r - what is the formula for the area?
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = pr^2
Cannot is 0 - must is 1 - all others are in between.
A = s^2 or A =d^2/2 where d is the diagonal

23. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
For any number a: a * 1 = a and a / 1 = a.
The two pairs of opposite angles formed are equal to each other.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Shifted up 2 units.

24. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Cannot is 0 - must is 1 - all others are in between.
The ratio of corresponding sides of similar triangles.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

25. What is true about the measures of the four angles formed by two intersecting lines?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
The two pairs of opposite angles formed are equal to each other.
Equal slopes.

26. How do you find the length of an arc of a circle?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Cannot is 0 - must is 1 - all others are in between.
Set y = 0 - and solve.
Arc = (x°/360)(2pr) where x is the central angle.

27. Properties of zero 1
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)
Shifted right 2 units.
0 is the only number that is neither positive nor negative.

28. What is a divisor and a factor of an integer?
360°
For any right triangle - a^2 + b^2 = c^2.
0 is the only number that is neither positive nor negative.
They are both the same. A divisor or factor of an integer leaves no remainder.

29. Properties of one 3
V = pr^2h
1 is a divisor (or factor) of every integer.
If a is negative and b is positive - then a < 0 < b.
An angle formed by extending the side of the polygon.

30. What are the properties of a rectangle?
Cannot is 0 - must is 1 - all others are in between.
Equal slopes.
They are both the same. A divisor or factor of an integer leaves no remainder.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

31. What is the formula for the area of a rectangle?
Shifted right 2 units.
A = lw
Is a right triangle with a ratio of sides x:xv3:2x.
A^m/b^m = (a/b)^m

32. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Avg = sum of n numbers/n

33. In a circle of radius r - what is the formula for the circumference?
A = bh
C = p2r
M = (y2 - y1)/(x2 - x1)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

34. Law of exponents 4
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.
A^m*b^m = (ab)^m
Shifted left 2 units.
An angle formed by extending the side of the polygon.

35. How do you find the slope of a line?
(b^m)^n = b^mn
Set y = 0 - and solve.
(Circumference/diameter) of a circle - or approximately 3.14.
M = (y2 - y1)/(x2 - x1)

36. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
(n - 2)(180°)
A^m*b^m = (ab)^m
M = (y2 - y1)/(x2 - x1)

37. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
A = pr^2
Then the quotient y/x is a constant.
All positive and negative whole numbers - and zero.

38. What is a Venn diagram?
For any integer n: 1^n = 1.
Shifted left 2 units.
180°. If two or more angles form a straight angle - their sum is 180°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

39. What is the probability of an event that cannot occur? That must occur?
A = bh
Cannot is 0 - must is 1 - all others are in between.
1 is a divisor (or factor) of every integer.
(b^m)^n = b^mn

40. Law of exponents 5
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A^m/b^m = (a/b)^m
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

41. What is an integer?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Corresponding sides of similar triangles are in proportion.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
All positive and negative whole numbers - and zero.

42. What are the quotient and the remainder?

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43. Law of exponents 1
The product of their slopes is -1 (negative reciprocal).
Shifted up 2 units.
(Circumference/diameter) of a circle - or approximately 3.14.
B^m*b^n = b^m+n

44. Properties of one 2
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
M = (y2 - y1)/(x2 - x1)
A = pr^2
For any integer n: 1^n = 1.

45. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Shifted right 2 units.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

46. How do you find the area of a sector of a circle?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Area = (x°/360)(pr^2) where x is the central angle.
(b^m)^n = b^mn
V = l^3

47. What is a percent?
(n - 2)(180°)
180°. If two or more angles form a straight angle - their sum is 180°.
A fraction whose denominator is 100 i.e. 17% = 17/100
1 is a divisor (or factor) of every integer.

48. What is the distributive law?
A = 2(lw + lh + hw)
V = l^3
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Write the percent over 100 and reduce.

49. How do we write the equation of a line?
A = pr^2
Equal slopes.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

50. What does it mean if y is directly proportional to x?
They are both the same. A divisor or factor of an integer leaves no remainder.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Then the quotient y/x is a constant.
A = 6(l^2)