Test your basic knowledge |

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. What is a prime number?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Shifted right 2 units.
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

2. What is true about the slopes of perpendicular lines?
A = pr^2
Cannot is 0 - must is 1 - all others are in between.
The product of their slopes is -1 (negative reciprocal).
Shifted right 2 units.

3. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
V = pr^2h
Shifted left 2 units.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

4. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
An integer greater than one that is not prime.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A = pr^2

5. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
V = l^3
Then the quotient y/x is a constant.
Cannot is 0 - must is 1 - all others are in between.

6. Properties of zero 5
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
The set of all ordered pairs (x -y) such that y = f(x).
For any number b: b = -b if and only if b = 0.

7. What is true about the areas of similar triangles?
For any integer n: 1^n = 1.
360°
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 two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

8. What is the formula for the volume of a rectangular solid?
Is a right triangle with a ratio of sides x:xv3:2x.
Then the product xy is a constant.
V = lwh
(n - 2)(180°)

9. In a circle of radius r - what is the formula for the diameter?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For any right triangle - a^2 + b^2 = c^2.
D = 2r

10. What is the Pythagorean theorem?
Is a right triangle with a ratio of sides x:xv3:2x.
An angle formed by extending the side of the polygon.
For any right triangle - a^2 + b^2 = c^2.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

11. What is a percent?
Shifted down 2 units.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A fraction whose denominator is 100 i.e. 17% = 17/100
The ratio of corresponding sides of similar triangles.

12. Law of exponents 3
A = [(s^2*v3)/4]
(b^m)^n = b^mn
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Is a right triangle with a ratio of sides x:xv3:2x.

13. Properties of one 1
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(n - 2)(180°)
For any number a: a * 1 = a and a / 1 = a.
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.

14. What is the ratio of similitude?
Shifted right 2 units.
The ratio of corresponding sides of similar triangles.
0 is a multiple of every integer.
Cannot is 0 - must is 1 - all others are in between.

15. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
An integer greater than one that is not prime.
360°
The set of all ordered pairs (x -y) such that y = f(x).

16. In a circle of radius r - what is the formula for the area?
An integer greater than one that is not prime.
V = l^3
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = pr^2

17. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Avg = sum of n numbers/n
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°.
Shifted down 2 units.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

18. Properties of one 3
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.
0 is the only number that is neither positive nor negative.
Shifted right 2 units.
1 is a divisor (or factor) of every integer.

19. What are the properties of a parallelogram?
A = (1/2)bh.
A^m*b^m = (ab)^m
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
1 is a divisor (or factor) of every integer.

20. What is the distributive law?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The two pairs of opposite angles formed are equal to each other.
B^m*b^n = b^m+n

21. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Corresponding sides of similar triangles are in proportion.
Shifted up 2 units.
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.

22. Properties of square roots
At least one of the factors is 0.
All positive and negative whole numbers - and zero.
Corresponding sides of similar triangles are in proportion.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

23. What are the properties of a rectangle?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

24. How do we write the equation of a line?
The set of all ordered pairs (x -y) such that y = f(x).
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.

25. In a circle of radius r - what is the formula for the circumference?
C = p2r
Area = (x°/360)(pr^2) where x is the central angle.
No matter how many angles there are - the sum around the point is 360°.
V = lwh

26. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
A = 6(l^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)

27. What is a proportion?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Shifted up 2 units.
An equation that states that two ratios are equivalent. 4/6 = 10/15

28. What important property do similar triangles have?
[(x1 + x2)/2] -[(y1 + y2)/2]
D = 2r
The ratio of corresponding sides of similar triangles.
Corresponding sides of similar triangles are in proportion.

29. Important binomial 2
The ratio of corresponding sides of similar triangles.
A = 6(l^2)
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

30. What are the important properties of 30-60-90 triangle?
Cannot is 0 - must is 1 - all others are in between.
They are both the same. A divisor or factor of an integer leaves no remainder.
The ratio of corresponding sides of similar triangles.
Is a right triangle with a ratio of sides x:xv3:2x.

31. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
0 is the only number that is neither positive nor negative.

32. Important binomial 3
They are both the same. A divisor or factor of an integer leaves no remainder.
V = l^3
Shifted left 2 units.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

33. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Is a right triangle with a ratio of sides x:xv3:2x.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

34. What is the volume of a cube?
0 is a multiple of every integer.
An angle formed by extending the side of the polygon.
V = l^3
How steep the line is. Horizontal line = 0 - vertical has no slope.

35. Law of exponents 2
Even numbers are divisible by 2 and odd numbers are not.
1 is the smallest positive odd integer.
B^m/b^n = b^m-n
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

36. What is a function?
Is a right triangle with a ratio of sides x:xv3:2x.
360°
How steep the line is. Horizontal line = 0 - vertical has no slope.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

37. What is special formula for the area of an equilateral triangle?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
0 is the only number that is neither positive nor negative.
1 is a divisor (or factor) of every integer.
A = [(s^2*v3)/4]

38. What is a multiple of an integer?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
1 is a divisor (or factor) of every 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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

39. Properties of zero 3
Set y = 0 - and solve.
No matter how many angles there are - the sum around the point is 360°.
0 is a multiple of every integer.
C = p2r

40. For what values of a function is the function undefined?
Avg = sum of n numbers/n
B^m*b^n = b^m+n
An angle formed by extending the side of the polygon.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

41. Properties of zero 1
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Write the percent over 100 and reduce.
0 is the only number that is neither positive nor negative.

42. What is p?
A = (1/2)bh.
The two pairs of opposite angles formed are equal to each other.
(Circumference/diameter) of a circle - or approximately 3.14.
A = [(s^2*v3)/4]

43. If you were given the graph of y = f(x) - what does f(a) represent?
(n - 2)(180°)
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
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

44. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
A = pr^2
1 is the smallest positive odd integer.
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.
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°.

45. What is a composite number?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.
An integer greater than one that is not prime.

46. How do you find the area of a sector of a circle?
Shifted up 2 units.
A = bh
Area = (x°/360)(pr^2) where x is the central angle.
Equal slopes.

47. What is the formula for the area of a triangle?
A = (1/2)bh.
180°. If two or more angles form a straight angle - their sum is 180°.
Write the percent as a decimal - and multiply.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

48. What are similar triangles?
A^m*b^m = (ab)^m
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Set x = 0 - and solve.
For any number b: b = -b if and only if b = 0.

49. What is true about the measures of the two acute angles in a right triangle?
Shifted down 2 units.
An integer greater than one that is not prime.
Their sum is 90°.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

50. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
In the expression x^b - x is the base and b is the exponent.
Their sum is 180°.
[(x1 + x2)/2] -[(y1 + y2)/2]
Shifted up 2 units.