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. Properties of zero 2
A = pr^2
Avg = sum of n numbers/n
If a is negative and b is positive - then a < 0 < b.
[(x1 + x2)/2] -[(y1 + y2)/2]

2. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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.
1 is the smallest positive odd integer.
0 is a multiple of every integer.

3. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
Shifted right 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Divide - then multiply by 100.

4. For what values of a function is the function undefined?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
0 is a multiple of every integer.

5. What is true about the measures of the three angles in a triangle?
For any integer n: 1^n = 1.
Their sum is 180°.
A = lw
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

6. Law of exponents 2
Write the percent as a decimal - and multiply.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
B^m/b^n = b^m-n
Area = (x°/360)(pr^2) where x is the central angle.

7. Law of exponents 4
The ratio of corresponding sides of similar triangles.
Area = (x°/360)(pr^2) where x is the central angle.
A^m*b^m = (ab)^m
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

8. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
[(x1 + x2)/2] -[(y1 + y2)/2]
Even numbers are divisible by 2 and odd numbers are not.
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°.

9. Properties of zero 1
0 is the only number that is neither positive nor negative.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
[(x1 + x2)/2] -[(y1 + y2)/2]
If a is negative and b is positive - then a < 0 < b.

10. What is a function?
In the expression x^b - x is the base and b is the exponent.
How steep the line is. Horizontal line = 0 - vertical has no slope.
All positive and negative whole numbers - and zero.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

11. Properties of one 4
1 is the smallest positive odd integer.
Shifted left 2 units.
A^m/b^m = (a/b)^m
A = 6(l^2)

12. Important binomial 1
360°
For any number b: b = -b if and only if b = 0.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(x + y)(x - y) = x^2 - y^2

13. What is true about the measures of the four angles formed by two intersecting lines?
Shifted up 2 units.
The two pairs of opposite angles formed are equal to each other.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Their sum is 180°.

14. What is the distributive law?
D = 2r
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Their sum is 90°.

15. Properties of square roots
At least one of the factors is 0.
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 positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = lw

16. What is the sum of the measures of all angles around a point?
(b^m)^n = b^mn
No matter how many angles there are - the sum around the point is 360°.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

17. If you were given the graph of y = f(x) - what does f(a) represent?
Write the percent over 100 and reduce.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Corresponding sides of similar triangles are in proportion.
Then the product xy is a constant.

18. What are the properties of a parallelogram?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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.
V = l^3
360°

19. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Avg = sum of n numbers/n

20. What formula is used for an average?
For any number n: x^-n means 1/x^n.
V = pr^2h
Avg = sum of n numbers/n
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

21. Properties of zero 4
A^m/b^m = (a/b)^m
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any number n: x^-n means 1/x^n.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

22. What is the formula for the volume of a rectangular solid?
V = lwh
Shifted down 2 units.
An integer greater than one that is not prime.
They are both the same. A divisor or factor of an integer leaves no remainder.

23. What are the properties of a square?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A^m/b^m = (a/b)^m
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.
Set y = 0 - and solve.

24. What is the formula for the area of a parallelogram?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = bh
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

25. What is true about the slopes of parallel lines?
Equal slopes.
Cannot is 0 - must is 1 - all others are in between.
All positive and negative whole numbers - and zero.
If a is negative and b is positive - then a < 0 < b.

26. Properties of one 3
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
1 is a divisor (or factor) of every integer.
An angle formed by extending the side of the polygon.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

27. Law of exponents 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.
B^m/b^n = b^m-n
1 is a divisor (or factor) of every integer.
(b^m)^n = b^mn

28. 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.
A fraction whose denominator is 100 i.e. 17% = 17/100
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Then the product xy is a constant.

29. How do we write the equation of a line?
An equation that states that two ratios are equivalent. 4/6 = 10/15
No matter how many angles there are - the sum around the point is 360°.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

30. What is the sum of the measures of the n angles of a polygon with n sides?
C = p2r
(n - 2)(180°)
All positive and negative whole numbers - and zero.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

31. What is the graph of a function?
0 is the only number that is neither positive nor negative.
The set of all ordered pairs (x -y) such that y = f(x).
Their sum is 180°.
An integer greater than one that is not prime.

32. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
V = lwh
0 is the only number that is neither positive nor negative.
A = bh

33. What is a composite number?
[(x1 + x2)/2] -[(y1 + y2)/2]
B^m/b^n = b^m-n
An equation that states that two ratios are equivalent. 4/6 = 10/15
An integer greater than one that is not prime.

34. What important property do similar triangles have?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Divide - then multiply by 100.
Corresponding sides of similar triangles are in proportion.

35. What does it mean if y is inversely proportional to x?
360°
Then the product xy is a constant.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
B^m*b^n = b^m+n

36. Properties of one 2
For any integer n: 1^n = 1.
B^m/b^n = b^m-n
Corresponding sides of similar triangles are in proportion.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

37. What are similar triangles?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A^m*b^m = (ab)^m

38. What is a Venn diagram?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(n - 2)(180°)

39. What is the formula for the area of a triangle?
A = lw
A = (1/2)bh.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
If a is negative and b is positive - then a < 0 < b.

40. Properties of zero 5
All positive and negative whole numbers - and zero.
For any number b: b = -b if and only if b = 0.
Write the percent as a decimal - and multiply.
For any right triangle - a^2 + b^2 = c^2.

41. What is the square root of a number?
Shifted right 2 units.
A = [(s^2*v3)/4]
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

42. What are the sum - difference - products - and quotient of two numbers?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
V = lwh
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

43. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
A^m/b^m = (a/b)^m
How steep the line is. Horizontal line = 0 - vertical has no slope.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

44. What is the formula for the area of a rectangle?
Set y = 0 - and solve.
A = lw
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
The set of all ordered pairs (x -y) such that y = f(x).

45. In a circle of radius r - what is the formula for the circumference?
An integer greater than one that is not prime.
Then the product xy is a constant.
The ratio of corresponding sides of similar triangles.
C = p2r

46. In a circle of radius r - what is the formula for the area?
Corresponding sides of similar triangles are in proportion.
A = pr^2
The ratio of corresponding sides of similar triangles.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

47. What is the triangle inequality?
Shifted left 2 units.
If a is negative and b is positive - then a < 0 < b.
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.
Their sum is 180°.

48. What is special formula for the area of an equilateral triangle?
Even numbers are divisible by 2 and odd numbers are not.
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.
A = [(s^2*v3)/4]
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

49. What is a negative exponent?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For any number n: x^-n means 1/x^n.
0 is the only number that is neither positive nor negative.
A = lw

50. If the product of two or more numbers is 0 - what do you know about the numbers?
M = (y2 - y1)/(x2 - x1)
[(x1 + x2)/2] -[(y1 + y2)/2]
V = lwh
At least one of the factors is 0.