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 percent?
Is a right triangle with a ratio of sides x:xv3:2x.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Their sum is 180°.
A fraction whose denominator is 100 i.e. 17% = 17/100

2. What is the measure of a straight angle?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
180°. If two or more angles form a straight angle - their sum is 180°.
(x + y)(x - y) = x^2 - y^2
All positive and negative whole numbers - and zero.

3. What is the formula for the area of a triangle?
A^m/b^m = (a/b)^m
A = (1/2)bh.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

4. What do we mean by the slope of the line?
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.
Shifted left 2 units.
Their sum is 180°.

5. What is the formula for the surface area of a cube?
For any number a: a * 1 = a and a / 1 = a.
A = 6(l^2)
Shifted down 2 units.
An equation that states that two ratios are equivalent. 4/6 = 10/15

6. In a circle of radius r - what is the formula for the circumference?
V = l^3
C = p2r
1 is the smallest positive odd integer.
A = 2(lw + lh + hw)

7. How do you find the probability that an event will occur?
(n - 2)(180°)
360°
A = 6(l^2)
P(e) = (# of favorable outcomes)/(# of possible outcomes)

8. What is the area of a square?
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°.
A = s^2 or A =d^2/2 where d is the diagonal
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.
C = p2r

9. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
The two pairs of opposite angles formed are equal to each other.
1 is a divisor (or factor) of every integer.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

10. Law of exponents 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(b^m)^n = b^mn
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
In the expression x^b - x is the base and b is the exponent.

11. Properties of zero 1
0 is the only number that is neither positive nor negative.
D = 2r
M = (y2 - y1)/(x2 - x1)
An integer greater than one that is not prime.

12. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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.
Their sum is 90°.

13. How do we write the equation of a line?
Is a right triangle with a ratio of sides x:xv3:2x.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For any number b: b = -b if and only if b = 0.
Their sum is 180°.

14. Law of exponents 2
The product of their slopes is -1 (negative reciprocal).
For any integer n: 1^n = 1.
B^m/b^n = b^m-n
Is a right triangle with a ratio of sides x:xv3:2x.

15. What is the sum of the measures of all angles around a point?
Is a right triangle with a ratio of sides x:xv3:2x.
Set y = 0 - and solve.
V = l^3
No matter how many angles there are - the sum around the point is 360°.

16. Important binomial 2
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Then the product xy is a constant.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Cannot is 0 - must is 1 - all others are in between.

17. Law of exponents 4
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.
A^m*b^m = (ab)^m
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

18. What is p?
A = 6(l^2)
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
(Circumference/diameter) of a circle - or approximately 3.14.

19. What are the properties of a rectangle?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
At least one of the factors is 0.
D = 2r
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

20. What is the formula for the volume of a cylinder?
Shifted up 2 units.
A = 6(l^2)
V = l^3
V = pr^2h

21. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
How steep the line is. Horizontal line = 0 - vertical has no slope.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

22. What is an exterior angle of a polygon?
A = s^2 or A =d^2/2 where d is the diagonal
(x + y)(x - y) = x^2 - y^2
An angle formed by extending the side of the polygon.
At least one of the factors is 0.

23. For what values of a function is the function undefined?
They are both the same. A divisor or factor of an integer leaves no remainder.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
360°
360°

24. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Even numbers are divisible by 2 and odd numbers are not.
For any number n: x^-n means 1/x^n.

25. Properties of zero 5
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
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 any number b: b = -b if and only if b = 0.
For any integer n: 1^n = 1.

26. What is a fractional exponent?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
(x + y)(x - y) = x^2 - y^2
The ratio of corresponding sides of similar triangles.
Then the product xy is a constant.

27. Properties of square roots
A = 2(lw + lh + hw)
For any integer n: 1^n = 1.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
1 is the smallest positive odd integer.

28. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Then the quotient y/x is a constant.
Shifted right 2 units.
[(x1 + x2)/2] -[(y1 + y2)/2]

29. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
The ratio of corresponding sides of similar triangles.
Set x = 0 - and solve.
The two pairs of opposite angles formed are equal to each other.

30. What is the midpoint formula?
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.
[(x1 + x2)/2] -[(y1 + y2)/2]
For any right triangle - a^2 + b^2 = c^2.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

31. If you were given the graph of y = f(x) - what does f(a) represent?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
(Circumference/diameter) of a circle - or approximately 3.14.
For any number b: b = -b if and only if b = 0.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

32. What is the formula for the area of a parallelogram?
V = l^3
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = bh
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

33. What is true about the slopes of parallel lines?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Equal slopes.
Arc = (x°/360)(2pr) where x is the central angle.
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.

34. How do you find the area of a sector of a circle?
1 is a divisor (or factor) of every integer.
If a is negative and b is positive - then a < 0 < b.
Area = (x°/360)(pr^2) where x is the central angle.
0 is a multiple of every integer.

35. What are the median and the mode of a set of data?
A = s^2 or A =d^2/2 where d is the diagonal
Shifted right 2 units.
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

36. What is an even and an odd number?
For any number a: a * 1 = a and a / 1 = a.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Even numbers are divisible by 2 and odd numbers are not.
At least one of the factors is 0.

37. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
The ratio of corresponding sides of similar triangles.
360°
Shifted up 2 units.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

38. Properties of one 2
For any integer n: 1^n = 1.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
V = l^3
For any number n: x^-n means 1/x^n.

39. What are the sum - difference - products - and quotient of two numbers?
360°
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An integer greater than one that is not prime.

40. What is the relationship between a radius of a circle and a line that is tangent to the circle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
They are both the same. A divisor or factor of an integer leaves no remainder.
The set of all ordered pairs (x -y) such that y = f(x).
0 is the only number that is neither positive nor negative.

41. What are the properties of a square?
Corresponding sides of similar triangles are in proportion.
A = (1/2)bh.
1 is a divisor (or factor) of every integer.
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.

42. What is a composite number?
An integer greater than one that is not prime.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
0 is a multiple of every integer.
180°. If two or more angles form a straight angle - their sum is 180°.

43. What is the graph of a function?
0 is the only number that is neither positive nor negative.
Set y = 0 - and solve.
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.
The set of all ordered pairs (x -y) such that y = f(x).

44. Law of exponents 5
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.
Set x = 0 - and solve.
A^m/b^m = (a/b)^m
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 are similar triangles?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Avg = sum of n numbers/n
For any integer n: 1^n = 1.
Their sum is 180°.

46. What is the formula for the area of a rectangle?
0 is a multiple of every integer.
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.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = lw

47. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
Then the quotient y/x is a constant.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Set y = 0 - and solve.

48. What is true about the measures of the four angles formed by two intersecting lines?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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.
Shifted right 2 units.
The two pairs of opposite angles formed are equal to each other.

49. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
Cannot is 0 - must is 1 - all others are in between.
The two pairs of opposite angles formed are equal to each other.
Write the percent as a decimal - and multiply.

50. What does it mean if y is directly proportional to x?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Shifted left 2 units.
Then the quotient y/x is a constant.
Corresponding sides of similar triangles are in proportion.