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 1
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
360°
How steep the line is. Horizontal line = 0 - vertical has no slope.
0 is the only number that is neither positive nor negative.

2. What is the volume of a cube?
Then the quotient y/x is a constant.
0 is the only number that is neither positive nor negative.
V = l^3
Arc = (x°/360)(2pr) where x is the central angle.

3. In a circle of radius r - what is the formula for the area?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = pr^2
For any right triangle - a^2 + b^2 = c^2.
180°. If two or more angles form a straight angle - their sum is 180°.

4. How you convert a fraction or a decimal to a percent?
For any number b: b = -b if and only if b = 0.
Divide - then multiply by 100.
An angle formed by extending the side of the polygon.
C = p2r

5. How do you find the x-intercept of a graph?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Set y = 0 - and solve.
In the expression x^b - x is the base and b is the exponent.

6. Important binomial 1
The two pairs of opposite angles formed are equal to each other.
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.
All positive and negative whole numbers - and zero.
(x + y)(x - y) = x^2 - y^2

7. 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.
An integer greater than one that is not prime.
Set x = 0 - and solve.
C = p2r

8. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
At least one of the factors is 0.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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 down 2 units.

9. Properties of zero 3
0 is a multiple of every integer.
No matter how many angles there are - the sum around the point is 360°.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For any number a: a * 1 = a and a / 1 = a.

10. Properties of square roots
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Arc = (x°/360)(2pr) where x is the central angle.
Even numbers are divisible by 2 and odd numbers are not.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

11. If the product of two or more numbers is 0 - what do you know about the numbers?
Their sum is 90°.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
No matter how many angles there are - the sum around the point is 360°.
At least one of the factors is 0.

12. What is the formula for the area of a rectangle?
For any number a: a * 1 = a and a / 1 = a.
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 = lw
M = (y2 - y1)/(x2 - x1)

13. What is p?
How steep the line is. Horizontal line = 0 - vertical has no slope.
A fraction whose denominator is 100 i.e. 17% = 17/100
(Circumference/diameter) of a circle - or approximately 3.14.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

14. What is the formula for the volume of a rectangular solid?
Even numbers are divisible by 2 and odd numbers are not.
Avg = sum of n numbers/n
A = 2(lw + lh + hw)
V = lwh

15. What is a multiple of an integer?
At least one of the factors is 0.
For any number b: b = -b if and only if b = 0.
A = 6(l^2)
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.

16. What is the midpoint formula?
The ratio of corresponding sides of similar triangles.
For any number a: a * 1 = a and a / 1 = a.
[(x1 + x2)/2] -[(y1 + y2)/2]
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

17. 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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
1 is the smallest positive odd integer.
Write the percent as a decimal - and multiply.

18. What is a composite number?
Arc = (x°/360)(2pr) where x is the central angle.
Shifted left 2 units.
An integer greater than one that is not prime.
How steep the line is. Horizontal line = 0 - vertical has no slope.

19. If you were given the graph of y = f(x) - what does f(a) represent?
A = 2(lw + lh + hw)
0 is a multiple of every integer.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
B^m*b^n = b^m+n

20. What is special formula for the area of an equilateral triangle?
[(x1 + x2)/2] -[(y1 + y2)/2]
A = [(s^2*v3)/4]
B^m*b^n = b^m+n
Arc = (x°/360)(2pr) where x is the central angle.

21. What are the properties of a rectangle?
Equal slopes.
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.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

22. What is an even and an odd number?
Then the product xy is a constant.
1 is the smallest positive odd integer.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Even numbers are divisible by 2 and odd numbers are not.

23. What is the relationship between a radius of a circle and a line that is tangent to the circle?
For any right triangle - a^2 + b^2 = c^2.
Is a right triangle with a ratio of sides x:xv3:2x.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = s^2 or A =d^2/2 where d is the diagonal

24. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A^m*b^m = (ab)^m
The set of all ordered pairs (x -y) such that y = f(x).

25. Properties of zero 2
A^m/b^m = (a/b)^m
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Cannot is 0 - must is 1 - all others are in between.
If a is negative and b is positive - then a < 0 < b.

26. What is a prime number?
1 is the smallest positive odd integer.
A = pr^2
Avg = sum of n numbers/n
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.

27. What is a function?
1 is the smallest positive odd integer.
Then the quotient y/x is a constant.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

28. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
Cannot is 0 - must is 1 - all others are in between.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For any number b: b = -b if and only if b = 0.

29. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
For any right triangle - a^2 + b^2 = c^2.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For any integer n: 1^n = 1.

30. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The set of all ordered pairs (x -y) such that y = f(x).
Shifted left 2 units.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

31. What is the formula for the area of a parallelogram?
They are both the same. A divisor or factor of an integer leaves no remainder.
A = bh
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Then the quotient y/x is a constant.

32. What does it mean if y is directly proportional to x?
A = pr^2
Then the product xy is a constant.
No matter how many angles there are - the sum around the point is 360°.
Then the quotient y/x is a constant.

33. What is the sum of the measures of the four angles in a quadrilateral?
360°
A = (1/2)bh.
(Circumference/diameter) of a circle - or approximately 3.14.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

34. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
At least one of the factors is 0.
Shifted right 2 units.
An equation that states that two ratios are equivalent. 4/6 = 10/15

35. In a circle of radius r - what is the formula for the circumference?
Corresponding sides of similar triangles are in proportion.
Equal slopes.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
C = p2r

36. Properties of one 3
1 is a divisor (or factor) of every 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.
Set y = 0 - and solve.
Their sum is 180°.

37. What formula is used for an average?
Then the quotient y/x is a constant.
Avg = sum of n numbers/n
A = lw
M = (y2 - y1)/(x2 - x1)

38. What is true about the areas of similar triangles?
Their sum is 180°.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Then the quotient y/x is a constant.

39. What is the measure of a straight angle?
1 is the smallest positive odd integer.
180°. If two or more angles form a straight angle - their sum is 180°.
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = (1/2)bh.

40. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.
A = 6(l^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°.

41. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
0 is a multiple of every integer.
A = [(s^2*v3)/4]
For any right triangle - a^2 + b^2 = c^2.

42. Properties of one 1
D = 2r
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any number a: a * 1 = a and a / 1 = a.
Avg = sum of n numbers/n

43. Important binomial 3
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(Circumference/diameter) of a circle - or approximately 3.14.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

44. What is a proportion?
A = bh
A = 6(l^2)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
An equation that states that two ratios are equivalent. 4/6 = 10/15

45. What is the square root of a number?
V = lwh
A^m/b^m = (a/b)^m
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

46. Law of exponents 3
Shifted down 2 units.
(b^m)^n = b^mn
For any number n: x^-n means 1/x^n.
(n - 2)(180°)

47. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Shifted up 2 units.
Their sum is 180°.
An angle formed by extending the side of the polygon.

48. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
How steep the line is. Horizontal line = 0 - vertical has no slope.
V = l^3
No matter how many angles there are - the sum around the point is 360°.

49. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Write the percent as a decimal - and multiply.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

50. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
A = s^2 or A =d^2/2 where d is the diagonal
Their sum is 180°.
Is a right triangle with a ratio of sides x:xv3:2x.