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 the relationship between the graph of f(x) the graph of y = f(x) + 2?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Shifted up 2 units.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
They are both the same. A divisor or factor of an integer leaves no remainder.

2. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Then the quotient y/x is a constant.
Shifted right 2 units.
An integer greater than one that is not prime.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

3. How do you find the length of an arc of a circle?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
They are both the same. A divisor or factor of an integer leaves no remainder.
For any integer n: 1^n = 1.
Arc = (x°/360)(2pr) where x is the central angle.

4. How do you calculate a weighted average?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Shifted right 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

5. If you were given the graph of y = f(x) - what does f(a) represent?
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
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.

6. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
M = (y2 - y1)/(x2 - x1)
Write the percent over 100 and reduce.
B^m/b^n = b^m-n

7. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The set of all ordered pairs (x -y) such that y = f(x).
360°
Cannot is 0 - must is 1 - all others are in between.

8. What are the quotient and the remainder?

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

9. What is the formula for the surface area of a cube?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = 6(l^2)
A fraction whose denominator is 100 i.e. 17% = 17/100
All positive and negative whole numbers - and zero.

10. 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.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
How steep the line is. Horizontal line = 0 - vertical has no slope.

11. What formula is used for an average?
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.
[(x1 + x2)/2] -[(y1 + y2)/2]
Avg = sum of n numbers/n

12. What are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
V = lwh

13. What is a divisor and a factor of an integer?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Then the product xy is a constant.
They are both the same. A divisor or factor of an integer leaves no remainder.
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.

14. What are the properties of a parallelogram?
(Circumference/diameter) of a circle - or approximately 3.14.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

15. What is an exterior angle of a triangle?
Write the percent over 100 and reduce.
(x + y)(x - y) = x^2 - y^2
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A = (1/2)bh.

16. Important binomial 2
V = lwh
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.
0 is the only number that is neither positive nor negative.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

17. What is a multiple of an integer?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Cannot is 0 - must is 1 - all others are in between.
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.
Shifted right 2 units.

18. What is an integer?
In the expression x^b - x is the base and b is the exponent.
All positive and negative whole numbers - and zero.
(Circumference/diameter) of a circle - or approximately 3.14.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

19. What does it mean if y is inversely proportional to x?
In the expression x^b - x is the base and b is the exponent.
Even numbers are divisible by 2 and odd numbers are not.
D = 2r
Then the product xy is a constant.

20. What is the midpoint formula?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Arc = (x°/360)(2pr) where x is the central angle.
V = pr^2h
[(x1 + x2)/2] -[(y1 + y2)/2]

21. Law of exponents 3
A = bh
Area = (x°/360)(pr^2) 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.
(b^m)^n = b^mn

22. What is a percent?
A = bh
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
C = p2r
A fraction whose denominator is 100 i.e. 17% = 17/100

23. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
Equal slopes.
V = pr^2h
The two pairs of opposite angles formed are equal to each other.

24. Law of exponents 5
A^m/b^m = (a/b)^m
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
All positive and negative whole numbers - and zero.

25. In a circle of radius r - what is the formula for the area?
At least one of the factors is 0.
A = pr^2
An equation that states that two ratios are equivalent. 4/6 = 10/15
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

26. How do you find the probability that an event will occur?
1 is a divisor (or factor) of every integer.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
No matter how many angles there are - the sum around the point is 360°.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

27. What is true about the areas of similar triangles?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.
For any right triangle - a^2 + b^2 = c^2.

28. How do you convert a percent to a fraction or a decimal?
(x + y)(x - y) = x^2 - y^2
Write the percent over 100 and reduce.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

29. What is a function?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any number n: x^-n means 1/x^n.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
1 is a divisor (or factor) of every integer.

30. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
In the expression x^b - x is the base and b is the exponent.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Write the percent as a decimal - and multiply.
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.

31. How do you find the slope of a line?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
M = (y2 - y1)/(x2 - x1)
A = (1/2)bh.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

32. How do you find the area of a sector of a circle?
A = 2(lw + lh + hw)
For any number n: x^-n means 1/x^n.
Area = (x°/360)(pr^2) where x is the central angle.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

33. If the product of two or more numbers is 0 - what do you know about the numbers?
1 is a divisor (or factor) of every integer.
At least one of the factors is 0.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

34. What is the graph of a function?
1 is the smallest positive odd integer.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
The set of all ordered pairs (x -y) such that y = f(x).
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.

35. What are the important properties of 30-60-90 triangle?
360°
Is a right triangle with a ratio of sides x:xv3:2x.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

36. What is the formula for the area of a rectangle?
A = (1/2)bh.
1 is a divisor (or factor) of every integer.
A = lw
360°

37. What is true about the measures of the four angles formed by two intersecting lines?
The two pairs of opposite angles formed are equal to each other.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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°.
1 is a divisor (or factor) of every integer.

38. What is an exponent?
Write the percent as a decimal - and multiply.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
In the expression x^b - x is the base and b is the exponent.

39. What is a prime number?
A = [(s^2*v3)/4]
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.
A = 6(l^2)
Then the product xy is a constant.

40. What is true about the measures of the two acute angles in a right triangle?
Then the product xy is a constant.
360°
Their sum is 90°.
M = (y2 - y1)/(x2 - x1)

41. For what values of a function is the function undefined?
(b^m)^n = b^mn
Is a right triangle with a ratio of sides x:xv3:2x.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.

42. Law of exponents 2
For any right triangle - a^2 + b^2 = c^2.
B^m/b^n = b^m-n
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

43. What is special formula for the area of an equilateral triangle?
The ratio of corresponding sides of similar triangles.
In the expression x^b - x is the base and b is the exponent.
A = [(s^2*v3)/4]
Then the product xy is a constant.

44. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
They are both the same. A divisor or factor of an integer leaves no remainder.
The ratio of corresponding sides of similar triangles.
0 is the only number that is neither positive nor negative.

45. Properties of zero 4
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
No matter how many angles there are - the sum around the point is 360°.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

46. How do you find the x-intercept of a graph?
They are both the same. A divisor or factor of an integer leaves no remainder.
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.
Set y = 0 - and solve.
(x + y)(x - y) = x^2 - y^2

47. What is the formula for the surface area of a rectangular solid?
Is a right triangle with a ratio of sides x:xv3:2x.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = 2(lw + lh + hw)

48. In a circle of radius r - what is the formula for the diameter?
(Circumference/diameter) of a circle - or approximately 3.14.
1 is a divisor (or factor) of every integer.
D = 2r
An integer greater than one that is not prime.

49. What is the relationship between the graph of f(x) the graph of y = f(x + 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°.
Then the product xy is a constant.
Shifted left 2 units.
(n - 2)(180°)

50. What is the area of a square?
A fraction whose denominator is 100 i.e. 17% = 17/100
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = s^2 or A =d^2/2 where d is the diagonal