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 ratio?
Shifted right 2 units.
D = 2r
An integer greater than one that is not prime.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

2. What is special formula for the area of an equilateral triangle?
1 is a divisor (or factor) of every integer.
Then the product xy is a constant.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A = [(s^2*v3)/4]

3. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.

4. If you were given the graph of y = f(x) - what does f(a) represent?
Cannot is 0 - must is 1 - all others are in between.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Is a right triangle with a ratio of sides x:xv3:2x.

5. What is the formula for the surface area of a cube?
A = 6(l^2)
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

6. What is true about the slopes of perpendicular lines?
In the expression x^b - x is the base and b is the exponent.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The product of their slopes is -1 (negative reciprocal).
Write the percent as a decimal - and multiply.

7. What is true about the slopes of parallel lines?
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.
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.
A^m/b^m = (a/b)^m
Equal slopes.

8. What is the formula for the area of a parallelogram?
A = bh
B^m*b^n = b^m+n
An integer greater than one that is not prime.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

9. How do you find the slope of a line?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
M = (y2 - y1)/(x2 - x1)
V = pr^2h
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

10. What is a fractional exponent?
360
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
The two pairs of opposite angles formed are equal to each other.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

11. How do we write the equation of a line?
Then the quotient y/x is a constant.
B^m/b^n = b^m-n
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
360

12. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
B^m*b^n = b^m+n
Equal slopes.
Write the percent over 100 and reduce.

13. What does it mean if y is directly proportional to x?
In the expression x^b - x is the base and b is the exponent.
A^m*b^m = (ab)^m
Then the quotient y/x is a constant.
V = pr^2h

14. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Divide - then multiply by 100.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.
[(x1 + x2)/2] -[(y1 + y2)/2]

15. Law of exponents 5
B^m/b^n = b^m-n
If a is negative and b is positive - then a < 0 < b.
A^m/b^m = (a/b)^m
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

16. How do you calculate percent increases and decreases?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.
An integer greater than one that is not prime.

17. What is true about the measures of the four angles formed by two intersecting lines?
Their sum is 180.
The two pairs of opposite angles formed are equal to each other.
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 n: x^-n means 1/x^n.

18. What is a divisor and a factor of an integer?
Area = (x/360)(pr^2) where x is the central angle.
They are both the same. A divisor or factor of an integer leaves no remainder.
An integer greater than one that is not prime.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

19. What formula is used for an average?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Avg = sum of n numbers/n

20. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
(x + y)(x - y) = x^2 - y^2
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.
How steep the line is. Horizontal line = 0 - vertical has no slope.

21. What are the quotient and the remainder?
Corresponding sides of similar triangles are in proportion.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

22. Properties of zero 5
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
For any number b: b = -b if and only if b = 0.
Is a right triangle with a ratio of sides x:xv3:2x.
(b^m)^n = b^mn

23. Properties of one 3
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.
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
1 is a divisor (or factor) of every integer.

24. Important binomial 1
The product of their slopes is -1 (negative reciprocal).
How steep the line is. Horizontal line = 0 - vertical has no slope.
(x + y)(x - y) = x^2 - y^2
For any number n: x^-n means 1/x^n.

25. Law of exponents 2
Arc = (x/360)(2pr) where x is the central angle.
B^m/b^n = b^m-n
If a is negative and b is positive - then a < 0 < b.
1 is the smallest positive odd integer.

26. What is the relationship between a radius of a circle and a line that is tangent to the circle?
A = 2(lw + lh + hw)
V = pr^2h
V = lwh
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

27. What is a prime number?
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.
B^m/b^n = b^m-n
0 is the only number that is neither positive nor negative.
V = l^3

28. 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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
At least one of the factors is 0.
Area = (x/360)(pr^2) where x is the central angle.

29. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = lw
(b^m)^n = b^mn

30. How do you find the area of a sector of a circle?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Area = (x/360)(pr^2) where x is the central angle.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Shifted down 2 units.

31. What is a negative exponent?
For any number n: x^-n means 1/x^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.
(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.

32. Properties of one 4
A^m/b^m = (a/b)^m
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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.
1 is the smallest positive odd integer.

33. Properties of one 2
(x + y)(x - y) = x^2 - y^2
Equal slopes.
For any integer n: 1^n = 1.
360

34. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
For any number a: a * 1 = a and a / 1 = a.
At least one of the factors is 0.
Shifted down 2 units.

35. Properties of zero 1
0 is the only number that is neither positive nor negative.
The set of all ordered pairs (x -y) such that y = f(x).
The product of their slopes is -1 (negative reciprocal).
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

36. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180 - and the diagonals bisect.

37. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
C = p2r
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

38. How do you find the probability that an event will occur?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Then the quotient y/x is a constant.
Is a right triangle with a ratio of sides x:xv3:2x.

39. How do you calculate a weighted average?
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.
For any integer n: 1^n = 1.
V = lwh

40. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
Is a right triangle with a ratio of sides x:xv3:2x.
(n - 2)(180)
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.

41. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
In the expression x^b - x is the base and b is the exponent.
The set of all ordered pairs (x -y) such that y = f(x).
If a is negative and b is positive - then a < 0 < b.

42. What are the properties of a rectangle?
Then the product xy is a constant.
A = pr^2
Divide - then multiply by 100.
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.

43. 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.
(b^m)^n = b^mn
A = 6(l^2)
Even numbers are divisible by 2 and odd numbers are not.

44. What important property do similar triangles have?
For any number n: x^-n means 1/x^n.
Corresponding sides of similar triangles are in proportion.
Shifted up 2 units.
0 is the only number that is neither positive nor negative.

45. What is true about the measures of the two acute angles in a right triangle?
(x + y)(x - y) = x^2 - y^2
Their sum is 90.
They are both the same. A divisor or factor of an integer leaves no remainder.
An integer greater than one that is not prime.

46. Law of exponents 3
Then the quotient y/x is a constant.
(b^m)^n = b^mn
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.

47. 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.
The product of their slopes is -1 (negative reciprocal).
(n - 2)(180)
[(x1 + x2)/2] -[(y1 + y2)/2]

48. Important binomial 3
Then the quotient y/x is a constant.
Arc = (x/360)(2pr) where x is the central angle.
Shifted left 2 units.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

49. What do we mean by the slope of the line?
V = lwh
For any number a: a * 1 = a and a / 1 = a.
How steep the line is. Horizontal line = 0 - vertical has no slope.
If a is negative and b is positive - then a < 0 < b.

50. What are the median and the mode of a set of data?
Shifted left 2 units.
A = 2(lw + lh + hw)
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.

Test your basic knowledge |

GRE Math: Facts

Top Scores

Link to This Test

Related Subjects