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. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Shifted right 2 units.
Avg = sum of n numbers/n

2. What is the measure of a straight angle?
180. If two or more angles form a straight angle - their sum is 180.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Even numbers are divisible by 2 and odd numbers are not.
Equal slopes.

3. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = [(s^2*v3)/4]
360
V = lwh

4. Properties of one 2
(x + y)(x - y) = x^2 - y^2
For any integer n: 1^n = 1.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For any number b: b = -b if and only if b = 0.

5. What is the sum of the measures of all angles around a point?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
No matter how many angles there are - the sum around the point is 360.
The product of their slopes is -1 (negative reciprocal).
B^m/b^n = b^m-n

6. What is true about the measures of the three angles in a triangle?
Shifted right 2 units.
Their sum is 180.
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

7. What is a percent?
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 fraction whose denominator is 100 i.e. 17% = 17/100
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

8. How do you find the slope of a line?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
M = (y2 - y1)/(x2 - x1)
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
B^m/b^n = b^m-n

9. What is the formula for the surface area of a cube?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = 6(l^2)
In the expression x^b - x is the base and b is the exponent.

10. How do you find the area of a sector of a circle?
Area = (x/360)(pr^2) where x is the central angle.
0 is the only number that is neither positive nor negative.
(n - 2)(180)
(x + y)(x - y) = x^2 - y^2

11. How do you convert a percent to a fraction or a decimal?
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Write the percent over 100 and reduce.

12. What are the properties of a rectangle?
The set of all ordered pairs (x -y) such that y = f(x).
M = (y2 - y1)/(x2 - x1)
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

13. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
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 = 2(lw + lh + hw)

14. Properties of zero 3
Their sum is 90.
A = (1/2)bh.
0 is a multiple of every integer.
Set x = 0 - and solve.

15. Properties of zero 1
0 is the only number that is neither positive nor negative.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Shifted down 2 units.

16. What is the formula for the surface area of a rectangular solid?
B^m/b^n = b^m-n
180. If two or more angles form a straight angle - their sum is 180.
A = 2(lw + lh + hw)
All positive and negative whole numbers - and zero.

17. What important property do similar triangles have?
A = (1/2)bh.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Corresponding sides of similar triangles are in proportion.
A^m*b^m = (ab)^m

18. If you were given the graph of y = f(x) - what does f(a) represent?
B^m/b^n = b^m-n
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.
A = 6(l^2)

19. What is the ratio of similitude?
The product of their slopes is -1 (negative reciprocal).
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
The ratio of corresponding sides of similar triangles.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

20. What is the triangle inequality?
Shifted up 2 units.
Then the quotient y/x is a constant.
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

21. How do you calculate percent increases and decreases?
Set y = 0 - and solve.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

22. Properties of one 1
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.
The ratio of corresponding sides of similar triangles.
For any number a: a * 1 = a and a / 1 = a.
A = bh

23. What is true about the measures of the four angles formed by two intersecting lines?
In the expression x^b - x is the base and b is the exponent.
No matter how many angles there are - the sum around the point is 360.
Their sum is 90.
The two pairs of opposite angles formed are equal to each other.

24. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(x + y)(x - y) = x^2 - y^2
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

25. What is the Pythagorean theorem?
360
The set of all ordered pairs (x -y) such that y = f(x).
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.
For any right triangle - a^2 + b^2 = c^2.

26. What is the distance formula?
For any number a: a * 1 = a and a / 1 = a.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A^m/b^m = (a/b)^m
(x + y)(x - y) = x^2 - y^2

27. What is the formula for the area of a triangle?
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.
Write the percent over 100 and reduce.
A = (1/2)bh.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

28. What are the quotient and the remainder?
360
A = bh
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
In the expression x^b - x is the base and b is the exponent.

29. What is the formula for the area of a parallelogram?
A = bh
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Equal slopes.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

30. For what values of a function is the function undefined?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
180. If two or more angles form a straight angle - their sum is 180.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(Circumference/diameter) of a circle - or approximately 3.14.

31. What is the sum of the measures of the four angles in a quadrilateral?
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.
360
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

32. Important binomial 2
Area = (x/360)(pr^2) where x is the central angle.
An angle formed by extending the side of the polygon.
All positive and negative whole numbers - and zero.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

33. What is a fractional exponent?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
At least one of the factors is 0.
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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

34. What is p?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
They are both the same. A divisor or factor of an integer leaves no remainder.
Write the percent over 100 and reduce.
(Circumference/diameter) of a circle - or approximately 3.14.

35. How you convert a fraction or a decimal to a percent?
Corresponding sides of similar triangles are in proportion.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Divide - then multiply by 100.

36. What is a divisor and a factor of an 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.
They are both the same. A divisor or factor of an integer leaves no remainder.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

37. What is true about the areas of similar triangles?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Is a right triangle with a ratio of sides x:xv3:2x.
1 is a divisor (or factor) of every integer.

38. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
M = (y2 - y1)/(x2 - x1)
(n - 2)(180)
Area = (x/360)(pr^2) where x is the central angle.

39. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
For any integer n: 1^n = 1.
Then the product xy is a constant.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

40. Law of exponents 3
At least one of the factors is 0.
In the expression x^b - x is the base and b is the exponent.
For any integer n: 1^n = 1.
(b^m)^n = b^mn

41. What is a function?
Set x = 0 - and solve.
(x + y)(x - y) = x^2 - y^2
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

42. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
The set of all ordered pairs (x -y) such that y = f(x).
Shifted down 2 units.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Shifted up 2 units.

43. How do you find a percent of a number?
Is a right triangle with a ratio of sides x:xv3:2x.
An integer greater than one that is not prime.
They are both the same. A divisor or factor of an integer leaves no remainder.
Write the percent as a decimal - and multiply.

44. How do we write the equation of a line?
Equal slopes.
(n - 2)(180)
A = lw
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

45. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
A = (1/2)bh.
Then the product xy is a constant.
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.
Then the quotient y/x is a constant.

46. What is the graph of a function?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.
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.
The set of all ordered pairs (x -y) such that y = f(x).

47. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
If a is negative and b is positive - then a < 0 < b.
360
A = 6(l^2)
(b^m)^n = b^mn

48. What is a composite number?
An integer greater than one that is not prime.
Shifted up 2 units.
In the expression x^b - x is the base and b is the exponent.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

49. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90.
An equation that states that two ratios are equivalent. 4/6 = 10/15
A^m*b^m = (ab)^m
V = l^3

50. What is an exponent?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The set of all ordered pairs (x -y) such that y = f(x).
In the expression x^b - x is the base and b is the exponent.
Divide - then multiply by 100.

Test your basic knowledge |

GRE Math: Facts

Top Scores

Link to This Test

Related Subjects