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 does it mean if y is inversely proportional to x?
0 is the only number that is neither positive nor negative.
Then the product xy is a constant.
(b^m)^n = b^mn
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

2. If you were given the graph of y = f(x) - what does f(a) represent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
(x + y)(x - y) = x^2 - y^2
B^m*b^n = b^m+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.

3. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Cannot is 0 - must is 1 - all others are in between.
Is a right triangle with a ratio of sides x:xv3:2x.
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°.
Avg = sum of n numbers/n

4. What is the relationship between the graph of f(x) the graph of y = f(x) + 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.
Cannot is 0 - must is 1 - all others are in between.
Shifted up 2 units.
An integer greater than one that is not prime.

5. What is the ratio of similitude?
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 ratio of corresponding sides of similar triangles.
(n - 2)(180°)
Corresponding sides of similar triangles are in proportion.

6. What is the volume of a cube?
V = l^3
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
[(x1 + x2)/2] -[(y1 + y2)/2]
Cannot is 0 - must is 1 - all others are in between.

7. How do you calculate a weighted average?
0 is the only number that is neither positive nor negative.
360°
Their sum is 90°.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

8. What is the formula for the area of a parallelogram?
If a is negative and b is positive - then a < 0 < b.
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.
A = bh

9. What is special formula for the area of an equilateral triangle?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
B^m/b^n = b^m-n
A = [(s^2*v3)/4]
The set of all ordered pairs (x -y) such that y = f(x).

10. Properties of zero 3
0 is a multiple of every integer.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Their sum is 180°.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

11. What is the formula for the area of a rectangle?
A = lw
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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°.
Shifted up 2 units.

12. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
[(x1 + x2)/2] -[(y1 + y2)/2]
Divide - then multiply by 100.
Write the percent over 100 and reduce.
Shifted down 2 units.

13. What are the properties of a square?
Write the percent as a decimal - and multiply.
A fraction whose denominator is 100 i.e. 17% = 17/100
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.

14. How do you calculate percent increases and decreases?
Their sum is 180°.
A fraction whose denominator is 100 i.e. 17% = 17/100
D = 2r
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

15. How do you find the x-intercept of a graph?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
0 is the only number that is neither positive nor negative.
Set y = 0 - and solve.

16. If the product of two or more numbers is 0 - what do you know about the numbers?
Set x = 0 - and solve.
At least one of the factors is 0.
Area = (x°/360)(pr^2) where x is the central angle.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

17. 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

18. What is a function?
Shifted down 2 units.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

19. Important binomial 1
(x + y)(x - y) = x^2 - y^2
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(n - 2)(180°)

20. 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.
(n - 2)(180°)
For any number n: x^-n means 1/x^n.
[(x1 + x2)/2] -[(y1 + y2)/2]

21. What is the triangle inequality?
For any number n: x^-n means 1/x^n.
0 is the only number that is neither positive nor negative.
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.
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.

22. What is an exterior angle of a polygon?
M = (y2 - y1)/(x2 - x1)
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
An angle formed by extending the side of the polygon.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

23. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Shifted down 2 units.
B^m*b^n = b^m+n
A fraction whose denominator is 100 i.e. 17% = 17/100
360°

24. What is the area of a square?
In the expression x^b - x is the base and b is the exponent.
A = [(s^2*v3)/4]
V = lwh
A = s^2 or A =d^2/2 where d is the diagonal

25. What is true about the areas of similar triangles?
B^m/b^n = b^m-n
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.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Equal slopes.

26. What is the distance formula?
180°. If two or more angles form a straight angle - their sum is 180°.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

27. Properties of one 2
(Circumference/diameter) of a circle - or approximately 3.14.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any integer n: 1^n = 1.
180°. If two or more angles form a straight angle - their sum is 180°.

28. What is the measure of a straight angle?
A^m*b^m = (ab)^m
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°.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

29. What is a composite number?
1 is a divisor (or factor) of every integer.
An integer greater than one that is not prime.
(x + y)(x - y) = x^2 - y^2
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.

30. What is the formula for the surface area of a rectangular solid?
V = lwh
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = 2(lw + lh + hw)
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

31. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Cannot is 0 - must is 1 - all others are in between.

32. What formula is used for an average?
B^m/b^n = b^m-n
For any integer n: 1^n = 1.
The set of all ordered pairs (x -y) such that y = f(x).
Avg = sum of n numbers/n

33. What is the midpoint formula?
Set y = 0 - and solve.
An angle formed by extending the side of the polygon.
D = 2r
[(x1 + x2)/2] -[(y1 + y2)/2]

34. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
A = [(s^2*v3)/4]
An integer greater than one that is not prime.
Then the product xy is a constant.

35. What do we mean by the slope of the line?
A = 2(lw + lh + hw)
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.
Then the quotient y/x is a constant.

36. Properties of one 3
Their sum is 180°.
Cannot is 0 - must is 1 - all others are in between.
An integer greater than one that is not prime.
1 is a divisor (or factor) of every integer.

37. Properties of zero 1
Shifted right 2 units.
Set x = 0 - and solve.
Their sum is 180°.
0 is the only number that is neither positive nor negative.

38. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
How steep the line is. Horizontal line = 0 - vertical has no slope.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Shifted left 2 units.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

39. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
An angle formed by extending the side of the polygon.
Set y = 0 - and solve.
An integer greater than one that is not prime.

40. What is a fractional exponent?
360°
The ratio of corresponding sides of similar triangles.
Shifted up 2 units.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

41. Law of exponents 2
How steep the line is. Horizontal line = 0 - vertical has no slope.
B^m/b^n = b^m-n
Even numbers are divisible by 2 and odd numbers are not.
Cannot is 0 - must is 1 - all others are in between.

42. What is an exterior angle of a triangle?
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.
1 is a divisor (or factor) of every integer.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

43. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
An integer greater than one that is not prime.
In the expression x^b - x is the base and b is the exponent.
If a is negative and b is positive - then a < 0 < b.

44. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
For any number n: x^-n means 1/x^n.
Cannot is 0 - must is 1 - all others are in between.
Set x = 0 - and solve.

45. What is the probability of an event that cannot occur? That must occur?
C = p2r
Cannot is 0 - must is 1 - all others are in between.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = 6(l^2)

46. Law of exponents 1
An equation that states that two ratios are equivalent. 4/6 = 10/15
B^m*b^n = b^m+n
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Their sum is 180°.

47. What is true about the measures of the three angles in a triangle?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Their sum is 180°.
1 is the smallest positive odd integer.
The product of their slopes is -1 (negative reciprocal).

48. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
Then the product xy is a constant.
A = lw
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

49. What are the properties of a parallelogram?
A = 6(l^2)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
C = p2r
The two pairs of opposite angles formed are equal to each other.

50. In a circle of radius r - what is the formula for the circumference?
C = p2r
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.