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 distributive law?
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.
For any right triangle - a^2 + b^2 = c^2.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

2. What is the formula for the surface area of a cube?
At least one of the factors is 0.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Is a right triangle with a ratio of sides x:xv3:2x.
A = 6(l^2)

3. What are the median and the mode of a set of data?
A = (1/2)bh.
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.
Cannot is 0 - must is 1 - all others are in between.
Shifted left 2 units.

4. Properties of one 3
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Divide - then multiply by 100.
1 is a divisor (or factor) of every integer.
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.

5. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
For any integer n: 1^n = 1.
All positive and negative whole numbers - and zero.
A = lw

6. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted down 2 units.

7. How do you find a percent of a number?
Equal slopes.
A = 2(lw + lh + hw)
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.

8. What are the important properties of a 45-45 - 90 triangle?
The product of their slopes is -1 (negative reciprocal).
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

9. 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.
Shifted up 2 units.
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^m*b^m = (ab)^m

10. What is the formula for the area of a rectangle?
A = lw
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A^m/b^m = (a/b)^m
1 is a divisor (or factor) of every integer.

11. How do we write the equation of a line?
B^m*b^n = b^m+n
Divide - then multiply by 100.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

12. What formula is used for an average?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Avg = sum of n numbers/n
If a is negative and b is positive - then a < 0 < b.
Then the quotient y/x is a constant.

13. What does it mean if y is inversely proportional to x?
At least one of the factors is 0.
Then the product xy is a constant.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

14. How do you find the slope of a line?
A = (1/2)bh.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
M = (y2 - y1)/(x2 - x1)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

15. What are the important properties of 30-60-90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Is a right triangle with a ratio of sides x:xv3:2x.
A^m/b^m = (a/b)^m

16. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The ratio of corresponding sides of similar triangles.
The two pairs of opposite angles formed are equal to each other.

17. What is the formula for the area of a parallelogram?
A = bh
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.
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 = 2(lw + lh + hw)

18. Properties of zero 1
For any number a: a * 1 = a and a / 1 = a.
0 is the only number that is neither positive nor negative.
(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.

19. In a circle of radius r - what is the formula for the diameter?
D = 2r
V = lwh
How steep the line is. Horizontal line = 0 - vertical has no slope.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

20. What is the formula for the volume of a rectangular solid?
V = lwh
(Circumference/diameter) of a circle - or approximately 3.14.
Arc = (x°/360)(2pr) where x is the central angle.
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.

21. In a circle of radius r - what is the formula for the circumference?
C = p2r
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = lw
[(x1 + x2)/2] -[(y1 + y2)/2]

22. What is the sum of the measures of the n angles of a polygon with n sides?
For any number n: x^-n means 1/x^n.
Shifted up 2 units.
1 is a divisor (or factor) of every integer.
(n - 2)(180°)

23. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = (1/2)bh.
M = (y2 - y1)/(x2 - x1)
C = p2r

24. Law of exponents 1
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
B^m*b^n = b^m+n
V = lwh
No matter how many angles there are - the sum around the point is 360°.

25. What is an integer?
Write the percent as a decimal - and multiply.
For any number n: x^-n means 1/x^n.
All positive and negative whole numbers - and zero.
A = pr^2

26. Important binomial 1
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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.
V = l^3
(x + y)(x - y) = x^2 - y^2

27. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
360°
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°.
Write the percent over 100 and reduce.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

28. How do you calculate a weighted average?
360°
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A fraction whose denominator is 100 i.e. 17% = 17/100

29. Important binomial 2
No matter how many angles there are - the sum around the point is 360°.
0 is the only number that is neither positive nor negative.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Divide - then multiply by 100.

30. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted right 2 units.
At least one of the factors is 0.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

31. What is a ratio?

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

32. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
Their sum is 90°.
Set y = 0 - and solve.
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°.

33. What is true about the areas of similar triangles?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Write the percent over 100 and reduce.
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.

34. How do you find the probability that an event will occur?
Set x = 0 - and solve.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
If a is negative and b is positive - then a < 0 < b.

35. What is the measure of a straight angle?
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.
Shifted right 2 units.
Corresponding sides of similar triangles are in proportion.
180°. If two or more angles form a straight angle - their sum is 180°.

36. 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.
Write the percent over 100 and reduce.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
V = lwh

37. What is the Pythagorean theorem?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any right triangle - a^2 + b^2 = c^2.
Area = (x°/360)(pr^2) where x is the central angle.
For any integer n: 1^n = 1.

38. Law of exponents 5
A^m/b^m = (a/b)^m
Divide - then multiply by 100.
The two pairs of opposite angles formed are equal to each other.
360°

39. What is true about the slopes of perpendicular lines?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
C = p2r
B^m*b^n = b^m+n
The product of their slopes is -1 (negative reciprocal).

40. How do you convert a percent to a fraction or a decimal?
The ratio of corresponding sides of similar triangles.
C = p2r
Their sum is 180°.
Write the percent over 100 and reduce.

41. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted down 2 units.
V = pr^2h
[(x1 + x2)/2] -[(y1 + y2)/2]
Shifted up 2 units.

42. What is the square root of a number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
The two pairs of opposite angles formed are equal to each other.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
For any number a: a * 1 = a and a / 1 = a.

43. What is the probability of an event that cannot occur? That must occur?
(x + y)(x - y) = x^2 - y^2
An equation that states that two ratios are equivalent. 4/6 = 10/15
Cannot is 0 - must is 1 - all others are in between.
[(x1 + x2)/2] -[(y1 + y2)/2]

44. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
If a is negative and b is positive - then a < 0 < b.
A fraction whose denominator is 100 i.e. 17% = 17/100
Set y = 0 - and solve.
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.

45. In a circle of radius r - what is the formula for the area?
All positive and negative whole numbers - and zero.
A = pr^2
A = 2(lw + lh + hw)
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.

46. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
If a is negative and b is positive - then a < 0 < b.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
C = p2r

47. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
B^m*b^n = b^m+n
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Arc = (x°/360)(2pr) where x is the central angle.

48. Properties of one 2
For any integer n: 1^n = 1.
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
For any number b: b = -b if and only if b = 0.

49. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
[(x1 + x2)/2] -[(y1 + y2)/2]
(x + y)(x - y) = x^2 - y^2
Shifted right 2 units.

50. 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