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 are the sum - difference - products - and quotient of two numbers?
No matter how many angles there are - the sum around the point is 360°.
B^m/b^n = b^m-n
Arc = (x°/360)(2pr) where x is the central angle.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

2. What is true about the slopes of perpendicular lines?
For any right triangle - a^2 + b^2 = c^2.
All positive and negative whole numbers - and zero.
The product of their slopes is -1 (negative reciprocal).
Area = (x°/360)(pr^2) where x is the central angle.

3. What is the formula for the volume of a rectangular solid?
V = lwh
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
If a is negative and b is positive - then a < 0 < b.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

4. 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.
A = bh
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.

5. What is true about the measures of the two acute angles in a right triangle?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A^m/b^m = (a/b)^m
Their sum is 90°.
In the expression x^b - x is the base and b is the exponent.

6. What is the volume of a cube?
V = l^3
Write the percent as a decimal - and multiply.
(Circumference/diameter) of a circle - or approximately 3.14.
Shifted down 2 units.

7. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.
(n - 2)(180°)

8. How do we write the equation of a line?
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any number a: a * 1 = a and a / 1 = a.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = [(s^2*v3)/4]

9. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
In the expression x^b - x is the base and b is the exponent.
M = (y2 - y1)/(x2 - x1)
Set x = 0 - and solve.

10. Properties of one 2
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
At least one of the factors is 0.
For any integer n: 1^n = 1.
A^m/b^m = (a/b)^m

11. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
1 is the smallest positive odd integer.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
If a is negative and b is positive - then a < 0 < b.

12. What is a multiple of an integer?
How steep the line is. Horizontal line = 0 - vertical has no slope.
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 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.

13. How do you find the area of a sector of a circle?
All positive and negative whole numbers - and zero.
Area = (x°/360)(pr^2) where x is the central angle.
For any number n: x^-n means 1/x^n.
Is a right triangle with a ratio of sides x:xv3:2x.

14. Properties of zero 2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Cannot is 0 - must is 1 - all others are in between.
If a is negative and b is positive - then a < 0 < b.

15. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
Corresponding sides of similar triangles are in proportion.
Shifted down 2 units.
Avg = sum of n numbers/n

16. 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.
Shifted left 2 units.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any integer n: 1^n = 1.

17. How you convert a fraction or a decimal to a percent?
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.
Divide - then multiply by 100.
A = bh

18. What is the midpoint formula?
Area = (x°/360)(pr^2) where x is the central angle.
[(x1 + x2)/2] -[(y1 + y2)/2]
B^m*b^n = b^m+n
Then the product xy is a constant.

19. Properties of one 3
A = 6(l^2)
A = lw
1 is a divisor (or factor) of every integer.
V = pr^2h

20. What is the distance formula?
Write the percent as a decimal - and multiply.
(n - 2)(180°)
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]

21. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Divide - then multiply by 100.
360°
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

22. In a circle of radius r - what is the formula for the circumference?
C = p2r
They are both the same. A divisor or factor of an integer leaves no remainder.
(x + y)(x - y) = x^2 - y^2
Shifted up 2 units.

23. What is special formula for the area of an equilateral triangle?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Even numbers are divisible by 2 and odd numbers are not.
A = [(s^2*v3)/4]
The ratio of corresponding sides of similar triangles.

24. If the product of two or more numbers is 0 - what do you know about the numbers?
An angle formed by extending the side of the polygon.
At least one of the factors is 0.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A = s^2 or A =d^2/2 where d is the diagonal

25. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
Write the percent as a decimal - and multiply.
In the expression x^b - x is the base and b is the exponent.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

26. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

27. What is the sum of the measures of the four angles in a quadrilateral?
360°
(n - 2)(180°)
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.

28. Important binomial 2
For any number b: b = -b if and only if b = 0.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
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.
C = p2r

29. What is the formula for the surface area of a rectangular solid?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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.
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.

30. What is the distributive law?
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.
Then the product xy is a constant.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

31. What important property do similar triangles have?
0 is the only number that is neither positive nor negative.
At least one of the factors is 0.
Corresponding sides of similar triangles are in proportion.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

32. What are the median and the mode of a set of data?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
V = pr^2h
Avg = sum of n numbers/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.

33. How do you find the slope of a line?
(Circumference/diameter) of a circle - or approximately 3.14.
M = (y2 - y1)/(x2 - x1)
Their sum is 90°.
A^m*b^m = (ab)^m

34. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
For any integer n: 1^n = 1.
Their sum is 180°.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

35. What is the probability of an event that cannot occur? That must occur?
The product of their slopes is -1 (negative reciprocal).
For any number b: b = -b if and only if b = 0.
Cannot is 0 - must is 1 - all others are in between.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

36. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A^m/b^m = (a/b)^m
Then the product xy is a constant.

37. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Divide - then multiply by 100.
Shifted right 2 units.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

38. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Set y = 0 - and solve.
M = (y2 - y1)/(x2 - x1)
If a is negative and b is positive - then a < 0 < b.

39. In a circle of radius r - what is the formula for the diameter?
D = 2r
If a is negative and b is positive - then a < 0 < b.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Shifted left 2 units.

40. Law of exponents 4
Set x = 0 - and solve.
An equation that states that two ratios are equivalent. 4/6 = 10/15
M = (y2 - y1)/(x2 - x1)
A^m*b^m = (ab)^m

41. What is a ratio?

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

42. What is the sum of the measures of all angles around a point?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
No matter how many angles there are - the sum around the point is 360°.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
V = pr^2h

43. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
0 is the only number that is neither positive nor negative.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
V = pr^2h

44. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
No matter how many angles there are - the sum around the point is 360°.
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.
A^m*b^m = (ab)^m
A = 2(lw + lh + hw)

45. What is true about the slopes of parallel lines?
Equal slopes.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
V = l^3

46. What is the triangle inequality?
How steep the line is. Horizontal line = 0 - vertical has no slope.
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 two pairs of opposite angles formed are equal to each other.
0 is the only number that is neither positive nor negative.

47. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Set x = 0 - and solve.
B^m/b^n = b^m-n
C = p2r

48. What are the properties of a square?
M = (y2 - y1)/(x2 - x1)
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.
Set y = 0 - and solve.
Avg = sum of n numbers/n

49. What is the formula for the area of a rectangle?
A = lw
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.
[(x1 + x2)/2] -[(y1 + y2)/2]

50. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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 product of their slopes is -1 (negative reciprocal).
All positive and negative whole numbers - and zero.