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Test your basic knowledge |
GRE Math: Facts
Start Test
Study First
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 true about the measures of the two acute angles in a right triangle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
They are both the same. A divisor or factor of an integer leaves no remainder.
Their sum is 90°.
No matter how many angles there are - the sum around the point is 360°.
2. 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.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Cannot is 0 - must is 1 - all others are in between.
M = (y2 - y1)/(x2 - x1)
3. What is the formula for the volume of a cylinder?
The product of their slopes is -1 (negative reciprocal).
A = [(s^2*v3)/4]
Shifted up 2 units.
V = pr^2h
4. What is the ratio of similitude?
Shifted up 2 units.
V = pr^2h
If a is negative and b is positive - then a < 0 < b.
The ratio of corresponding sides of similar triangles.
5. How do we write the equation of a line?
360°
M = (y2 - y1)/(x2 - x1)
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
6. How do you find the y-intercept of a graph?
No matter how many angles there are - the sum around the point is 360°.
Set x = 0 - and solve.
V = l^3
Shifted up 2 units.
7. What is the graph of a function?
For any right triangle - a^2 + b^2 = c^2.
The set of all ordered pairs (x -y) such that y = f(x).
Avg = sum of n numbers/n
Corresponding sides of similar triangles are in proportion.
8. How do you calculate a weighted average?
A = lw
For any integer n: 1^n = 1.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
9. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
An angle formed by extending the side of the polygon.
A = pr^2
360°
10. What is a proportion?
Their sum is 90°.
An equation that states that two ratios are equivalent. 4/6 = 10/15
1 is the smallest positive odd integer.
A^m*b^m = (ab)^m
11. What are similar triangles?
Their sum is 180°.
D = 2r
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
At least one of the factors is 0.
12. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Is a right triangle with a ratio of sides x:xv3:2x.
The product of their slopes is -1 (negative reciprocal).
Shifted right 2 units.
An equation that states that two ratios are equivalent. 4/6 = 10/15
13. What is the formula for the volume of a rectangular solid?
V = lwh
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A^m*b^m = (ab)^m
C = p2r
14. Properties of zero 5
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
C = p2r
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.
For any number b: b = -b if and only if b = 0.
15. What is the midpoint formula?
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.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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.
[(x1 + x2)/2] -[(y1 + y2)/2]
16. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = [(s^2*v3)/4]
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.
17. How do you calculate percent increases and decreases?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
B^m/b^n = b^m-n
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Their sum is 180°.
18. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
For any right triangle - a^2 + b^2 = c^2.
A^m*b^m = (ab)^m
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
19. What are the median and the mode of a set of data?
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.
Arc = (x°/360)(2pr) where x is the central angle.
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.
V = lwh
20. How do you convert a percent to a fraction or a decimal?
A = bh
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Write the percent over 100 and reduce.
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.
21. What are the properties of a rectangle?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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.
Set y = 0 - and solve.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
22. 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
A = pr^2
V = l^3
23. What is a divisor and a factor of an integer?
Divide - then multiply by 100.
Shifted down 2 units.
They are both the same. A divisor or factor of an integer leaves no remainder.
V = pr^2h
24. 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.
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.
180°. If two or more angles form a straight angle - their sum is 180°.
Cannot is 0 - must is 1 - all others are in between.
25. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
No matter how many angles there are - the sum around the point is 360°.
A = pr^2
A = s^2 or A =d^2/2 where d is the diagonal
26. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
V = l^3
(x + y)(x - y) = x^2 - y^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
27. In a circle of radius r - what is the formula for the circumference?
D = 2r
C = p2r
A = (1/2)bh.
(n - 2)(180°)
28. Properties of zero 3
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Corresponding sides of similar triangles are in proportion.
0 is a multiple of every integer.
29. What is the formula for the area of a triangle?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
360°
A = (1/2)bh.
They are both the same. A divisor or factor of an integer leaves no remainder.
30. 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.
A = (1/2)bh.
Shifted right 2 units.
For any integer n: 1^n = 1.
31. Law of exponents 4
Set y = 0 - and solve.
A^m*b^m = (ab)^m
V = lwh
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
32. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Arc = (x°/360)(2pr) where x is the central angle.
Shifted down 2 units.
They are both the same. A divisor or factor of an integer leaves no remainder.
Divide - then multiply by 100.
33. What is an exterior angle of a polygon?
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.
Shifted left 2 units.
Even numbers are divisible by 2 and odd numbers are not.
An angle formed by extending the side of the polygon.
34. What is the Pythagorean theorem?
Shifted left 2 units.
0 is the only number that is neither positive nor negative.
For any right triangle - a^2 + b^2 = c^2.
(n - 2)(180°)
35. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
A^m/b^m = (a/b)^m
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
How steep the line is. Horizontal line = 0 - vertical has no slope.
36. What is a composite number?
360°
(Circumference/diameter) of a circle - or approximately 3.14.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An integer greater than one that is not prime.
37. What is an even and an odd number?
A = bh
Even numbers are divisible by 2 and odd numbers are not.
(n - 2)(180°)
B^m*b^n = b^m+n
38. How do you find a percent of a number?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.
Write the percent as a decimal - and multiply.
39. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
For any right triangle - a^2 + b^2 = c^2.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A^m*b^m = (ab)^m
40. What is the sum of the measures of all angles around a point?
Even numbers are divisible by 2 and odd numbers are not.
No matter how many angles there are - the sum around the point is 360°.
For any number n: x^-n means 1/x^n.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
41. How do you find the x-intercept of a graph?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
(n - 2)(180°)
A^m/b^m = (a/b)^m
Set y = 0 - and solve.
42. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
0 is a multiple of every integer.
A = [(s^2*v3)/4]
A^m/b^m = (a/b)^m
43. What is special formula for the area of an equilateral triangle?
Corresponding sides of similar triangles are in proportion.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = [(s^2*v3)/4]
A = bh
44. 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.
Corresponding sides of similar triangles are in proportion.
Shifted down 2 units.
Then the quotient y/x is a constant.
45. What is a prime number?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = pr^2
Then the quotient y/x is a constant.
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. What is the measure of a straight angle?
An angle formed by extending the side of the polygon.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Then the product xy is a constant.
180°. If two or more angles form a straight angle - their sum is 180°.
47. What is the triangle inequality?
They are both the same. A divisor or factor of an integer leaves no remainder.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A fraction whose denominator is 100 i.e. 17% = 17/100
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.
48. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Shifted left 2 units.
B^m*b^n = b^m+n
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
49. 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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any number a: a * 1 = a and a / 1 = a.
They are both the same. A divisor or factor of an integer leaves no remainder.
50. What is the formula for the area of a rectangle?
1 is the smallest positive odd integer.
An integer greater than one that is not prime.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = lw