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Test your basic knowledge |
GRE Math: All In One
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 are congruent triangles?
13
No - only like radicals can be added.
An arc is a portion of a circumference of a circle.
Triangles with same measure and same side lengths.
2. Slope of any line that goes down as you move from left to right is
441000 = 1 10 10 10 21 * 21
1.7
A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables. (3x - 4x^2 and 2a/c)
Negative
3. What are the irrational numbers?
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183
4. What is the sum of the angles of a triangle?
87.5%
1:sqrt3:2
180 degrees
9 : 25
5. What are the roots of the quadrinomial x^2 + 2x + 1?
x^(2(4)) =x^8 = (x^4)^2
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
The two xes after factoring.
A tangent is a line that only touches one point on the circumference of a circle.
6. Obtuse Angle
angle that is greater than 90° but less than 180°
x²-2xy+y²
1
360°
7. What is the 'union' of A and B?
The set of elements which can be found in either A or B.
(2x7)³
288 (8 9 4)
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
8. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
A reflection about the origin.
180°
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
An infinite set.
9. 30 60 90
A 30-60-90 triangle.
3 - 4 - 5
180
3
10. How to find the circumference of a circle which circumscribes a square?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Null
12.5%
Lies opposite the greater angle
11. Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
500
12! / 5!7! = 792
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
12. What is the 'Solution' for a system of linear equations?
y/x is a constant
X
The point of intersection of the systems.
D/t (distance)/(time)
13. Ø Is neither
Positive or Negative
1.0843 X 10^11
C = (pi)d
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
14. The sum of the measures of the n angles in a polygon with n sides
Sum of digits is a multiple of 3 and the last digit is even.
x²-2xy+y²
(n-2) x 180
26
15. a<b then a - b is positive or negative?
A-b is negative
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
Ab-ac
4sqrt3. The triangle can be divided into two equal 30-60-90 triangles with side 6 as the side in which 6 = xsqrt3. So x =2sqrt3...
16. 1n
48
4sqrt3. The triangle can be divided into two equal 30-60-90 triangles with side 6 as the side in which 6 = xsqrt3. So x =2sqrt3...
Sector area = (n/360) X (pi)r^2
1
17. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
A= (1/2) b*h
2²
0
An infinite set.
18. What is the empty set?
72
A set with no members - denoted by a circle with a diagonal through it.
(x+y)(x-y)
Positive or Negative
19. a^2 - 2ab + b^2
y2-y1/x2-x1
An angle which is supplementary to an interior angle.
(a - b)^2
A+c<b+c
20. How do you solve proportions? a/b=c/d
Smallest positive integer
P(E) = ø
Sum of digits is a multiple of 3 and the last digit is even.
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
21. Probability of Event all cases
The sum of the digits is a multiple of 9.
Ø=P(E)=1
F(x) + c
3/2 - 5/3
22. Ø Is
EVEN
Smallest positive integer
1
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
23. Find the surface area of a cylinder with radius 3 and height 12.
A tangent is a line that only touches one point on the circumference of a circle.
90pi
A=pi*(r^2)
An is positive
24. Is 0 even or odd?
Even
Arc length = (n/360) x pi(2r) where n is the number of degrees.
The steeper the slope.
An expression with just one term (-6x - 2a^2)
25. -3³
Two (Ø×2=Ø)
The interesection of A and B.
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
27
26. Legs: 3 - 4. Hypotenuse?
V=Lwh
5
The objects within a set.
Its divisible by 2 and by 3.
27. Volume of a rectangular box
V=Lwh
Ø
The sum of the digits is a multiple of 3 (i.e. 45 ... 4 + 5 = 9 so the whole thing is a multiple of 3)
D/t (distance)/(time)
28. What is the order of operations?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
The sum of the digits is a multiple of 9.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
29. factored binomial product of (x-y)²
x²+2xy+y²
Smallest positive integer
x²-2xy+y²
D/t (distance)/(time)
30. What is the graph of f(x) shifted right c units or spaces?
F(x-c)
180°
The empty set - denoted by a circle with a diagonal through it.
Positive
31. Volume of a cube
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
y = (x + 5)/2
9
Edge³
32. When dividing exponential #s with the same base - you do this to the exponents...
y2-y1/x2-x1
Subtract them. i.e (5^7)/(5^3)= 5^4
4sqrt3. The triangle can be divided into two equal 30-60-90 triangles with side 6 as the side in which 6 = xsqrt3. So x =2sqrt3...
The direction of the inequality is reversed.
33. What are the smallest three prime numbers greater than 65?
67 - 71 - 73
Move the decimal point to the right x places
3 - -3
360°
34. binomial product of (x+y)²
Do not have slopes!
C = 2(pi)r
The set of output values for a function.
(x+y)(x+y)
35. Slope given 2 points
M= (Y1-Y2)/(X1-X2)
Triangles with same measure and same side lengths.
An infinite set.
V=Lwh
36. 60 < all primes <70
27^(-4)
V=l×w×h
A central angle is an angle formed by 2 radii.
61 - 67
37. 10^6 has how many zeroes?
Positive or Negative
1
6
2^9 / 2 = 256
38. The consecutive angles in a parallelogram equal
Do not have slopes!
180°
(x+y)(x+y)
52
39. What is a minor arc?
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40. 5/6 in percent?
Ø
83.333%
3/2 - 5/3
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
41. Formula for the area of a sector of a circle?
18
F(x-c)
The empty set - denoted by a circle with a diagonal through it.
Sector area = (n/360) X (pi)r^2
42. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
2.4. We calculate the area (6) and then turn the triangle on its side and use x as the height to calculate again. (5x)/2=6
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
10! / (10-3)! = 720
61 - 67
43. 1/2 divided by 3/7 is the same as
Two angles whose sum is 90.
1/2 times 7/3
0
A percent is a fraction whose denominator is 100.
44. What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
The sum of the digits it a multiple of 3 and the last two digits is a multiple of 4. (i.e 144: 1+4+4=9 which is a multiple of 3 - and 44 is a multiple of 4 - so 144 is a multiple of 12.)
5
x - x(SR3) - 2x
45. In a rectangle - all angles are
Right
27
The steeper the slope.
Two angles whose sum is 90.
46. formula for the volume of a cube
3x - 4x - 5x
5
M= (Y1-Y2)/(X1-X2)
V=side³
47. Circumference of a circle
61 - 67
2(pi)r
26
x - x(SR3) - 2x
48. Which is greater? 27^(-4) or 9^(-8)
27^(-4)
A 30-60-90 triangle.
A=½bh
180
49. Describe the relationship between 3x^2 and 3(x - 1)^2
1/2 times 7/3
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
180
3/2 - 5/3
50. Formula to find a circle'S circumference from its radius?
1:1:sqrt2
Sum of digits is a multiple of 3 and the last digit is even.
The triangle is a right triangle. The triangle is isosceles (AC=BC). The ratio of the lengths of the three sides is x:x:xv2.
C = 2(pi)r