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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. 1/6 in percent?
V=l×w×h
16.6666%
Positive or Negative
An is positive
2. Simplify the expression [(b^2 - c^2) / (b - c)]
1
Diameter(Pi)
72
(b + c)
3. The larger the absolute value of the slope...
Null
1
A central angle is an angle formed by 2 radii.
The steeper the slope.
4. If the 80th percentile of the measurements is 72degrees - about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth
The objects within a set.
Every number
Negative
18
5. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
1:sqrt3:2
A grouping of the members within a set based on a shared characteristic.
2
6
6. Volume of a cube
(amount of decrease/original price) x 100%
Edge³
(a - b)(a + b)
2^9 / 2 = 256
7. What is a tangent?
A tangent is a line that only touches one point on the circumference of a circle.
A reflection about the axis.
Ab+ac
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)
8. Area of a circle
(x+y)(x+y)
9 & 6/7
A=pi*(r^2)
1
9. The product of any number x and its reciprocal
1
C=2 x pi x r OR pi x D
A grouping of the members within a set based on a shared characteristic.
Lies opposite the greater angle
10. If y is directly proportional to x - what does it equal?
No - only like radicals can be added.
y = 2x^2 - 3
y/x is a constant
P= 2L + 2w
11. 3 is the opposite of
3
F(x-c)
1
A chord is a line segment joining two points on a circle.
12. 25/2³
2²
A<-b
2^9 / 2 = 256
180 degrees
13. (x^2)^4
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
90pi
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
x^(2(4)) =x^8 = (x^4)^2
14. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
The longest side is opposite the largest (biggest) angle. The shortest side is opposite the smallest angle. Sides with the same lengths are opposite angles with the same measure.
A reflection about the axis.
A grouping of the members within a set based on a shared characteristic.
Two (Ø×2=Ø)
15. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
3/2 - 5/3
26
Ø Ø=Ø
70
16. Pythagorean theorem
The objects within a set.
A²+b²=c²
The set of elements found in both A and B.
An isosceles right triangle.
17. What is the measure of an exterior angle of a regular pentagon?
13
ODD number
72
Infinite.
18. If a lamp decreases to $80 - from $100 - what is the decrease in price?
Null
(a + b)^2
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
Can be negative - zero - or positive
19. How to recognize a # as a multiple of 3
3
The longest side is opposite the largest (biggest) angle. The shortest side is opposite the smallest angle. Sides with the same lengths are opposite angles with the same measure.
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
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)
20. (x+y)²
x²+2xy+y²
Negative
6
(base*height) / 2
21. 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?
Relationship cannot be determined (what if x is negative?)
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)
10! / (10-3)! = 720
(length)(width)(height)
22. 3/8 in percent?
37.5%
Yes - like radicals can be added/subtracted.
The sum of the digits is a multiple of 9.
1
23. What are the integers?
(a + b)^2
All numbers multiples of 1.
4:5
11 - 13 - 17 - 19
24. What is the set of elements found in both A and B?
The interesection of A and B.
10! / (10-3)! = 720
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Null
25. Slope given 2 points
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
(n-2) x 180
M= (Y1-Y2)/(X1-X2)
The point of intersection of the systems.
26. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
y2-y1/x2-x1
A central angle is an angle formed by 2 radii.
1
180 degrees
27. x^4 + x^7 =
9
x^(4+7) = x^11
83.333%
55%
28. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
x²-y²
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
F(x-c)
1/a^6
29. Hector invested $6000. Part was invested in account with 9% simple annual interest - and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments - how much did he invest in each account?
An arc is a portion of a circumference of a circle.
$3 -500 in the 9% and $2 -500 in the 7%.
NOT A PRIME
27
30. What is the maximum value for the function g(x) = (-2x^2) -1?
An is positive
The two xes after factoring.
1
Infinite.
31. What is a subset?
72
P(E) = 1/1 = 1
A grouping of the members within a set based on a shared characteristic.
180°
32. Simplify the expression (p^2 - q^2)/ -5(q - p)
The triangle is a right triangle. The hypotenuse is twice the length of the shorter leg. The ratio of the length of the three sides is x:xv3:2x
(p + q)/5
Cd
ODD number
33. Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
1
(a - b)(a + b)
2^9 / 2 = 256
9 : 25
34. What is the slope of a vertical line?
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35. Describe the relationship between 3x^2 and 3(x - 1)^2
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 graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
62.5%
(pi)r²
36. -3²
(distance)/(rate) d/r
A set with a number of elements which can be counted.
2.592 kg
9
37. 0^0
A percent is a fraction whose denominator is 100.
Undefined
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)
y = (x + 5)/2
38. factored binomial product of (x+y)²
31 - 37
1
x²+2xy+y²
3
39. The reciprocal of any non-zero #x is
Triangles with same measure and same side lengths.
1/x
A=pi*(r^2)
2
40. Consecutive integers
NOT A PRIME
x - x+1 - x+2
3
The shortest arc between points A and B on a circle'S diameter.
41. What number between 70 & 75 - inclusive - has the greatest number of factors?
180
3
The union of A and B.
72
42. Area of a Parallelogram:
A=(base)(height)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
An angle which is supplementary to an interior angle.
43. a(b-c)
Ab-ac
N! / (k!)(n-k)!
Ø
NOT A PRIME
44. What is the 'domain' of a function?
The set of input values for a function.
Members or elements
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
D/t (distance)/(time)
45. Can you simplify sqrt72?
Can be negative - zero - or positive
x²+2xy+y²
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
46. A prime number (or a prime)
Pi(diameter)
M
Distance=rate×time or d=rt
A natural number greater than 1 that has no positive divisors other than 1 and itself
47. Area of a triangle?
1
(base*height) / 2
12sqrt2
(x+y)(x+y)
48. Ø Is neither
12sqrt2
1/x
The set of output values for a function.
Positive or Negative
49. In a rectangle - all angles are
Right
6
Ab=k (k is a constant)
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
50. What is the 'Range' of a series of numbers?
angle that is greater than 90° but less than 180°
(amount of decrease/original price) x 100%
Even
The greatest value minus the smallest.