Appendix B: 100 Math Drills
Line A has the equation y=-7x-7. Line B is perpendicular to Line A and passes through the point (-3,-2). What is the equation for Line B?
y = 1/7x - /11/17
Line A has the equation y= -9x+4. Line B is perpendicular to Line A and passes through the point (5,9). What is the equation of Line B?
y= 1/9x + 76/9
A line ahs a slope of 8 and passes through the point (-9, -80). What is the y-intercept of the line?
y=-8
What is the remainder when 196 is divided by 13?
1
What is the x-intercept of the line y= 10x-10?
1
If the average (arithmetic mean) of 19, 16, and x is 12, what is the value of x?
1
What is the average (arithmetic mean) of -4, 8, 3, and -3?
1
The first term of a sequence is -48, and every term after the first is 3/4 of the previous term. What is the 7th term of the sequence?
-2187/256
If the average (arithmetic mean) of 11, 11, -10, x, and y is -2, what is the value of x+y?
-22
What is the average (arithmetic mean) of 12, -19, -9, and 4?
-3
The first term of a sequence is 3, and every term after the first is 5 less than the previous term.What is the 93rd term of the sequence?
-457
S1= -9, and Sn=S(n-1)-2 for all n>=1. What is the value of S27?
-61
Simplify: (-(-3*1)) * (-10) * (1+2) * (-(-8))
-720
A certain set contains 5 unique integers: -4, a, -9, -10, and -17. If the median of the set is -9, what is the smallest possible value of a?
-8
Solve for y: -5y+8 = -2y+32
-8
Solve for y: -4y+7 = 5y+88
-9
Simplify: -(4 *(-1)-(-6+2))
0
If 113 objects are divided into 8 groups of equal size, what is the smallest possible number of objects that will be left over?
1
What are the factors of 75?
1,3,5,15,25, and 75
What are the factors of 105?
1,3,5,7,15,21,35, and 105
2/7 / 4/7
1/2
2/15 + 2/8
1/30
The ratio of cars to trucks in a parking lot is 5:13. If there are 36 cars and trucks in the parking lot in total, how many cars are in the parking lot?
10
166 is p% greater than 83. Solve for p.
100
182 is p% greater than 91. Solve for p.
100
72 is 28% less than what number?
100
x is 10% of y. Y is what percent of x?
1000
10/12 * 11/15
11/18
A right triangle has a hypotenuse of length 150. One of the two legs of the right triangle has length 90, what is the length of the other leg?
120
The ratio of hippos to alligators in a river is 4:5. If there are 94 hippos in the river, how may alligators are in the river?
120
Simplify: -(-(5+8))
13
S1 = 7, and Sn=Sn-1+5 for all n>= 1. What is the value of S28?
142
If Machine A produces 25 widgets per day and Machine B produces 4 widgets per day, how many widgets can they produce in 5 days by working together?
145
18 is 12% of y. Solve for y.
150
What is the x-intercept of y= -1/2x +9?
18
If the circumference of a circle is 2pi, what is the area of the circle?
1pi
2 is 10% of y. Solve for y.
20
A right triangle has leg lengths of 20 and 40. What is the length of the hypotenuse?
20(square root 5)
x is 50% of y. Y is what percent of x?
200
If the radius of a circle is 10, what is the circumference of the circle?
20pi
A triangle has angles measuring 126, 31, and x degrees. What is the value of x?
23
If b=3, what is the value of |10b-5|?
25
The total number or hats and scarves in a thrift store is 28. If there are 8 hats in the hrift store, what is the ratio of hats to scarves?
2:5
Simplify:2^-2y+1* 2^y+2
2^-y+3
A certain set consists of 4 consecutive integers. If the median of the set is 1.5, what is the largest integer in the set?
3
If 39 objects are divided into 4 groups or equal size, what is the smallest possible number of objects that will be left over?
3
Solve for y: 3y+5 = 2y+8
3
What are the prime factors of 1029?
3,7,7, and 7
Simplify:(3* (-3)+(-8+2)) * (6-8)
30
16 is p% of 50. Solve for p.
32
In how many ways can a committee of 7 people be selected from a group of 9 people?
36
If a vehicle travels 324 miles in 9 hours, what is the average speed in miles perhour?
36 Miles Per Hour
The code for a particular combination lock can only include letters, symbols, and digits from a selection of 7 letters, 3 digits and 5 symbols. A valid code for the lock must consist of exactly 2 letters, 1 symbol, 1 digit, and 1 symbol, in that order, and repetition is allowed. How many different codes are possible?
3675
24 is 40% less than what number?
40
The prime factors of x are [2,2,3,5,7]. What is the value of x?
420
A cylindrical can has a circular base with radius 7. The height of the can is 9. What is the volume of the can?
441pi
109 objects are divided into groups that each contain 8 objects. If as many groups as possible are created, how many objects will be left over?
5
257 objects are divided into groups that each contain 14 objects. If as many groups as possible are created, how many objects will be left over?
5
Solve for z: -z-1 = z-11
5
What is the absolute value of 5?
5
What is the greatest common factor of 25 and 10?
5
A certain sequence begins with the terms 4, -4, -1, 5, -1, 4, -4, -1, 5, -1, 4, -4, -1, 5, -1,... and continues to repeat indefinitely. What is the sum of the first 81 terms of the sequence?
52
Simplify the following ratio: 100:60
5:3
Simplify: 5^c-3/5^-2
5^c-1
A cylindrical can has a circular base with diameter 18. The volume of the can is 486pi. What is the height of the can?
6
If Vehicle A can complete a 72 mile trip at a rate of 36 miles per hour, at what rate would Vehicle B have to travel to complete a trip of 120 miles in the same amount of time?
60 Miles Per Hour
Simplify: (6-(-10) - 3^2 + 10 - 0 +4 * 2 )^2
625
5/13 +9/15
64/65
A triangle has angles measuring 66, 46 and y degrees. What is the value of y?
68
Simplify: 6^6z+1/6^2z-5
6^-z+6
A certain school has 2 second graders and 7 first graders, In how many different was can a team consisting of 2 second graders and 1 first grader be selected from among the students at the school?
7
A certain set consists of 7 integers: 15, 6, 4, 7, 8, 16, and x. If x<= 3, what is the median of the set?
7
Solve for z: z+9=4z-12
7
If x identical machines can assemble 24 gadgets in 6 hours, how long will it take 3x such machines to assemble 84 gadgets?
7 Hours
In how many different ways can 6 people be arranged in a straight line?
720
84 is p% less than 336. Solve for p.
75
The total number of roses and tulips in a garden is 40. If there are 28 roses in the garden, what is the ration of roses to tulips?
7:3
Simplify: 7^-x-5 * 7
7^-x-4
A certain salad bar offers a selection of 2 types of lettuce, 4 types of nuts, and 3 proteins. How many different salads can be created consisting of exactly 1 type of lettuce, exactly 4 types of nuts, and at least 2 proteins?
8
A certain set consists of 4 integers; 8,8,19, and x. If x <= 4, what is the median of the set?
8
If a vehicle traveling at 84 kilometers per hour can currently complete a certain trip in 10 hours, how long would the vehicle take to complete the same trip at a rate of 105 kilometers per hour?
8 Hours
5/9 +1/3
8/9
A right triangle has one leg of length 48. If the area of the right triangle is 1536, what is the length of the hypotenuse?
80
Two circles both have their centers at the same point. The diameter of the smaller circle is 16 units and the diameter of the larger circle is 24 units. What is the area of the region contained inside the larger circle, but outside the smaller circle?
80pi square units
If c=-3, what is the value of |-6c-9|?
9
If the average (arithmetic mean) of -17, -11, 20, 14, and x is 3, what is the value of x?
9
What is the absolute value of -9?
9
What is the median of a set of 7 consecutive integers, if the smallest of those integers is 6?
9
Simplify:9^-2a+4/9^-2a-1
9^5
If a is odd and b is even, is 7ab + 7a + 9b + 7 even or odd?
Even
If a is odd and b is odd, is 5ab+9b+4 even or odd?
Even
If x>0, Z>0, and x^7y^7z^5<0, is y positive or negative?
Negative
If y>0, z<0, and x^3yz^4<0, is x positive or negative?
Negative
If 3a+6 is odd, is a even or odd?
Odd
If 9a+8 is odd, is a even or odd?
Odd
If a is even, is a+3 even or odd?
Odd
If a<0, b>0, and a^2b^5c^5>0, is c positive or negative?
Positive
If b<0 and a^5b^6> 0, is a positive or negative?
Positive
If y>0, z>0 and xy^6z^6>0m is x positive or negative?
Positive
For which values of a, if any, does |-6a+52| = 10a+76
a=6
