Variables
A bird traveled 72 miles in 6 hrs flying at constant speed. At this rate, how many miles did the bird travel in 5 hours.
A. 12 B. 30 C. 60 D. 14.4
C. 60
What is the correct order for PEMDAS
Parenthesis, exponents, Multiplication, Division, Addition, Subtraction
There are 5 pencil cases on the desk. Each pencil case contains at least 10 pencils, but not more than 14 pencils. Which of the following would be the total number of pencils in all 5 cases?
A. 35 B. 45 C. 65 D. 75
C. 65
Explanation: All pencil cases have a minimum 10 pencils inside. The total minimum would be 10 × 5 =50 pencils. If all pencil cases have a max of 14 then the total max would be 14×5=70 pencils. The answer would be between 50 and 70.
A triangle is composed of angles represented as:
3x + 10, −2x + 40, and x + 40. What is the value of x?
A. 45 B. 50 C. 55 D. 60
A. 45
Explanation: 3x + 10 + −2x + 40 + x + 40 = 180
2x + 90 = 180
2x = 90
x = 45
The sum of two positive integers is 13. The difference between these numbers is 7. What is their product?
A. 12 B. 22 C. 30 D. 40
C. 30
Explanation: x+y=13, and x-y=7.
x+x=13+7. 2x/2=20/2. X=10
Subtract 10 from both sides, 10(-10)+y=13(-10). Y=3
Magazine subscriptions cost $9.99 a month per magazine after an initial contract fee of $24.99. Which expression represents the cost of m magazines?
A. $9.99+$24.99 B. $9.99m+$24.99
C. $24.99-$9.99m D. $24.99+m+$9.99
B. $9.99m+$24.99
Explanation: m, the number of magazines times the monthly price. Then add the contract fee
The constant quantity placed before the variable in expressions to represent that they are meant to be multiplied by each other.
Coefficient
Three kids own a total of 96 comic books. If one of the kids owns 16 of the comic books, solve the average number of comic books owned by the other two kids?
A. 40 B. 42 C. 44 D. 46
A. 40
Explanation: 96-16=80. Divide 80 by 2 people and each person gets 40.
If 60% of a number is 12, what is 165% of the same number?
A. 20 B. 22 C. 28 D. 33
D. 33
Explanation: x * 0.6 = 12 x = 20
20 × 1.65 = 33
What is the difference between the median and the mode in the following set of data.
72,44,58,32,34,58,94,22,67,45,58
A.0 B. 2 C. 4 D. 6
A. 0
Mode (Occurs most) is 58. Median (Data value in the middle) is 58. 58-58=0
If 7+3x =22, then 2x = ?
A. 5 B. 10 C. 12 D. 14
B. 10
Explanation: 7+3x=22 (7-7)+3x=(22-7)
3x=15 15/3=5
2×5=10
The endpoint to a ray or line segment.
Vertex
If david has twice as many many nickels as tom, and tom has 15 more nickels than john ,what is the value in dollars of davids nickels if john has 6 nickels.
A. 2.18 B. 1.40 C. 42.00 D. 21.00
A. 2.18
Explanation: If john has 6 nickels and tom has 15 more, tom has 21. If tom has 21 and david has twice as much, david has 42. 42×5=2.18
35% of 15% of x is equivalent to which of the following?
A. 0.0525x B. 0.125x C. 0.25x D. 0.525x
A. 0.0525x
Explanation: 35%=0.35 and 15%=0.15
0.35× 0.15=0.0525x
Richard wants to buy every possible combination of meals available at his favorite restaurant. They offer 4 appetizers, 5 entrees, and 3 desserts. How many meals will richard have tried by the time he finishes.
A. 12 B. 15 C. 20 D. 60
D. 60
Explanation: 4×5×3=60
A consultant charges $45 for each hour she works on a consultation, plus a flat $30 consulting fee. ow many hours of work are included in a $210 bill for a consultation
A. 2 4/5 B. 4 C. 4 2/3 D. 5 1/2
B. 4
45x + 30= 210 45x+ (30-30)= (210-30)
45x=180 180/45= 4
x=4
Divides a line segment into two equal parts
Midpoint
Your in charge of buying T-shirts for your schools math club. There are 27 club members, who will each receive a shirt. The T-shirts come in boxes. Each box contains 4 T-shirts and cost $23.50. What is the total cost for the T-shirts.
A. 164.50 B. 634.50 C. 141.00 D. 150.65
A. 164.50
Explanation: 27/4= 6.75= 7
7× 23.50= 164.50
If 68% of a number is 102, what is 250% of the same number
A. 186 B. 246 C. 255 D. 287
D. 287
Explanation: 0.68× X = 102 X= 102/ 0.68= 150
Find 250% of 150:
150 × 2.5 = 375
The quantity that may change within the context of a mathematical problem
Variables
If 4x + 3x − 2(x + 5) = −9, then x = ?
A. -1/2 B. 0 C. 1/5 D. 2/3
C. 1/5
7x - 2x - 10= -9 5x=1
x=1/5
An operation involving a base and power. The power represents ow many times the base is multiplied by itself.
Exponent
A farmer has a rectangular field that measures 125 feet by 200 feet. He wants to enclose the field with a fence. What is the total length, in feet, he will need for the job?
A. 350 B. 450 C. 550 D. 650
D.650
(125×2) + (200×2)=650
A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. What is the maximum marks
A. 500 B. 600 C. 800 D. 1000
A. 500
Explanation:
The minimum pass mark = 125 + 40 = 165
Given that minimum pass mark = 33% of the total mark
total mark =33/100 =165
total mark = 16500/33 = 500
If x is an even integer and y is an odd integer, which of the following must be an odd integer?
A. 2x + 2y B. 2x - 2y C. x + y + 1 D. x + y +2
D. x + y + 2
Set x = 0 and y = 1 → only x + y + 2 will evaluate to an odd integer.