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WorksheetsMiddle Grades Practice Questions 2018-2019
Total questions: 50
Worksheet time: 8mins
In an American football game, a touchdown and a kicked extra point associated with the touchdown is worth 7 points and a field goal is worth 3 points. If only the two types of scoring previously described were done in a football game, which of these scores would be the highest score impossible to achieve?
8
11
22
29
What is the sum of the digits of the least positive integer, N, that when divided by 2, or 3, or 4, or 5 all leave a remainder of 1?
3
5
7
9
What is the greatest common divisor of 2464 and 7469?
99
97
83
77
Below are the first 6 terms of a sequence. What is the sum of the next three terms of the sequence? 5, 7, 14, 16, 32, 34, …
278
244
216
182
The drawing to the right shows the seating pattern at tables in a banquet hall. Each ‘X’ represents a seat for a person and each rectangle represents a table. How many people could be seated at a 9-table arrangement?
34
36
38
40
Two terms of an arithmetic sequence are shown below. What is the value of the term that is nearest zero? …, __, __, __, 17/4, __, 27/4, __, __, __, …
-3/4
-1/2
1/2
3/4
Which of the following integers has the largest remainder when divided by 17?
A. 29
B. 81
C. 122
D. 312
Tom has a string that is 6 1/4 meters long. He cuts 1 2/3 meters off one end and then cuts the remaining string into 5 equal pieces. When the length of each of the 5 equal pieces of string is expressed as a fraction, what is the numerator of this fraction?
A. 55
B. 44
C. 22
D. 11
Evaluate the expression, j (h - |h|), when h = -1 and j = 5.
A. -10
B. -5
C. 5
D. 10
Including 7% tax, Sarah paid $202.22 for a bicycle that had a sticker price of $269.99 not including tax. To the nearest tenth, what was the percentage discount on the bicycle Sarah bought?
A. 23.7%
B. 25.1%
C. 28.2%
D. 30.0%
Eddie does contract hauling with his semi-truck. Last year Eddie averaged 623.5 miles per day while driving 10.25 hours per day when he was under contract. Use the averages given to calculate, to the nearest minute, how long Eddie would be on the road if a contracted trip was 3690 miles.
A. 59 hours 39 minutes
B. 59 hours 42 minutes
C. 60 hours 38 minutes
D. 60 hours 40 minutes
Alex saves nickels, dimes, and quarters. After a few months Alex discovers the ratio of nickels to dimes to quarters is 2:3:6. If Alex has 38 nickels, use the ratio to determine the value of the coins he has saved up to this point.
A. $34.20
B. $36.10
C. $37.30
D. $38.40
Use the conversion factor, 2.54 centimeters equals one inch, to calculate the number of whole centimeters in 1.43 miles.
A. 230,136 cm
B. 226,512 cm
C. 221,981 cm
D. 90,604 cm
Judy has 1.53 gallons of a liquid fragrance that needs to be placed into one teaspoon containers for resale. How many one teaspoon containers can Judy completely fill with the fragrance?
1087
1156
1175
1201
What is the volume, to the nearest hundredth cubic foot, of a rectangular prism that measures 13 inches by 27 inches, by 48 inches?
9.50 ft³
9.75 ft³
10.25 ft³
117.00 ft³
Find the value of x in the drawing shown to the right. (Figure not drawn to scale and all angles are measured in degrees.)
120
110
100
90
In the drawing to the right AB and DE are parallel. What is the measure of ∠ACB?
75°
79°
101°
105°
AD is the diameter of circle O and AB is a chord in the circle. If AD is 50 inches and AB is 48 inches what is the perpendicular distance from chord AB to the center of circle O?
2 inches
5 inches
7 inches
8 inches
The sides of a rectangle (length and width) are in the ratio 5:3. If the perimeter of the rectangle is 288 centimeters, find the width of rectangle.
90 cm
84 cm
72 cm
54 cm
Rover’s leash is tied to a stake that allows him to make a circular pattern. If the area of the circle created by Rover’s path is 242 m², to the nearest tenth of a meter, what is the circumference of the circle?
55.1 m
65.7 m
81.6 m
121.0 m
A right circular cone is made of solid gold. The cone has a radius of 4 centimeters and a height of 2 centimeters. If the cone is melted and then remade into a sphere, what is the radius of the sphere?
1 cm
2 cm
3 cm
4 cm
The radius of a sphere is equal to the radius of a right circular cylinder. If the volume of the sphere is two-sevenths the volume of the cylinder, what is the ratio of the height of the cylinder to its radius?
7:2
7:3
14:5
14:3
A large holding tank can hold a volume of 147 kiloliters. If water is poured into the tank at 49 liters per minute, how long will it take to fill the holding tank?
50 hours
55 hours
60 hours
500 hours
A single container of chocolate is 13 centimeters long, 6 centimeters wide, and 3 centimeters deep. How many containers of chocolate can be packed into a container that is 130 centimeters long, 42 centimeters wide, and 39 centimeters deep?
901
910
913
920
In triangle ABC shown to the right, AB = 2 units. What is the length of BC?
2√6 units
√6 units
6 units
2√3 units
In right triangle XYZ, ∠X equals 90°. If XY equals 3 units and YZ equals 5 units, what is the value of cos (Y) + tan (Z)?
8/5
6/5
27/20
31/20
In the drawing to the right triangle CGL is similar to triangle MPS. The similarity ratio between triangle CGL to triangle MPS is 5/2. What is the length of PS? (Triangles not drawn to scale.)
8 units
12 units
16 units
20 units
On the first five of seven tests in his Geography class Kai averaged 74.2. If Kai needs to have an average of exactly 80.0, what would need to be the sum of his grades on the final two tests in the class? (Each test is worth 100 points.)
179
182
189
Not possible, there are not enough points available to raise his grade to 80.0
The graph below shows the increases in the Federal Hourly Minimum Wage since its inception until September 1997. In what time frame did the minimum wage have the greatest increase as measured in cents?
January 1981 and April 1990
April 1990 and April 1991
April 1991 and October 1996
October 1996 and September 1997
The graph to the right shows Millie’s food and telephone bills for the first six months of the year. On average, how much more did Millie spend on food per month than telephone?
$5.83
$5.92
$6.03
$6.17
If a prime number is less than 31, what is the probability the prime number is less than 17?
5/9
3/5
2/3
8/15
Pete and Sam both flip a fair coin 3 times. What is the probability that Pete and Sam have the same number of heads on their flips?
3/8
5/16
9/32
19/64
Four science books and 3 math books are to be arranged on a shelf. The math books will be placed on the left and the science books will be placed on the right of the shelf. How many ways can the books be arranged?
12
72
144
216
What is the sum of the solutions of the following equation: |1 - 3x| = |3 - 2x|?
-6/5
-2/5
6/5
14/5
How many positive integers are solutions for the following equation? (7x - 1)/3 + 6 > 5x - (5 + 3x)/2
0
3
6
9
Solve for x: |x - 2|/(x - 2) > 0
x > -2
x > 2
x < -2
x < 2
What is the sum of the coefficients when (5t + 8s + 9p)^2 is expanded?
287
329
431
484
If (x + 1) is a factor of 2x^3 - 2x^2 + kx + 6, find the value of k.
2
1
-1
-2
Simplify \(\frac{x+1}{4y} \div \frac{x+4}{8y}\).
\(\frac{2x+1}{x+4}\)
\(\frac{x+4}{2(x+1)}\)
\(\frac{2(x+1)}{x+2}\)
\(\frac{2x+1}{x+2}\)
It takes 4 workers 6 hours to repair a road. How long will it take 7 workers to do the job if they work at the same rate?
\(10 \frac{2}{5}\) hours
\(5 \frac{1}{4}\) hours
\(3 \frac{6}{7}\) hours
\(3 \frac{3}{7}\) hours
Which statement below is true regarding the ordered pairs shown below? \((-2, -1), (1, -4), (7, -10), (8, -11)\)
The ordered pairs are a relation only.
The ordered pairs are a function only.
The ordered pairs are both a relation and a function.
The ordered pairs are neither a relation nor a function.
Let \(f(x) = 2x - 1\) and \(g(x) = 3x\). Find \(g(f(0))\).
-3
0
1
3
On the graph of the linear equation \(5x + 3y = 42\), there is a point such that \(y = 3x\). Find the coordinates of the point.
(3.5, 10.5)
(3, 9)
(2.5, 7.5)
(4, 12)
For the equation, \(8x - y = 8\), at what points does the graph of the equation cross the x-axis and the y-axis?
x-axis: (0, 1), y-axis: (0, -8)
x-axis: (-1, 0), y-axis: (0, 8)
x-axis: (0, -1), y-axis: (8, 0)
x-axis: (1, 0), y-axis: (0, -8)
Solve the following system of equations for x and y. What is the value of xy? 3x + 2y = 7 y = -3x + 11
20
-20
18
-18
Simplify \((\sqrt{a} + b + \sqrt{a} - \sqrt{b})(\sqrt{a} + b - \sqrt{a} + \sqrt{b})\).
2√ab
√ab
ab
ab/2
If the mean of three numbers, x, y, and z is 4, what is the value of \((5^{x+y-z})(5^{y+z-x})(5^{z+x-y})\)?
5^4
5^12
125^5
125^12
What is the vertex of the quadratic function: \(x = x^2 + 4x - 8\)?
(0, -8)
(-4, -8)
(-1, -11)
(-2, -12)
What is the sum of the roots for the following quadratic equation? x^2 + 5x - 100 = 0
-5
5
-5/2
5/2
The sum of the squares of two positive numbers, A and B where A < B, is 208. If the square of the larger number is 18 times the smaller number, find 3A + 2B.
48
52
54
60
