Mathematical Reasoning
25 Questions(various formats)
Directions: For multiple-choice questions, choose the best answer. For fill-in-the-blank questions, write
your answer in the blank. For “drop down” questions, follow the directions given.
For 1-4 questions , no calculator may be used.
1. Estimate 513 × 284 by rounding each factor to the nearest hundred.
2.
3.
3.
4. Evaluate thefollowing formula:
N = a +c -2ac , if a =5 and c =3
(A) –22
(B) 22
(C) 28
(D) 38
5. There are 63 candy bars in seven boxes. How many candy bars are
there in each box?
A. 3
B. 6
C. 7
D. 9
6. Randy traveled 120 kilometers (km) in 2 ½hours. What is his
average speed in kilometers per hour?
A. 48 k/hr
B. 53 k/hr
C. 60 k/hr
D. 300 k/hr
7. Find the product: (2x − 3)(5 − 4x)
A. 8xˆ2 − 2x − 15
B. −8xˆ2 + 22x − 15
C. 8xˆ2 + 22x − 15
D. −8xˆ2 − 2x − 15
4.
8. Factor 32xˆ5− 162x completely.
A. 16x(xˆ4 − 10)
B. 2x(16xˆ4 − 81)
C. 2x(4xˆ2 + 9)(2x − 3)
D. 2x(4xˆ2 + 9)(4xˆ2 − 9)
9. Solve: 2(x + 4) < 5(x − 20)
A. x < 6
B. x > 6
C. x < 36
D. x > 36
10.
11. Out of 25 students in a class, 5 students receive a grade
of A on the science test. What percent of the students
did NOT receive an A on the science test?
A. 20%
B. 25%
C. 75%
D. 80%
12. 16% of what number is 192?
13. Find the mean, median, and mode for this data set?
1, 6, 5, 11, 10, 14, 21, 5, 8
14. There are 5 white balls, 6 blue balls, and 11 green balls
in a jar. If one ball is picked at random, what is the
probability that it will NOT be a green ball?
5.
15. The diameterof the sun is approximately
140,000,000,000 cm. Which of the following
correctly represents the diameter of the sun
in scientific notation?
A. 1.4 × 10ˆ−12 cm
B. 1.4 × 10ˆ12 cm
C. 1.4 × 10ˆ−11 cm
D. 1.4 × 10ˆ11 cm
16. Simplify 5ˆ−2 and write your answer as a fraction.
17. Where on a graph would the point (-4,-4) be?
(A) four units to the right and four units below the
corresponding axis
(B) four units to the left and four units below the
corresponding axis
(C) four units to the left and four units above the
corresponding axis
(D) four units to the right and four units above the
corresponding axis
18.
19. Evaluate: 7 − 3 + 14 ÷ 7 × 12 ÷ 3
A. 0.64
B. 3.94
C. 10.29
D. 12.00
20. Sarah buys three t-shirts on sale. Each t- shirt
costs $9.98. What is the total cost of the
purchase?
A. $3.33
B. $12.98
C. $19.96
D. $29.94
6.
21. Find thearea of a triangle with height 5 and a base of 10.
22. What is the diameter of a circle with area 36π?
23. A cylinder is 9cm high and has a radius of 4cm. What is the
volume of the cylinder?
24.
25.
7.
1. In whichmonth did the number of scooter-related injuries decrease?
2. To the nearest 10, how many emergency room visits were due to
scooter injuries in August, September, and October combined?
3. Which of the following shows the greater percent of increase: the
change in injuries from June to July or the change from August to
September?
8.
4. About howmuch more did it cost to buy a ticket to Park A than a ticket
to Park B in 2009?
5. What was the percent of increase in the ticket prices at Park B from
2005 to 2010?
6. To the nearest 10, how much more did it cost to buy a ticket to Park A
in 2010 than in 2005?
9.
1. What percentof the total sports camp budget is spent on equipment
and umpires?
2. What fraction of the sports camp budget is spent on permits?
3. What amount does the camp spend each week on busing?
10.
4. A family’senergy bill is $180. Assuming the family’s energy use is
typical, how much did the family spend on water heating?
5. Which section is greater than 50 percent of an energy dollar?
6. Which energy cost is about 1/10 of the energy dollar?
11.
1. What wasthe total number of test drives of black and white cars
combined?
2. How many more drivers chose red than silver cars?
3. What was the ratio of red cars to white cars chosen for test-drives?
12.
4. What isthe ratio of customers under 18 to those over 55?
5. What was the total number of customers from 18 to 40 years of age?
6. What percent of the total customers were from 41 to 55 years of age?
(Round your answer to the nearest whole percent.)