Math Basics

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Questions 1-5 test on the topics of basic math skills, such as number sense, whole numbers, fractions, percents, decimals and corresponding operations.
1. Approximately how much larger is the population of Pennsylvania than the population of Ohio? Pennsylvania’s population is 12,604,767, and Ohio’s population is 11,542,645.
A. 1,060,000
B. 1,070,000
C. 170,000
D. 160,000
2. Calculate 6 x 23
A. 1728
B. 14
C. 48
D. 36
3. How many widgets can you buy for $40 if each widget costs $2.50
A. 15
B. 16
C. 17
D. 20
4. A 10-foot fence was set 2 5/6 feet into the ground. What is the exact length of the fence above ground?
A. 43/5
B. 8 5/6
C. 7 3/12
D. 7 1/6
5. John receives a 2.5% real estate commission when he sells a home for his client. How much will the client receive from the sale of their $346,000 home?
A. $8,650
B. $337,350
C. $346,000
D. $354,650
Algebra – Questions 6-10
Questions 6-10 test on the topics of intermediary math skills, such as single and multistep equations and operations, measurements and conversions, and graphing equations.
6. Write the following expression in factored form using the greatest common factor.
50a3 + 10a2
A. 10a2(5a + 1)
B. 5a2(10a + 2)
C. 10a2(5a – 1)
D. 10a(5a2 + 1a)
7. If five times a number is subtracted from twelve times a number, the result is seven less than twice the number. Find the number.
A. 5/7
B. -1
C. 7/9
D. 7
A. x > -11
B. x = -11
C. x < -11
D. x = 11
10. Simplify the following expression by combining like terms.
9y3 + x – 2x + 3y3
A. 12y3 + 3x
12y3 – x
C. 11y3 + x
D. 6y3 – 3x
Geometry – Questions 11-15
Questions 11-15 test on the study of geometry, including angle and figure measurements, triangular relationships and Pythagorean Theorem.
11. Find the perimeter of this triangle.
A. 443 in.
B. 35 in.
C. 91 in.
D. 195 in.
12. Which of the following shapes is not a quadrilateral?
A. Parallelogram
B. Square
C. Trapezoid
D. Hexagon
13. What is the area of a circle whose diameter is 18 inches?
A. 56.52 sq in.
B. 1017.36 sq in.
C. 254.34 sq in.
D. 28.26 sq in.
14. A right triangle has a 50° angle. What is the measure of the third angle?
A. 180°
B. 50°
C. 90°
D. 40°
15. Find the length of side c of a triangle if side a = 15 and side b = 20.
A. 25
B. 17.5
C. 20
D. 15
Data Analysis, Statistics, Probability – Questions 16-20
Questions 16-20 test on the topics of charts, graphs, ratios, proportions and probabilities.
16. A single die has six faces each with a number from 1-6 that is only used once. What is the probability of rolling a number less than 5?
A. 0
B. 5/6
C. 24
D. 662/3%
17. What is the median age of the following recreational softball team roster?
Amber 36
Tanner 27
Sarah 31
Mark 35
Lori 22
Jim 28
Katie 27
Jennifer 34
Guy 30
Billy 21
Molly 23
A. 28
B. 36
C. 21
D. 29
18. According to the chart below, if you make $48,000 per year what is your annual contribution to FICA?
A. $36,000
B. $3,360
C. $3,600
D. $44,400
19. According to the graph below, which month had the largest sales growth over the last ten years?
A. January
B. August
C. October
D. December
20. Solve the following proportions for the missing element.
3
=
x
7
21
A. 3
B. 9
C. 6
D. 7
Trigonometry, Pre-Calculus – Questions 21-25
Questions 21-25 test on more advanced mathematic topics, such as trigonometric ratios and compound functions.
21. Find the height of the triangle below.
A. 10.38 ft.
B. 4.2 ft.
C. 29.89 ft.
D. 27.72 ft.
22. Find the cos 32°
A. 0.625
B. 0.848
C. 0.53
D. 1.18
23. Find the sine, cosine and tangent for angle A of the triangle below.
A. sin = 1.2, cos = .56, tan = .67
B. sin = .56, cos = .67, tan = 1.2
C. sin = .67, cos = .56, tan = 1.2
D. sin = .56, cos = 1.2, tan = .67
24. Find the slope of the line that passes through the points (4 , 2) and (5 , 8).
A. 6
B. Undefined
C. Zero
D. 1/6
25. What is the slope of the line parallel to the line whose equation is given by
-y = – 4x + 6?
A. 6
B. 4
C. -4
D. 1/4

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