Download Math I - Abu Dhabi Polytechnic

ABU DHABI POLYTECHNIC
ACADEMIC SUPPORT
DEPARTMENT
Challenge Exam
Sample version
Mathematics I
Students answer on the question paper
Calculators are allowed
No additional materials are required
STUDENT NAME
STUDENT
NUMBER
A
CRN
DEPARTMENT
READ THESE INSTRUCTIONS CAREFULLY
Write your name, number, CRN and department clearly in the
boxes above.
Answer all questions. Use the 3 blank pages at the end.
Show all your working and use appropriate units. Otherwise,
you may lose marks.
Total number
of correct
answers
Score
You may use a pencil for all your work.
Answers that are not clearly readable, if any, will not be marked.
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There are 40 questions. Each question is 2.5 points.
Pass if Total Points ≥70, Fail if Total Points < 70
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to cheat a serious offense that will result in disciplinary
action taken against involved individuals.
RESULT
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Formula Sheet
1. 𝑎𝑚 × 𝑎𝑛 = 𝑎𝑚+𝑛
2.
𝑎𝑚
𝑎𝑛
= 𝑎𝑚−𝑛
3. (𝑎𝑚 )𝑛 = 𝑎𝑚𝑛
4. √𝑎𝑏 = √𝑎√𝑏 (a and b are positive real numbers)
5. (𝑎𝑏)𝑛 = 𝑎𝑛 𝑏 𝑛
6. Factorization
7. General formula for solving second order equation:
9. Properties of logarithmic functions
𝑏 𝑥 = 𝑦 𝑡ℎ𝑒𝑛 𝑥 = 𝑙𝑜𝑔𝑏 𝑦
𝑙𝑜𝑔𝑏 (𝑢𝑣) = 𝑙𝑜𝑔𝑏 (𝑢) + 𝑙𝑜𝑔𝑏 (𝑣)
𝑢
𝑙𝑜𝑔𝑏 ( ) = 𝑙𝑜𝑔𝑏 (𝑢) − 𝑙𝑜𝑔𝑏 (𝑣)
𝑣
𝑙𝑜𝑔𝑏 𝑢𝑛 = 𝑛𝑙𝑜𝑔𝑏 (𝑢)
𝑙𝑜𝑔𝑏 𝑥 =
𝑙𝑜𝑔𝑎 𝑥
𝑙𝑜𝑔𝑎 𝑏
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the value of the expression.
1) - - 5 - - 13 - 12
A) 30
B) -20
C) 20
D) -30
Determine whether the first literal expression is equal to the second literal expression.
2) -a - b, -b + (-a)
A) Yes
B) No
Round off the approximate number as indicated.
3) 79.95 3 significant digits
A) 80
B) 80.0
C) 79.9
1)
2)
D) 80.1
3)
Simplify.
4)
x5
3
-3
A)
27
x15
4)
B)
x15
27
C)
Express the number in standard notation.
5) 2.42 × 10-4
A) 0.00242
B) 0.0000242
D) 27x15
D) 0.000242
C) 5.82 x 10-4
D) 5.82 x 10-3
7)
B) 7
D) Not a real number
B) -12b + 3
C) -14b - 3
D) -12b + 13
Solve the equation.
1
1
9) (10x - 20) = (8x - 4)
5
2
A) -6
5)
6)
64 + 225
A) 17
C) 23
Simplify the expression.
8) b - {9b - [b - (5b - 8) - 5]}
A) -2b + 13
27x15
C) -242,000
Express the number in scientific notation.
6) 0.000582
A) 5.82 x 104
B) 5.82 x 10-5
Simplify.
7)
1
8)
9)
B) -1
C) 1
1
D)
1
6
Solve the problem.
10) A tree 11 feet high grows at the rate of 3 feet each year. How many years will it take for the tree to
grow to a height of 38 feet?
A) 9 years
B) 24 years
C) 14 years
D) 23 year(s)
Determine the principal value without using a calculator.
11) 3 512
11)
A) 64
C) 22
B) Not real number
D) 8
Solve the system by graphing.
12) 3x + y = -12
x + 3y = -20
A) (-2, -6)
Find the product.
13) -3x4 (9x - 4)
A) 27x5 - 12x4
Factor completely.
14) 2x4 + 12x3
A) 2x4 (1 + 6)
12)
B) (-6, 6)
C) (-2, -3)
D) (2, -6)
B) -27x5 + 12x4
C) -15x5
D) -27x4 + 12
B) x4 (2 + 12)
C) x3 (2x + 12)
D) 2x3 (x + 6)
15) 16x2 - 25
C) (4x + 5)(4x - 5)
Solve for the specified variable.
E
for r
16) I =
R+r
17) 8 x +
E - IR
I
-5y
8 xy - 3
14)
16)
B) r =
IR
E
C) r =
E
- IR
I
D) r =
E-R
I
5
3
for z
=
z
y
A) z =
13)
15)
B) (4x - 5)2
D) (4x + 5)2
A) (16x + 1)(x - 25)
A) r =
10)
17)
B) z =
-5y
8x - 3
C) z =
2
3 - 8 xy
5y
D) z =
5y
3 - 8x
Simplify.
18)
18)
2 3
+
x y
3 2
x y
A) -y
B)
x+y
y- 1
C)
2y + 3x
3y - 2x
Solve the quadratic equation by factoring.
19) 6n 2 + 4n = 0
2
A) - , 4
3
2
B) 3
C) 0
3
D)
y+x
x
2
D) - , 0
3
19)
Graph the parabola.
20) y = -x2 - 5
20)
A)
B)
C)
D)
Simplify.
21)
252 + 5 2
A) 15
21)
B) 5 30
D) 5 26
C) 30
Solve the formula for the specified variable.
nE
for n
22) I =
nr + R
A) n =
IR
E - Ir
B) n =
22)
-R
Ir - E
C) n =
4
IR
Ir + E
D) n = IR(Ir - E)
Evaluate the function.
23) Find f(-7) when f(x) = -5x - 28.
A) 6
B) 7
24) Find f(a + 2) when f(x) = x2 + 1
A) a 2 + 4a + 4
B) a 2 + 4
C) -7
D) -28
C) a 2 + 4a + 5
D) a 2 + 3
State the instructions of the function in words.
25) f(y) = 1 - 4y
A) Add the product of the independent variable and 4 to 1.
B) Raise the independent variable to the power 4. Subtract the result from 1.
C) Subtract 4 from 1. Multiply the independent variable by the result.
D) Multiply the independent variable by 4. Subtract the result from 1.
Solve the problem.
26) The area of a circle is given by A(C) =
A) 800 mm2
C) 130 mm2
Find the domain and range.
27) f(x) = 6 + x
A) Domain: All real numbers; range: y -6
B) Domain: x -6; range: y 0
C) Domain: All real numbers; range: All real numbers
D) Domain: : x 0; range: All real numbers
5
24)
25)
C2
, where C is the circumference. Find A(71 mm).
4
B) 18 mm2
23)
26)
D) 400 mm2
27)
Graph the function.
1
28) y =
x-3
28)
A)
B)
C)
D)
6
29) Temperature in degrees Celsius C is given by C =
5
(F - 32), where F is degrees Fahrenheit. Plot C
9
as a function of F.
A)
B)
C)
D)
Sketch the line with the given slope and y-intercept.
7
29)
30) m =
1
, (0, 3)
6
30)
A)
B)
C)
D)
Find the slope and the y-intercept of the line with the given equation.
31) 4x + 3y = 31
4
31
3
3
)
)
A) Slope - ; y-intercept (0,
B) Slope - ; y-intercept (0,
3
3
4
31
C) Slope
4
31
; y-intercept (0,
)
3
3
D) Slope
8
3
3
; y-intercept (0,
)
4
31
31)
Solve the system by graphing.
32) 5x + y = 4
x + 2y = -10
A) (-1, 9)
32)
B) (2, 1)
C) (2, -6)
D) (-2, -6)
Simplify the given expression. Express answer with positive exponents.
-1
3 k-6 (9 k-2 )
33)
6 k3/2
A) - 9k13
Solve.
B) -
1
18k12
C)
1
18 k11/2
33)
D)
3
k15/2
1
34) 4 -x =
256
A) 4
34)
B)
1
64
Use a graphing calculator to solve the equation.
35) ln(x + 2) - ln(4) = -ln x
A) 1.7321
B) 2.0101
Collect like terms and write in descending order.
36) -9y3 - 6y2
1
4
C) -4
D)
C) 1.9111
D) 2.2361
36)
B) -15y2
D) -15y5
A) Can't be simplified
C) -15y3
Perform the indicated operation.
37) (2n 6 - 14n 5 - 12) - (-18n 5 + 5n 6 + 4)
A) -3n 6 - 9n 5 - 8
B) -15n 11
C) -3n 6 + 4n 5 - 16
D) -3n 6 + 4n 5 - 8
Solve the problem. Assume all data are accurate to two significant digits unless greater accuracy is given.
38) A company sold 4.9 million items in a two-year period. Sales increased by 100,000 the second year.
How many were sold the second year?
A) 3,000,000
B) 2,500,000
C) 2,400,000
D) 3,750,000
9
35)
37)
38)
Evaluate the function.
39) Find f(p) when f(x) =
A) px - 2
5x - 2
B)
39)
5x - p
C)
5p - 2
Find the domain and range.
6
40) f(x) =
6-x
D) 5p - 2
40)
A) Domain: All real numbers; Range: All real numbers
B) Domain: All real numbers; range: All real numbers except 0
C) Domain: All real numbers except 6; range: All real numbers except 0
D) Domain: All real numbers except 6; Range: All real numbers
10