DIVISION OF DAVAO DEL NORTE
Division Unified Test in Secondary Mathematics 10
SECOND QUARTERLY EXAMINATION
S.Y. 2014-2015
Name: _________________________________________ Year and Section: __________________
School: ________________________________________ Date: ___________ Score: ________
Directions: Read and analyze each item carefully. Choose the correct answer from the choices 1, 2, 3,and 4.
Blacken the circle of the number that corresponds to your answer. You have one hour to answer the test. GOOD
LUCK!
1. Which of the following is a polynomial function?
①f(x) = 4x – 2 ② f(x) = x4 + 9x– 3 – 5
5 x3 x
+7 x 2 − +1
③ f(x) = x1/2 -√7 ④ f(x) = 6 3
2. What is the degree of the given polynomial function x + 2 = 0 ?
① -2 ②0 ③1 ④2
3. Use synthetic division to find the quotient and remainder for (2 x 3 − x 2 + 2 x + 4) ÷ (x − 3).
① The quotient is 2 x 2 + 5 x + 17, and the remainder is 55.
② The quotient is 2 x 2 + 5 x + 7, and the remainder is 29.
③ The quotient is 2 x 2 + x + 5, and the remainder is 19.
④ The quotient is 2 x 2 + x + 3, and the remainder is 7.
4. Find the value of k so that the remainder when P(x) = x3 – kx2 + x + 4 divided by x – 2 is 2.
① 3 ②–3 ③ 2 ④ 6
5. Find all zeros for f(x) = x 3 − 6 x 2 + 13 x − 10.
① −2, 2 ± i ② 2, 2 ± i ③ 2, 1 ±2 i ④ −2, 1 ±2 i
6. What value of k will make x + 3 a factor of 2x3 + x2 – ( 3k – 2 ) x + 6?
① -5 ② -3 ③ 3 ④ 5
7. What theorem states that if a polynomial P(x) is divided by x – c, where c is a real number, then the remainder is P(c)?
① Factor Theorem ② Remainder Theorem
③ Rational Root Theorem ④ Number of Roots Theorem
8. Find the value of k so that x – 2 is a factor of 4x3 – kx2 – 8x – 4.
①3 ② 4 ③ 6 ④ 8
9. Find by inspection the zeros of the function f(x) = ( x + 1 ), ( x – 2 ), ( x – 3 ).
① 2, 3, - 1 ② 2, - 3, - 1 ③ - 2, - 3, 1 ④ 1, - 2, - 3
10. Find the zeros of the polynomial equation x3 – x = 0.
① 0, 1, 1 ② - 1 , -1 ③ -1, 1, 0 ④ 0, 1, 3
11. What is the graph of the given function f(x) = 2 x 2 ( x − 1)( x + 2) = 2 x 4 + 2 x 3 − 4 x 2
① ② ③ ④
12. Based on the exponential function y = ax where a>0 and is not equal to 1, if 0 < a < 1, the curve ..
① continuously rises as x increases. ② does not pass through the point ( 0, 1 )
③ continuously falls as x increases. ④ is found in the 3rd and 4th quadrant.
13. What theorem states that if p(c) = 0, then x – c is a factor of p(x)?
① Factor Theorem ② Remainder Theorem
③ Rational Root Theorem ④ Number of Roots Theorem
14. Given the function , use the remainder theorem to find f(-2).
① 13 ② 23 ③ 33 ④ 43
15. What is the graph of the exponential function f(x) = 3.5x?
① ② ③ ④
16. Find x from the exponential expression ( 16 ) x – 4 = 8 – x + 2.
−22 22
① x = 22 ② x = 22 -1 ③x= ④ x=
7 7
17. Factor completely the polynomial x3 – 3x2 – x + 3.
①(x–1)(x+1)(x+3) ②(x–1)(x+1)(x–3)
③(x+1)(x+1)(x–3) ④(x–1)(x–1)(x–3)
18. Based on the exponential function y = ax where a > 0, and a is not equal to 1, if a > 1, its graph …
① continuously falls as x increases. ② continuously rises as x increases
③ does not pass through the point (0, 1 ). ④ is found in the 3rd and 4th quadrant.
19.The graph of an exponential function is said to be asymptotic to the x-axis. Why is it so?
① Its graph is a curve. ② Its graph intersects the x-axis.
③ Its graph does not intersect the x-axis. ④ Its graph always passes through the point (0, 1).
20. Find the value of x if ( 81 ) 2 – x = ( 27 ) - 2x + 3.
1
① x=-1 ②x=1 ③x= -2 ④ x=
2
21. Solve for the value of x if log 2x + log 2( x – 6 ) = 4.
① x = 6 and 4 ② x = - 2 and 4 ③x= 2 ④ x=8
22. Solve for x given : log ax = 2 log a4 – log a2
① x = 16 ②x=8 ③ x= 4 ④ x= 2
23. Which of the following represents the inverse of f(x) = 8x, given that the function is one-to-one?
②
① X 0 1 2 3 4 x 0 1 2 3 4
f(x) 0 1 1 3 1 f(x) 0 -8 -16 -24 -32 ④
③ - - - -
x 0 18 24 38 42 X 0 1 2 3 4
f(x) 0 8 16 24 32 f(x) 0 1 1 3 1
-
8 4 8 2
24. Which of the following tables best describe an exponential function?
① ②
x 3 4 5 6 7
x -2 -1 0 1 2
y 11 12 13 14 15
y 1/16 1/4 1 4 16
③ ④
x -2 -1 0 1 2
x -2 -1 0 1 2 y 4 1 0 1 4
Y -1/4 -1/2 1 -2 -4
25. Which of the following graphs is the graph of a logarithmic function?
① ② ③ ④
26. Which statement below is true for the domain of the graph of an exponential function?
① the domain is always one ② the domain is a set of all real numbers
③ the domain is a set of positive real numbers ④ the domain is a set of negative real numbers
27. Divide using synthetic division the given function f(x) =
① x2 – 3 r. 7 ② x2 + 3 r. 8 ③ x2 – 3 r. 8 ④ x2 + 3 r. 7
28. Which statement below is true for the range of the graph of an exponential function f(x) = 3x?
① the range is always zero ② the range is a set of all real numbers
③ the range is a set of all positive real numbers ④ the range is a set of negative real numbers
29. What is the degree of the polynomial function defined by f(x)=6xn – 2 + 4x3n – 5 – 7x2n+1 if n=2?
① 0 ②1 ③5 ④10
30. Which of the following will determine if x – 2 is a factor of 2x4 – 4x2 – 12x + 8?
① P(2) = 2(2)4+4(2)2+12(2) – 8 ② P(2) = 2(2)4 – 4(2)2 – 12(2) + 8
③ P(2) = 2( - 2)4+4( - 2)2+12( - 2) + 8 ④ P(2) = 2( - 2)4+4( - 2)2 - 12( - 2) – 8
31. What is the remainder when 4x3 – 7x2 + 20x – 15 is divided by x – 2 using synthetic division?
① 22 ② 29 ③ 39 ④ 44
32. What is/are the characteristic/s of the graph of polynomial function?
① broken ② straight ③smooth and broken ④ smooth and continuous
33. How do you define the turning points of the graph of polynomial functions?
① ( n – 1 ) 180 ② n+1 ③ n–1 ④n + 2
34. What are the roots of f(x) = X4 – x3 – 19 x2 – 11x + 30 ?
① 5,1,5,2 ② 1, 4, 3, 5 ③ 0, 2, 5, 3 ④ - 3, - 2, 1, 5
35. Which of the following defines an exponential function?
8
x
① f(x) = x ②f(x) = ( )2 ③ f(x) = 8x+1 ④f(x) = x4 – 9
5
2x
36. What is the inverse function of f(x) = ?
x−2
−2 x 2x x−2 −2 x
① f −1 (x) = ② f −1 (x) = ③ f −1 (x) = ④ f −1 (x) =
2−x 2+ x 2x 2x
II. Solve the following:
37. The half-life of a radioactive substance is 10 days and there are 10 grams initially. Determine the amount of substance
left after 20 days.
38. Dannah deposited Php 1,000 in a bank that pays 6% compound interest annually. How much money will she have after
4 years?
39. Evaluate: log 5 5 √ 5
40. Show that f and g are inverse of one another.
1
f(x) = 3x + 6 ; g(x) = x−2
3
DIVISION OF DAVAO DEL NORTE
Division Unified Test in Secondary Mathematics IV
SECOND QUARTERLY EXAMINATION
S.Y. 2014-2015
TABLE OF SPECIFICATION
Item Competency Easy Moderate Difficult Answer
(60%) (30%) (10%) key
1 D1.1 Identify a polynomial function from a given set of relations. / 4
2. D1.2 Determine the degree of the polynomial function / 3
3 D1.4 Find by synthetic division the quotient and remainder when P(x) / 1
is divided by x – c.
4. D1.6 Find the value of P(x) for x = k synthetic division and Remainder / 1
theorem.
5. D1.8 Find the zeros of polynomial functions of degree greater than 2 / 2
by factor theorem, factoring, synthetic division and depressed
equations.
6. D1.6 Find the value of P(x) for x = k synthetic division and Remainder / 4
theorem.
7 D1.5 State and illustrate Remainder theorem. / 2
8. D1.6 Find the value of P(x) for x = k synthetic division and Remainder / 1
theorem.
9. D1.8 Find the zeros of polynomial functions of degree greater than 2 / 1
by factor theorem, factoring, synthetic division and depressed
equations.
10 -do- / 3
11. D1.9 Draw the graph of polynomial function of degree greater than 2. / 3
12 E1.4 Describe some properties of the exponential function, f(x) =ax / 3
from its graph.( 0<a<1)
13 D1.7 State and illustrate the Factor Theorem / 2
14 D1.5 Illustrate Remainder theorem. / 3
15. E1.3 Draw the graph of an exponential function f(x) =ax . / 1
16. E1.7 Use the laws on exponents to find the zeros of exponential functions / 4
17 D1.8 Find the zeros of polynomial functions of degree greater than 2 / 2
by factor theorem, factoring, synthetic division and depressed
equations.
18 E1.4 Describe some properties of the exponential function, f(x) =ax / 2
from its graph.(a>1)
19 E1.6 Describe the behavior of the graph of an exponential function / 3
20 E1.7 Use the laws on exponents to find the zeros of exponential function. / 4
21 E2.5 Solve Simple logarithmic equations / 4
22. E2.4 Apply the laws of logarithms / 2
23 E1.9 Determine the inverse of a given function. / 4
24 E1. 2 Given a table of ordered pairs, state whether the trend is / 2
exponential or not.
25 E1. 3 Draw the graph of the logarithmic function f(x)= logax / 1
26 E1. 5 Given the graph of an exponential function determine the / 2
domain, range, intercepts, trend and asymptote.
27. D1.4 Find by synthetic division the quotient and remainder when P(x) / 1
is divided by x – c.
28 E1. 5 Given the graph of an exponential function determine the / 3
domain, range, intercepts, trend and asymptote.
29 D1.2 Determine the degree of a given polynomial function / 3
30 D1.7 Illustrate the Factor Theorem / 2
31 D1.4 Find by synthetic division the quotient and remainder when P(x) / 2
is divided by x – c
32 Demonstrate knowledge and skills related to polynomial functions. / 4
(Graph of polynomial Function)
33 Demonstrate knowledge and skills related to polynomial functions. / 3
(Graph of polynomial Function)
34 D1.8 Find the zeros of polynomial functions of degree greater than 2 / 4
by factor theorem, factoring, synthetic division and depressed
equations.
35 E1.1 Demonstrate knowledge and skill related to exponential function. / 3
36 E1.9 Determine the inverse of a given function. / 1
37 E2.6 Solve problems involving exponential function. / 2.5 grams
38 E2.6 Solve problems involving exponential function. / P1,262.48
39 E2.5 Solve Simple logarithmic equations / 3
x=
2
40 D1.9 Determine the inverse of a given function / inverse
Total 24 12 4
Solution:
()
t
1 10
37. y = 10
2
()
20
1 10
= 10
2
()
2
1
= 10
2
= 10 ( 14 )
= 2.5 grams
38. A = P( 1 + r )t
= P 1,000 ( 1 + .06 ) 4
= P 1,000 ( 1.06 ) 4
= P 1,000 ( 1.26247696 )
A = Php 1,262.48
39. Let x = log 5 5√ 5
5x = 5√ 5
1
5x = 5 • 5 2
3
5x = 5 2
3
x=
2
1
40. f(x) = 3x + 6 ; g(x) = x−2
3
f(g(x)) = 3 ( 13 x−2)+ 6
=x–6+6
=x
1
g(f(x)) = ( 3 x+ 6 ) - 2
3
=x+2–2
= x
1
Since f (3x + 6) = g( x−2), then f(x) and g(x) are inverse functions
3
Rubrics for scoring
Score
3 Complete solutions with correct answer.
2 Complete solution with incorrect answer.
1 There is an attempt but incorrect solutions and answer.
