Adama Science And Technology University 2023

Special School Grade 10 Mathematics

Work sheet - 2
Set by: Gezahegn.K
I. Choose the best answer form the given alternative
1. Which of the following is a polynomial?
3
𝑥 2 −4 1
A. 𝑥 2 + 𝑥 4 + 1 B. 𝑥+2
C. 3
𝑥 2 - √2𝑥 + 1 D. √(𝑥 − 1)2

2. Which of the following is not a polynomial function?

A. f (x) = |𝑥 2 +1| C. f(x) = √𝑥 4
𝑥 4 −16
B. f(x) = D. 3𝑥 +2x+1
𝑥2+ 4

3. What is the remainder when f(x) = -5𝑥 4 + 7x -2 is divided by 𝑥 2 -1?”

A. -22 + 7√2 B. 7x- 22 C. -5𝑥 2 -10 D. None
4. Which of the following is not true about any polynomial function?
A. Its rang is the set of all real numbers
B. Its domain is the set of all real number
C. Its graph has not horizontal asymptote
D. The set of all polynomial function is closed under multiplication
5. If x+2 is a factor of f(x) = 𝑥 4 + k𝑥 3 + h𝑥 2 + 12x -16 and 6 is the remainder when f(x) is
divided by x +1, then which of the following is true?
A. K = -1 and h = 4 C. k = 2 and h = 6
B. k = 1 and h = 8 D. None
6. Which of the following is a factor of f(x) = 𝑥 4 + 5𝑥 2 + 4?
A. x +1 B. x + 2 C. x2+1 D. x2+2
7. Which of the following could be the graph of a polynomial function
A. C.
f(x)

B. f(x) D.

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 Adama Science And Technology University 2023
Special School Grade 10 Mathematics
Work sheet - 2
Set by: Gezahegn.K

8. One of the following is not an example of polynomial function.

A. x5-3x3 + 2x2+5x-6 B. x+1 C. x2+x-1+3 D. 2x3-3
9. If f(x) = x2+3x+5 is divided by g(x) = x+1, the remainder will be
A. 2x+5 B. 2x+2 C. 0 D. 3
10. What is the zero and its multiplicity of f(x) = 6(x+2)2 respectively
A. 2 and 2 B. 0 and 2 C. 2 and -2 D. -2 and 2
11. Which one is correct?
A. 2x + 1 is a factor of 2x2 + 4x + 1 B. x – 1 is a factor of (x-2) (x+1)
C. x – 1 is a factor of x2-2x+1 D. none
12. If f(x) = x+2 and g(x) = 2x2+x-3, then f(x). g(x) will be
A. 2x3 + 5x2 + x - 6 B. 2x3 + 5x2 - 5x - 6
C. 2x3 + 5x2 + 5x - 6 D. 2x3 + 5x2 - x – 6
13. The solution set of x2<3(2x-3) is

A. x/x≥3 B. x/x<3 C. 3 D. ∅

The following graph represent the relation

R= (x,y):Y>3x+1,Y   x and x+2y  9 then the range of R is

A. x:-9  x<1 Y
B. y:-9  x<1 Y=3x+1
1
C. X: <x<9 y=-x
4

D. Y: 1 <x≤9
4

x+2y=9

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 Adama Science And Technology University 2023
Special School Grade 10 Mathematics
Work sheet - 2
Set by: Gezahegn.K
14. Which of the following is not true about a quadratic inequality
A. For ax2+bx+c<0, If b2-4ac<0 and a>0 then the solution set is empty set.
B. For ax2+bx+c>0, If b2-4ac<0 and a>0 then the solution set is all real
Numbers
C. For ax2+bx+c<0, If b2-4ac<0 and a<0 then the solution set is empty set.
D. None
15. Which one of the following is a true statement

A. When you divided 3x5-4x4+2x3+x-2 by x-2 the remainder is 46

B. 2x+3 is a factor of 32x5-243

C. When we divided Px5-3x3+qx+2 by x+1 the constant term of the quotient is

p+q-3

D. If you divided x2+5x-7 by x-3 the remainder is 11

16. The solution set of 9x2+6x+1≥0 is

1 1
A. x:x≥0 B. R C. x:0≤x≤ D. x:x≥
3 3

17. In the figures below the shaded region represents the graph of the relation R.

Which of the following is false. y

A. R= (x,y):-Y≤-x2+1 and Y≤-x+1 y=x2-1

B. Domain of R= x:-2≤x≤1
C. R= (x,y):Y≥x2-1 and Y<-x+1 R
D. Range of R= y:-1≤y≤3 x

Y=1-x

18. What is the axis of symmetry of f(x)= x2

A. x= 7 4 B. x= 5 2 C. x=  5 2 D. x=  7 4

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 Adama Science And Technology University 2023
Special School Grade 10 Mathematics
Work sheet - 2
Set by: Gezahegn.K
2x  3 x2 f
19. Let f(x) = and g(x)= then (2f- ) (3) becomes
3x 3x  1 g

A.  2 15 B. 15 2 C. 7 5 D. 2 15

20. For which of the following polynomials is (𝑥 + 1) not a factor

A. 𝑥 3 − 𝑥 2 − 𝑥 + 1 B. 𝑥 3 + 𝑥 2 + 𝑥 + 1 C. 𝑥 3 + 𝑥 2 − 𝑥 + 1 D. 𝑥 3 + 𝑥 2 − 𝑥 +
21. Which of the following is not a factor of the polynomial 𝑥 3 − 𝜋𝑥 2 − 𝑥 + 𝜋
A. 𝑥 − 1 B. 𝑥 + 𝜋 C. 𝑥 + 1 D. 𝑥 − 𝜋
22. If 𝑥 3 − 𝑎𝑥 2 + 𝑏𝑥 + 4 is divisible by (𝑥 − 1)and (𝑥 − 2)then a and b are given by
A. 𝑎 = 4, 𝑏 = 1 𝐵. 𝑎 = 1, 𝑏 = −4 𝐶. 𝑎 = 4, 𝑏 = −1 𝐷. 𝑎 = −1, 𝑏 = 4
23. Which of the following does not have (𝑥 + 1)as a factor
A. 𝑥 3 + 𝑥 2 + 𝑥 + 1 𝐵. 𝑥 3 − 𝑥 2 − 𝑥 + 1 𝐶. 𝑥 3 − 2𝑥 2 − 2𝑥 + 1 𝐷. 𝑛𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒
24. Which of the following is not an x-intercept of the graph of the graph of 𝑦 = 𝑥 3 −
2𝑥 2 − 𝑥 + 2?
A. -1 B. -2 C. 2 D. 1
25. If 3𝑥 4 − 2𝑥 3 + 𝑥 + 2 𝑖𝑠 𝑑𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 𝑥 − 2 𝑡ℎ𝑒 𝑟𝑒𝑚𝑎𝑖𝑛𝑑𝑒𝑟 𝑖𝑠 ∶
A. 𝑥 + 2 𝐵. 2 𝐶. −2 𝐷. 36
26. Which of the following is a factor of 2𝑥 3 − 6𝑥 2 − 5𝑥 − 12?
A. 𝑥 + 4 𝐵. 𝑥 + 3 𝐶. 𝑥 − 3 𝐷. 𝑥 − 4
27. If ( 𝑥 − 3) 𝑖𝑠 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑎𝑥 3 + 2𝑥 2 + 2𝑥 + 3 𝑡ℎ𝑒𝑛 𝑎 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜: ?
A. 1 B. 0 C. -1 D. 3
28. If (𝑥 − 1) 𝑖𝑠 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑎𝑥 3 + 𝑥 2 − 12𝑥 + 9, 𝑡ℎ𝑒𝑛 𝑎 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜:
A. 1 B. -2 C. 2 D. -3
29. The factorization of 𝑥 3 + 3𝑥 2 + 3𝑥 + 2 𝑖𝑠
A. (𝑥 + 2)(𝑥 + 1)2 C. (𝑥 + 2)(𝑥 2 + 𝑥 + 1)
B. (𝑥 − 2)(𝑥 2 + 𝑥 + 1)(𝑥 + 1)2 D. (𝑥 − 2)(𝑥 + 1)2
30. If −𝑥 3 + 𝑎𝑥 2 + 𝑏𝑥 + 3 is divisible by (𝑥 + 1) 𝑎𝑛𝑑 (𝑥 − 2) then the values of a and b are
respectively:
−1 7 7 −1 −1 17 9 13
A. ,2 𝐵. 2 , 𝐶. , 𝐷. 2 ,
2 2 6 6 2

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 Adama Science And Technology University 2023
Special School Grade 10 Mathematics
Work sheet - 2
Set by: Gezahegn.K
31. If the polynomial 𝑝(𝑥) = 2𝑥 3 + 𝑏𝑥 2 + 𝑐𝑥 − 12 is divisible by 𝑥 + 2 but gives remainder-3,
when divided by (x+1), then the values of b and c are respectively:
A. -3, -8 B. -8, -3 C. 3, -8 D. -8, 3
32. Which of the following is not an intersection of the graph of 𝑦 = 𝑥 𝑎𝑛𝑑 𝑦 = 𝑥 3
A. (0, 0) B. (1, 1) C. (1, −1) D. (−1, −1)
33. When 𝑥 5 − 𝑥 4 + 𝑥 3 + 𝑥 2 − 1 is divided by 𝑥 + 1 the remainder is equal to
A. -3 B. 6 C. -6 D. -4
34. The complete factorization of 𝑥 4 − 2𝑥 3 − 5𝑥 2 + 18𝑥 − 36 𝑖𝑠
A. (𝑥 − 3)(𝑥 − 3)(𝑥 2 − 2𝑥 + 4) C. (𝑥 − 3)(𝑥 + 3)(𝑥 2 − 2𝑥 + 4)
B. (𝑥 − 3)(𝑥 + 3)(𝑥 2 + 2𝑥 + 4) D. (𝑥 + 3)(𝑥 + 3)(𝑥 2 − 2𝑥 + 4)
2 4
35. Factorizing the expression 𝑥 3 + 3 𝑥 2 − 2𝑥 − 3 gives,
2 2
A. (𝑥 + 3) (𝑥 2 + 2) C. (𝑥 − 3) (𝑥 2 − √2)(𝑥 2 + √2)
2 2
B. (𝑥 − 3) (𝑥 2 + 2) D. (𝑥 + 3) (𝑥 2 − √2)(𝑥 2 + √2)

36. Which of the following is not a factor of 𝑥 4 − 𝑥 3 − 7𝑥 2 + 𝑥 + 6 ?

A. 𝑥 − 3 B. 𝑥 + 2 C. 𝑥 − 2 D. 𝑥 + 1
37. If one of the roots of the equation 𝑥 3 − 𝑎𝑥 + 2 = 0 𝑖𝑠 − 1, then which of the following
statement is true?
A. 𝑥 3 − 𝑎𝑥 + 2 = (𝑥 + 1)(𝑥 2 + 𝑥 + 2) C. 𝑥 3 + 𝑎𝑥 + 2 = (𝑥 + 1)(𝑥 2 − 𝑥 + 2)
B. 𝑥 3 + 𝑎𝑥 + 2 = (𝑥 − 1)(𝑥 2 − 𝑥 − 2) D. 𝑥 3 + 𝑎𝑥 + 2 = (𝑥 + 1)(𝑥 2 + 𝑥 − 2)
38. Which one of the following expressions is a polynomial?
𝑥 2 −1 𝑥 𝑥 3 −𝑥
A. B. √2 C. 𝜋𝑥 2 − √3 D.
𝑥+1 𝑥−1

39. Which one of the following is the remainder when 4𝑥 5 − 12𝑥 3 + 1 is divided by 𝑥 + 2?
A. -7 B. -15 C. -31 D. -53
40. Which of the following is a polynomial?

𝑥 2 −4 1
A. 𝑥 −2 + 𝑥 −1 + 1 B. 𝑥+2
C. 3
𝑥 3 - √2𝑥 + 1 D. √(𝑥 − 1)2

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 Adama Science And Technology University 2023
Special School Grade 10 Mathematics
Work sheet - 2
Set by: Gezahegn.K
41. What is the remainder when f(x) = -5𝑥 4 + 7x -2 is divided by 𝑥 2 -2?”

A. -22 + 7√2 B. 7x- 22 C. -5𝑥 2 -10 D. -68

42. Which of the following is not true?

A. P (x) = |x -2| + 2 –x is a polynomial function over R
B. P (x) = (-3x) (1-2⁄3x) is a polynomial function over Z
𝑥 3 − 5𝑥 2 +𝑥−5
C. P (x) = is a polynomial function over Q
𝑥2+ 1
𝑥 75
D. P (x) = + √15 𝑥 7 + 𝜋𝑥 − 1 is a polynomial function over R
3

43. Which of the following is true about any polynomial function?

A. Its rang is the set of all real numbers
B. Its domain is the set of all real number
C. Its graph has at least one horizontal asymptote
D. The set of all polynomial function is not closed under multiplication
44. If x+2 is a factor of f(x) = 𝑥 4 + k𝑥 3 + h𝑥 2 + 12x -16 and 6 is the remainder when f(x) is
divided by x-1, then which of the following is true?
A. K = -1 and h = 4 C. k = 2 and h = 6
B. k = 1 and h = 8 D. k = 5 and h = 3
45. Which of the following is a factor of f(x) = 𝑥 4 + 5𝑥 2 + 4?
A. x +1 B. x + 2 C. x2+1 D. x2+2
46. Let f(x) = x3+2x2 + x- 1, then f(x) necessarily has a zero between
A. 1 and 2 B. 0 and 1 C. -2 and -1 D. -1 and 0
47. Of the zeros of a polynomial f(x) of degree 3 are -1,2 and 1 then which of the
following is necessarily true?
A. F(x) = (x2 -1) ( x- 2) C. f(3) = 8
B. F(x) = - x2 + 3x -2 is factor of f(x) D. the constant term is 2
48. Which of the following is not a factor of 2𝑥 3 − 𝑥 2 − 3𝑥?
A. 𝑥 B. 2𝑥 2 − 3𝑥 C. 2𝑥 2 − 𝑥 − 3 D. 𝑥 − 3

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 Adama Science And Technology University 2023
Special School Grade 10 Mathematics
Work sheet - 2
Set by: Gezahegn.K
49. If x-3 is a common factor of 𝑎𝑥 2 − 𝑏𝑥 − 9 𝑎𝑛𝑑 𝑥 3 + 𝑎𝑥 2 + 𝑏 then which of the following
is the value of b?
A. -9 B. 1 C. -2 D. 3
50. When 𝑓(𝑥) = 𝑥 4 + 𝑎𝑥 2 + 3𝑥 + 𝑏 is divided by 𝑥 + 1 𝑎𝑛𝑑 𝑥 − 2 the remainder is 3 and -6
respectively what is the value of 𝑎 − 2𝑏?
A. -25 B. -36 C. -47 D. -43
51. Let 𝑓(𝑥) = 2𝑥 3 + 𝑘𝑥 2 + 𝑘𝑥 − 1. If the graph of 𝑓 contains the point 𝑃(−2, 5), then what is
the value of k?
A. 10 B. 13 C. 12 D. 11
52. Let 𝑓(𝑥) = (𝑥 − 3)(𝑥 2 + 1) 𝑎𝑛𝑑 𝑔(𝑥) = (𝑥 − 3)2 (𝑥 + 3) then which of the following is not
true?
A. 𝑥 + 3 𝑖𝑠 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 (𝑓 + 𝑔)(𝑥) C. 𝑇ℎ𝑒 𝑑𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 (𝑓𝑔)(𝑥) 𝑖𝑠 6
B. 𝑇ℎ𝑒 𝑑𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 (𝑓 + 𝑔)(𝑥) 𝑖𝑠 3 D. None of the above
53. What are the zeros of 𝑓(𝑥) = 𝑥 3 − 7𝑥 − 6?
A. -3, 2, -1 B. 2, -2, 3 C. -2, -1, 3 D. 1, -2, -3
54. What are the zeros of the polynomial function 𝑓(𝑥) = 𝑥 3 + 3𝑥 2 − 𝑥 − 3?
A. -3, 2 and 3 C. -3, -1 and 1
B. -2, 1 and 2 D. -2, -1 and 3
55. The rational root of the polynomial equation 6𝑥 4 + 𝑥 3 + 2𝑥 − 24 = 0 is
5 7 −1 −3
A. B. C. D.
2 3 3 2

56. What number should be subtracted from x3  4x2  7x 12 , if it is to be perfectly divisible by x  3 ?

A. 42 B. 13 C. 39 D. None
57. If the graph of a polynomial functions f (x)  kx4  x2  kx  20 pass through the point (k,12). Then the value of k is
equal to

A. 2 B. 4 C. 2 and -2 D. 4 and -4
58. If the zeros of a polynomial function of p(x) are -2 and 0, then the zeros of p(x  5x  4) is equal to
2

A. 1, 2 and 3 B. 1, 2, 3 and 4 C. -2, 0, 1 and 4 D. 2, 3 and 4

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 Adama Science And Technology University 2023
Special School Grade 10 Mathematics
Work sheet - 2
Set by: Gezahegn.K
59. The polynomial function p(x) is divided by x 1 and x 1 , the remainders are 3 and 5 respectively. Then what
2
is the remainder if p(x) is divide by (x 1) ?
A. 4x 1 B. x  4 C.  x  4 D.  4x 1

60. When 2x3  5x2  4x  8 is divided by ax2  bx  c, the quotient is x  2, remainder is bx  a , then the value of
a,b, c are respectively__________
A. 2, 1 and 3 B. 2, -1 and 3 C. -2, 1 and 3 D. 2, 1 and -3
61. The degree of zero polynomial function is
A. 0 C. Not defined
B. 1 D. Any natural number
62. The zeros of zero polynomial is
A. 0 C. Any real number
B. 1 D. Not defined
63. One of the factor of a polynomial function of p(x)  (25x2 1)  (1 5x)2 is
a. 5  x b. 5  x c. 5x 1 d. 10x

64. What the value of remainder if a polynomial ax3  4x2  3x  4 and x3  4x  a leave the same remainder

when dived by x  3 ?
A. -14 B. 1 C. 14 D. -1
65. The area of rectangle in square unit is 4x2  4x  3 . How much longer is the length than the width of the
rectangle?

a. 2x  3 b. 2x 1 c. 3 D. 4

66. If f and g are a polynomial function with degree m and n , then which one of the following is necessary
true
a. f 2 is of degree 2m C. f is of degree n  m
g
b. f  g is of degree m  n D. fg is of degree mn
67. Which one of the following can be the graph of the polynomial function of degree 4 with positive leading
coefficient?
A. B. C. D.

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Adama Science And Technology University 2023
Special School Grade 10 Mathematics
Work sheet - 2
Set by: Gezahegn.K
68. If f (x) and h(x) are polynomial function such that f (x)  x2  x  24 and h(t)  x2. If 3h(t)  f (2x), what

are the possible values of x?

A. {-6} B. {4} C. {-4, 6} D. {-6, 4}
69. For what values of a and b x 1 is a common factor of g(x)  x6  4x3  ax2  bx  3 &

f (x)  x4  ax3  7bx 1respectively?

A. ½ and 6 B. 11/2 and ½ C. ½ and 11/2 D. -11/2 and ½
70. For a polynomial function f (x)  (1 5x)2 (x  5)3 , then which one of the following is true?
a. The graphs of f (x) rise to the left and fall to the C. The leading coefficient is positive
right D. The degree of polynomial function is odd

b. The constant term is -5

71. Which one of the following is not necessary true?
a. x 1 is a factor of xn 1, where n is even positive integer
b. x  a is a factor of xn  an , where n is positive integer
c. x  a is a factor of xn  an , where n is odd positive integer

d. x  a is a factor of xn  an for any real number a and positive integer n

72. Which one of the following is true about the graph of polynomial function of degree n?
a. The graph of every polynomial function of degree n crosses the x – axis n times
b. The range of any polynomial function of degree n is the set of real number.
c. The graphs of any polynomial function of degree n can cross y-axis exactly at one point.
d. The values of any polynomial function is large in positive When |𝑥| large

73. Which one of the following is not true about the graph of polynomial function of degree n?
a. The least turning point of polynomial function of an odd degree have zero while even degree one.
b. The maximum number of x-intercepts the graph of a polynomial function of degree n can have n
c. The polynomial function of degree n can have maximum of n real zeros
d. The least number of x-intercepts the graph of a polynomial function of an odd degree have zero while
even degree one.
74. Let f (x) and g(x) be a polynomial with g(x)  0 and degree of g(x)  degree of f (x) . Therefore,

According to polynomial division theorem, there exist a unique polynomials (𝑥)𝑎𝑛𝑑 𝑟(𝑥) such that,
a. f (x)  g(x)q(x)  r(x)
b. f (x)  g(x)q(x)  r(x) and r(x)  0 for any polynomial function f (x) and g(x)
c. f (x)  g(x)q(x)  r(x) where the degree of r(x)  degree of g(x)

d. f (x)  g(x)q(x)  r(x) where the degree of r(x)  degree of g(x)

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 Adama Science And Technology University 2023
Special School Grade 10 Mathematics
Work sheet - 2
Set by: Gezahegn.K
75. The area of a rectangle in square feet is x 13x  36. How much longer is the length than the width
2

of the rectangle?
A. 4feet B. 5feet C. 9feet D. 13feet
76. Which one of the following is not true about the graphs of polynomials of degree n?
A. The least number of turning point of zero for odd degree and one for even degree
B. The maximum number of x-intercept the graph at most n.
C. The maximum number of real zeros are at most n
D. The least number of x-intercept of the graph is one for even and zero for odd degree respectively.
77. Which one of the following can be the graph of the polynomial function of degree three with positive
leading coefficient?
A. B. C. D.

78. Which one of the following can be the graph of the polynomial function of degree 3 with negative
leading coefficient?
A. B. C. D.

II. Work out

79. Let f(x) = (x-1)2 (x+2) (x2 +x -2) find the zeros of f(x) with their multiplicity.
80. If 8 is the remainder when a polynomial f(x) = x3 + ax2 – 5x +2 is divided by x +
2, find the value of a.
81. If 2x -1 is a factor of f(x) = ax3 + x2 -3x + b and the remainder when f(x) divided
by x +2 is -5, find the value of a and b
82. Divided x4 + 5x2 – 3x -2 by x2 – 2x +1
83. Find the remainder when f(x) = 7x17 - 12x3 +13 is divided by d(x) x -1.
84. Let f(x) = 3x10 -2x15 + 2x3 + 5
A. The degree of f(x) = _________________________

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Adama Science And Technology University 2023
Special School Grade 10 Mathematics
Work sheet - 2
Set by: Gezahegn.K
The leading coefficients of f(x) =________________
85. If 8 is the remainder when a polynomial f(x) = x3 + ax2 – 5x +2 is divided by x +
2, find the value of a.
86. If 2x -1 is a factor of f(x) = ax3 + x2 -3x + b and the remainder when f(x) divided
by x +2 is -5, find the value of a and b (2)
87. Divided -5x4 + 7x –2 by x2 – 2
88. f(x) = -2-3x+5x4 + 6x2 find the following
a. degree of f(x)
b. leading coefficient of f(x)
c. constant term of f(x)
89. f(x) =3x3 –5𝑥 2 − 1 and g(x) = 3x3+4 find f(x).g(x)
90. Find the value of k such that:
P (x) = x3 + 2x2 – 3kx – 10 is divided by x+3 has a remainder of 8
91. Find the zeros and their multiplicity of x16 (x – √2 )4
92. When the polynomial P(x) = ax3 - x2 + bx + 3 is divided by x-1 and x-2 the
remainders are 4 and 9 respectively. Find the value of a and b
93. Verify that f(x) = x3+x+2 has a zero between -2 and 2 and locate the zeros
94. Find a numbers a and k so that x + 2 is a factor of P(x) = ax3 – 2x2+ kx-18 and
p (-1) = 8
95. An open box is to be made from a 20 cm long square piece of material, by cutting equal squares of length
𝑥 cm from the corners and turning up the sides.
a. Verify that the volume of the box is given by the function 𝑣 (𝑥) = 4𝑥 3 – 802 400𝑥.
b. find the volume of the box, when 𝑥 = 1 𝑎𝑛𝑑 𝑥 = 3.
96. A person wants to make an open box by cutting equal squares from the corners of a piece of metal 160
cm by 240 cm. If the edge of each cut-out square is x cm, find the volume of the box, when 𝑥 = 2 and
𝑥 = 5.
97. Find a polynomial function 𝑓 of degree 3 such that 𝑓 (10) = 17 and the zeros of 𝑓 are 0, 5 and 8.
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98. A polynomial function 𝑓 of degree 3 has zeros -2, and 3 and its leading coefficient is negative. Write
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an expression for 𝑓. How many different polynomial functions are possible for 𝑓 ?

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Adama Science And Technology University 2023
Special School Grade 10 Mathematics
Work sheet - 2
Set by: Gezahegn.K
99. The height above ground level in meters of a missile launched vertically, is given by ℎ(𝑡) = −16𝑡 3 +
100𝑡 At what time is the missile 72 m above ground level? [t is time in seconds].
100. A psychologist finds that the response to a certain stimulus varies with age group according to R =
𝑦 4 + 2𝑦 3 − 4𝑦 2 − 5𝑦 + 14 where R is response in microseconds and 𝑦 is age group in years. For
what age group is the response equal to 8 microseconds?
101. The profit of a football club after a takeover is modelled by P(t) = 𝑡 3 − 14𝑡 2 + 20𝑡 + 120 , where 𝑡 is the
number of years after the takeover. In which years was the club making a loss?
102. Factorize fully:
a. 𝑓(𝑥) = 𝑥 3 − 4𝑥 2 − 7𝑥 + 10
b. 𝑓(𝑥) = 2𝑥 5 + 6𝑥 4 + 7𝑥 3 + 21𝑥 2 + 5𝑥 + 15
103. Sketch the graph of the following polynomial function.
a. 𝑓(𝑥) = 𝑥 3 − 4𝑥 2 − 7𝑥 + 10
b. 𝑓(𝑥) = 2𝑥 5 + 6𝑥 4 + 7𝑥 3 + 21𝑥 2 + 5𝑥 + 15
c. 𝑓(𝑥) = 2𝑥 5 − 6𝑥 4 + 7𝑥 3 − 21𝑥 2 + 5𝑥 − 15
104. Find all the rational zeros of:
a. 𝑓(𝑥) = 𝑥 3 − 4𝑥 2 − 7𝑥 + 10
b. 𝑓(𝑥) = 2𝑥 5 + 6𝑥 4 + 7𝑥 3 + 21𝑥 2 + 5𝑥 + 15
c. 𝑓(𝑥) = 2𝑥 5 − 6𝑥 4 + 7𝑥 3 − 21𝑥 2 + 5𝑥 − 15
105. Prove that 𝑥 + 1 is a factor of 𝑥 𝑛 + 1 where n is an odd positive integer.
106. Find the two real numbers whose difference is 12 and whose product is the minimum.
107. Find the two real numbers whose sum is 14 and whose product is the maximum.
108. A farmer has 200 meters of fencing material to use to make a rectangular enclosure for sheep as
shown. He will leave an opening of 3 meters for the gate. Find the value of x that will give maximum
area.

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