Mathematics Sample of Question
Grade 12 Advanced
Choose the correct answer:
1- The complete factorization of x4- 81 is :
a) (x – 9)2( x+ 9 )2 b) (x-9)(x+9) c) (x-3)(x+3)(x2+9) d) (x-3)(x+3)(x2-9)
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2- Which of the following is the simplest form of +
a) b) c) d)
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3- The partial fraction decomposition of
a) - b) + c) - d) +
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4- When 8x3 + 2x -1 is divided by 2x + 1 the remainder is :
a) -13 b) 9 c) 3 d) - 3
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5- If (x – 2) is a factor of x 4 + x 2 + k then k =
a ) 4 b) - 4 c) - 20 d) 20
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6- The simplest form of is:
a) b) c) d)
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7- Simplify
a) b) c) d)
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8- Find :
a) b) c) d)
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9- If : then
a) A=2 ; B=2 b) A=2 ; B=-2 c) A=-2 ; B=-2 d) A=-2 ; B=2
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10- When we divide f(x) = 3x3 + 5x2 – 4x – 7 by x + 2 the remainder is:
a) 3 b) 29 c) – 3 d) - 45
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11- If P(x) = x3 – 2x2 – x + 2 , one of the following is a factor of P(x), which one?
a) x + 3 b) x + 2 c) x – 2 d) x
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12- Evaluate:
a) b) c) d)
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13- Simplify: =
a) b) c) d)
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14- If 7= a and 5= b , then =
a) a + b b) a + b + 2 c) a + b -2 d) a – b - 2
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15- Find 25 to 2 decimal places
a) 1.18 b) 1.65 c) 0.55 d) 2.24
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16- If ln(x) = -2 ,then x =
a) b) e2 c) – 2e d)
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17- The graph of the function y = is :
a) always increasing b) always decreasing
c) constant d) cuts y-axis at (0,0)
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18- =
a) b) c) d)
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19– Given then =
a) 0 . 4 b) 0.36 c ) 0.216 d ) 1.8
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20- If then x =
a) 17 b) 9 c) 15 d) 7
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21- The graph of y = e2x has:
a) Horizontal b) Horizontal c) Vertical d) Vertical
asymptote x =2 asymptote y = 0 asymptote x = 0 asymptote x = 2
22- One of the following is the graph of y = e-x:
a- b- c- d-
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23- The domain of the function f(x) = ln (x-2 ) is :
a) ]2,[ b) 2, [ c) ]-, 2[ d) ], -2
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24- The inverse of the function f (x) = ln x is :
a) (x) = b) (x) = c) (x) = d) (x) =
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25- If f(x) = 3x-1 and g (x) = , then f (g(3)) =
a) 2 b) 5 c) -5 d)
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26- If f (x) = 4x - 3 , then (x) =
a) b) c) d) 4(x+3)
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27- If f(x) and g(x) are inverse for each other, then the graph of f (x) is the reflection
of the graph of g (x) about :
a) y = -x b) y = x c) x-axis d) y-axis
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28- The domain of the function y = ln x is :
a) R b) R-{0} c) x ≥ 0 d) x 0
29- If then f(x) is continuous
a) everywhere except at x = 1 b) everywhere except at x = 0
c) everywhere except at x = -2 d) everywhere.
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30- If f(x) = ln x then f-1(2)
a) 0.69 b) 0.3 c) 7.39 d) 2.7
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31- If fog(x) = , x ≥1 then one of the following must be true :
a) g(x) = b) g(x) = x – 1 c) f(x) = (x – 1)2 d ) f(x) = + 1
f(x) = x - 1 f(x) = g(x) = g(x) = x -2
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32 - Which of the following functions have inverse function:
A B C D
33- For the given graph of f(x)
the graph of f-1(x) is :
a- b- c- d-
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34– The given graph of f(x) :
a) Continuous on R. b) Discontinuous on R.
c) Discontinuous at x= -1 d) Discontinuous at x=1.
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35- solve the equation 2= 10 is
a) ln 5 b) ln 10 c) ln 5 d) 2ln 5
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36- The solution of the equation 3 e2x-1 = 3 is :
a) - 0.5 b) 1 c) 0 d) 0.5
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37- The solution of ln2x = 1 is :
a) e b) c)2e d) - e
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38- For , then
a ) 4 b) -2 c) 2 d) – 4
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39- A function whose derivative is given by :
has a local minimum
at x =
a) 1 b) c) 0 d)
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40- If the graph of has a local minimum at x = -1, then the value of k is:
a) 1 b) 4 c) -1 d) -4
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41- If , then the function f has:
a) a local maximum at x = a b) a local maximum at x = 7
c) a local minimum at x = a d) a local minimum at x = 7
42- The slope of y = ex is equal to 1 at the point :
a) (e,0) b)(0,e) c)(1,0) d) (0,1)
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43- One of the following functions its second derivative gives an expression the same
as the original function :
a) f(x) = cos x b) f(x) = sin x c) f(x) = e-x d) f(x) = xe
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44- The derivative function of is:
a) b) c) d)
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45- If y = 2sin π – 5cos θ , then
a) 5sin θ b) 2cosπ - 5sin θ c) -5sin θ d) 2-5sin θ
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46- The third derivative of y = cos
a) b) c) d)
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47- The derivative of y= tan (4θ) is:
a) b) c) d)
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48- If f() = cos – sin, then the slope of the tangent to the curve of f() at = 0 is :
a) 1 b) -1 c) 0 d) 2
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49- If h(x) = f(x) g(x) , and it is known that f(3) = -4, f`(3) = 5, g(3) = 1 , g`(3) = 2
Then h`(3) =
a) -1 b)1 c) 3 d) -3
50-
a) 0 b) c) d)
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51- The graph alongside represents a function f(x):
One of the following is not true
a) f ¢(x) 0 for all x - 2
b) f ¢(x) 0 for all - 2 x 1
c) f ¢(x) = 0 for all - 2 £ x £ 1
d) f ¢(3) 0
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52- The function represented by the graph alongside has :
a) Only one local maximum, one local minimum and
one inflection point.
b) Two local maximum and one inflection point.
c) Three local maximum
d) No local maximum, no local minimum no inflection point
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53- If c is a stationary value and f¢¢(c) 0 ,then :
a) f(x) has a local maximum at x = c. b) f(x) has a local minimum at x = c .
c) The second derivative test fails. d) f(x) has an inflection point at x = c.
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54- The slope of the tangent line to the curve of at x = 0 is
a) 1 b) 5 c) e d) 6
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55- One of the following functions satisfies f ¢ ( x) = f (x ) ,which one ?
a) f (x) = x2 b) f (x) = ln (x) c) f (x) = e- x d) f (x) = ex
56- If g' (2) = 5 and f(x) = -3 g(x) +5 , then
f' (2) =
a)10 b) -10 c) 15 d) -15
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57- If
a) b) c) d)
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58- If y = (x3- 5)4 , then =
a) 108x6 b) 4(x3-5)3 c) 12x2(x3-5)3 d) 81x3
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59- One of the following functions has the derivative function
a) b) c) d)
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60- One of the following is equal to the slope of the tangent to y2-x2 = 1 at (1,)
a) b) - c) d) -
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61- If y is a function of x such that > 0 for all x and < 0 for all x , which of the
following could be part of the graph of y = f(x)
a b c d
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62- If y = ln (x ) then
a) b) c) d) ex
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63- If y = 2sin x + cos 3x , then =
a) 2 cos x b) 2sin x + 3cos x c) - 2cos x + sin3 x d) 2cos x - 3sin3 x
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64- If y = tan 5x , then =
a) 5 cot 5x b) 5sec2 5x c) sec2 5x d)
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65- If f ¢ ( 1) = 3 and g ¢ ( 1) = 5 then (f + g) ¢ ( 1) =
a) 8 b) 15 c) 3 d) 5
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66- If y = x2.lnx then =
a) 2 b) 2x.lnx - x c) 2x.lnx + x d) x
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67- If y = f(x). g (x) then y ¢ =
a) f ¢ (x). g ¢ (x) b) f ¢ (x). g (x) - f(x). g ¢ (x)
c) d) f ¢ (x). g (x) + f(x). g ¢ (x)
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68- If a flu is spreading at the rate of , where P(t) is the total number of
students infected t days after the flu first started to spread, then one of the
following is the initial number of students infected.
a) 1 b) 8 c) 7 d) 3
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69- If particle’s position is given by
s(t) = 3t2 + 2t – 4 , then the acceleration at time t = 2
a) 0 b) 6 c) 12 d) 14
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70-
a) b) c) d)
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71-
a) b) c) d)
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72-
a) f ¢ ( g(x)) .g¢ (x) b) f ¢ ( g(x)) c) f ¢ ( g¢ (x)) .g¢ (x) d) f ( g¢ (x)) .g¢ (x)
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73-
a) b) c) d)
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74- If x2 + y2 = 5 then =
a) b) c ) –x d) 0
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75- If the slope of the tangent line to the graph of y= eax at x = 0 is 3 ,
then the constant a =
a) 1 b) 3 c) d) – 1
76- A particle moves along a straight line. Its position function, in cm, is S(t) = t3 – 3t -1
Where the time is in seconds. The initial velocity for the particle is :
a) 1 cm/s to the left from the origin
b) 1 cm/s to the right from the origin
c) 3 cm/s to the left from the origin
d) 3 cm/s to the right from the origin
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77- The antiderivative of g(x) = 3x2 + 5 is :
a) 6x + 5 b) 6x c) x3 + c d) x3 + 5x + c
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78- =
a) ln│x│+c b) + c c) 2+ c d) + c
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79- If = + c then f(x) =
a) +c b) c) + c d) 2( )
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80- =
a) cos 2x +c b) cos 2x +c c) 2cos 2x+c d) - 2 cos 2x+c
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81- If then =
a ) 0 b) 10 c) 15 d) -10
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82- If , then k =
a) - b) c) d)
83- The area of the region bounded by y = , the x-axis from x = 1 to x = 2 is :
a) - ln 2 b) ln 2 c) 0.5 d) 2
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84- If the area of the given region is 8 unit2 then one of the following must be true:
a) b) c) d)
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85- A particle moves in a straight line with acceleration a(t) = 2 - 6t cm/s2.
If v(1) = 2 cm/s , Then its velocity when t = 3 seconds is :
a) 20 cm/s b) -20 cm/s c ) -18 cm/s d ) -24 cm/s
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86- particle moves with velocity function v(t) = cos( cm/s . The total distance
travelled from t= 0 to t = π second is :
a) 0 cm b) 2 cm c) 1 cm d) -1cm
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87- =
a) b) c) d)
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88-
a) b) c) d)
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89- =
a) b) c) d)
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90- If then
a) ln│x2 -3x│ b) ln│x2 -3x│+c c) ln│x│+ ln│x-3│+c d) ln│x│+ 2 ln│x-3│+c
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91-
a) 3 x2 b) x3 + c c) 6 x d) 3x2 + c
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92-
a) b)x4 + x2 + c c) x5 + c d) x4 + 2 ln∣x∣+ c
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93- ∫ e2x dx =