FBQ1: Given that \(f(x)=2x+1\), then \(f(3)\) is ____________________
Answer: *7*
FBQ2: ____________________ is the value of f(-5) in the function \(f(x)=x^{2}+2x-3\).
Answer: *12*
FBQ3: The value of \(\frac{f(a+h)-f(a)}{h}\) in the function \(f(x)=x^{2}-2x+7\) is ____________________
Answer: *2a+h-2*
FBQ4: Let f(z-1) = z2- 2z +13, then f(-1) is ____________________
Answer: *13*
FBQ5: Let h(x) = x2+ x, then h(x+1) – h(x) is ____________________
Answer: *2x+1*
FBQ6: Let f(t-1) = t2+ 2t, then f(2) is ____________________
Answer: *15*
FBQ7: is called the ____________________ of A
Answer: *range*
FBQ8: ____________________ of H
Answer: *domain*
FBQ9: is ____________________
Answer: *½*
FBQ10: The rate at which is changing with respect to x when x = 1 is ____________________
Answer: *½*
FBQ11: The position at time t of an object moving along a line is given by s(t) = t3 -6t2 + 9t + 5. The acceleration of the object at t = 1 is ____________________
Answer: *-6*
FBQ12: The slope of the secant line through the point (1, f(1)) and (4, f(4)) on the graph of y=f(x) is ____________________
Answer: *15*
FBQ13: Suppose is ____________________
Answer: *-7*
FBQ14: An object moves along the y-axis (marked in metres) so that its position at the time (in seconds) is \(f(x)=x^{3}-6x^{2}+9x\). The velocity at \(x=2\) is ____________________ m/s
Answer: *-3*
FBQ15: A function f(x) is called an even function if ____________________
Answer: *f(-x)=f(x)*
FBQ16: The evaluation of is ____________________
Answer: *4*
FBQ17: The evaluation of is ____________________
Answer: *4/3*
FBQ18: F The value of x at the maximum point of the curve is ____________________
Answer: *-1*
FBQ19: ____________________
Answer: *-7*
FBQ20: Suppose the total cost in Naira of manufacturing q units of a certain commodity is given by the function C(q) = q3 - 30q2 + 500q + 200. The cost of manufacturing 5 units of the commodity is ____________________
Answer: *N2,075*
FBQ21: The position at time t of an object moving along a line is given by s(t) = t3 - t2 + 9t + 5. The acceleration of the object at t = 4 is ____________________
Answer: *22*
FBQ22: The position at time t of an object moving along a line is given by s(t) =2 t3 - t2 + 3t -15. The velocity of the object at t =2 is ____________________
Answer: *23*
FBQ23: Differentiate P(x) = (x – 1)(3x – 2) with respect to x.
Answer: *6x-5*
FBQ24: Suppose assigns to each negative integer -2 and to each positive integer 2.Then, the domain of is ____________________
Answer: *{…-2, -1, 1, 2, …}*
FBQ25: The exact area of the piece of land which is bounded by the y-axis on the west, the x-axis in the south, the lake described by the function $$f(x)=100+(\frac{x}{100})^2$$ in the north and the line x=1000 in the east is ____________________
Answer: *133, 333.33*
FBQ26: The evaluation of is ____________________
Answer: *8*
FBQ27: The evaluation of is ____________________
Answer: *-3*
FBQ28: Suppose a certain car supplies a constant deceleration of A meters per second per second. If it is traveling at 90 kilometers per hour (25meters per second) when the brakes are applied, its stopping distance is 50 meters. The value of A is ____________________
Answer: *6.25*
FBQ29: Suppose a certain car supplies a constant deceleration of A meters per second per second. If it is traveling at 90 kilometers per hour (25meters per second) when the brakes are applied, its stopping distance is 50 meters. ____________________ metres would the stopping distance have been if the car had been traveling at only 54 kilometers per hour when the brakes wereapplied
Answer: *42*
FBQ30: The evaluation of is ____________________
Answer: *0*
FBQ31: After its brakes are applied, a certain car decelerates at the constantrate of 6 meters per second per second. If the car is traveling at 108kilometres per hour when the brakes are applied, ____________________ metres is the distance travelled before coming to a complete stop? (Note: 108 kmph is the same as 30 mps.)
Answer: *75*
FBQ32: Suppose is defined by , then is --------------
Answer: *62*
FBQ33: The evaluation of \(\int_{2}^{5} (2+2t+3t^{2})dt\) is ____________________
Answer: *144*
FBQ34: The evaluation of definite integral $$\int_{0}^{6} x^{2} (x-1) dx$$ is ____________________
Answer: *252*
FBQ35: The maximum value of the function is ____________________
Answer: *9*
FBQ36: The evaluation of is ____________________
Answer: *-3/4*
FBQ37: A is the region bounded by the curve $$y=4x^{3}$$, the line x=2 and the x-axis. The area under the region is ____________________
Answer: *16*
FBQ38: The area of the region B is ____________________ , where B is the region bounded by the curves \(y=x^{2}-2x\) and \(y=1-x^{2}\) between x=-2 and x=1
Answer: *12*
FBQ39: Let \(f(x)=x^{2}-5x+5\), the value \(\frac{(x+\Delta x)-f(x)}{\Delta x}\) as \(\Delta x\) approaches zero is ____________________
Answer: *2x-4*
FBQ40: The value of $$f(x)=x^{2}-5x+1$$ when x=4 is ____________________
Answer: *-3*
FBQ41: If $$f(x)=x^{2}-2x+7$$, then f(-5) is ____________________
Answer: *42*
FBQ42: Given \(f(x)=2x-4\) and \(g(x)=x^{2}+3\), the composite functions \(f(g(x))\)is ____________________ when x=2
Answer: *6*
FBQ43: Let functions \(f(x)=2x-4\) and \(g(x)=x^{2}+3\), the composite functions \(g(f(x))\) is ____________________ when \(x=1\)
Answer: *5*
FBQ44: The inverse function of $$f(x)=\sqrt (2x-3)$$ is ____________________ when x=1
Answer: *2*
FBQ45: The evaluation of $$\lim {x\rightarrow 1} \frac{x^{2}-1}{x-1}$$ is ____________________
Answer: *2*
FBQ46: The differentiation of y= 2 sin 3x is ____________________
Answer: *10 cos 5t*
FBQ47: The differential coefficient of y=7 sin 2x-3 cosx is ____________________
Answer: *14 cos 2x+ 12 sin 4x*
FBQ48: The gradient of the curve $$f(x)=x^{2}$$ at x=2 is ____________________
Answer: *4*
FBQ49: An alternating voltage is given by: v=100 sin 200t volts, where t is the time in seconds. The rate of change of voltage at t =0.005 s is ____________________ volts per second
Answer: *10806*
FBQ50: An alternating voltage is given by: v=100 sin 200t volts, where t is the time in seconds. The rate of change of voltage at t =0.01 s is ____________________ volts per second
Answer: *-8323*
Multiple Choice Questions (MCQs):
MCQ1: If f(x) = x2- 4x+ 3, evaluate f(x+1)
Answer: x2- 2x
MCQ2: Let f(x-3) = x2- 2x+ 7, find f(-1)
Answer: x2+ 7x - 7
MCQ3: Let G(x) = x2+ x - 5, find G(x+2) – G(-x)
Answer: 6x +6
MCQ4: Let H(x) = x2+ 4x - 5, determine H(x+d) – H(x).
Answer: x2+2xd+4d
MCQ5: Let f(x-1) = x2+ 5x- 1, find f(4) +f(-2).
Answer: 28
MCQ6: Let f(x) = 2x – 1 and g(x) =x2- 4, find f (g(x)).
Answer: 2x2 – 9
MCQ7: Let f(x) = 2x – 1 and g(x) =x2- 4, find g (f(x)).
Answer: x2+ 6x +2
MCQ8: Let h(x) = (x+2)sin (x+1) and p(x) =3x-5, find p (h(x)).
Answer: (x+6) sin (3x+1)-5
MCQ9: Let h(x) = (x+2 )sin (x+1) and p(x) =3x-5, find h(p(x)).
Answer: (3x-3)sin (3x-4)
MCQ10: Find the inverse of f(x) = 3x +5.
Answer: (5 x-3)/5
MCQ11: Which of the following terms best describe a mapping?
Answer: a transformation
MCQ12: Let be a mapping. The set is called
Answer: range of P
MCQ13:
Answer: domain of H
MCQ14:
Answer: Function of H
MCQ15: find the image set of f .
Answer:
MCQ16: find the range of p.
Answer:
MCQ17: Let be a mapping defined by find the range of
Answer:
MCQ18:
Answer: 4
MCQ19:
Answer: ½
MCQ20: Suppose the total cost in Naira of manufacturing q units of a certain commodity is given by the function C(q) = q3 - 30q2 + 500q + 200. The cost of manufacturing 10 units of the commodity is ..........
Answer: N3,200
MCQ21: Let y = x3 be a curve. The equation of the tangent line at the point where x = -1 is y =
Answer: 3x + 2
MCQ22:
Answer:
MCQ23: The position at time t of an object moving along a line is given by s(t) = t3 - 6t2 + 9t + 5. The velocity of the object at t = 1 is
Answer: 0
MCQ24:
Answer:
MCQ25: Differentiate the function e-2x with respect to x.
Answer: -2e-2x
MCQ26: Let y = ln (6x – 4). dy/dx is
Answer:
MCQ27: If f(x) = 2x3 – 4x. Then f(x) is
Answer: odd
MCQ28:
Answer: 17
MCQ29: Let . Suppose f assigns to each negative integer -3 and to each positive integer 3. What is the co-domain of f ?
Answer:
MCQ30: A A function f(x) is called an even function if
Answer: f(-x) = f(x)
MCQ31:
Answer:
MCQ32:
Answer: -1/2
MCQ33:
Answer:
MCQ34:
Answer:
MCQ35:
Answer:
MCQ36:
Answer:
MCQ37: Find if x and y are given by the parametric equations, y = cos4t, x = sin3t
Answer:
MCQ38:
Answer:
MCQ39: find if y = sin2x + 3cos5x
Answer: -4sin2x - 75cos5x
MCQ40: find the value of x at the minimum point of the curve
Answer: 1
MCQ41: Integrate 1/1-x2 with respect to x.
Answer: sin-1x
MCQ42: Find ∫4x3x2+1 dx
Answer: 86x2+13/227
MCQ43: Evaluate ∫013xex2 dx.
Answer: 32(e-1)
MCQ44: Integrate (3x2+2x-1)/x3 with respect to x
Answer: 3lnx-2x+12x2
MCQ45: Obtain ∫(2x+11)10dx
Answer: 2x+51122
MCQ46: Determine: ∫dxx+1(x+2)
Answer: 86lnx6+11
MCQ47: Determine: ∫dxx+1(x+2)
Answer: lnx+1x+2
MCQ48:
Answer: 12π
MCQ49: Evaluate ∫x+1x dx
Answer: 2x13x+1
MCQ50: Integrate sin3xcosx with respect to x
Answer: 14sin4x