P3 Quiz 1 Welcome to your P3 Quiz 1 Question 1Express the following as a single fraction in its simplest form. (2(3x+2))/(9x^2-4) - 2/(3x+1) 6/ (9(x)^2-3x-2) (12x+6)/(9(x)^2-3x-2) 6/(9(x)^2+3x-2) (12x-6)/(9(x)^2-3x-2) Question 2 a)Express 4cosec^2〖2θ-〗 cosec^2θ in terms of sin θ and cos θ 2/sinθcosθ - 1/((sin)^2 θ) 4/(2sinθcosθ)^2 - 1/((sin)^2 θ) 4/2sinθcosθ - 1/((sin)^2 θ) 4/(sinθcosθ)^2 - 1/((sin)^2 θ) Question 2 b)Express 4cosec^2〖2θ-〗 cosec^2θ in terms of sec θ (sec)^2 θ (sec)^2 2θ 2(sec)^2 θ 1/((sec)^2 θ) Question 2 c)Hence or otherwise solve, for 0 < θ<π , giving your answers in terms of π 4 (cosec)^2(2θ) - (cosec)^2 θ=4 θ=π/6 & -π/6 θ=π/4 & 3π/4 θ=π/4 & -π/4 θ=π/3 & 2π/3 Question 3 a)Find algebraically the exact solutions to the equations: ln (4 – 2x) + ln (9 – 3x) = 2ln (x + 1), –1 < x < 2 x= 7/5 x= (-7)/5 x= 5 x= -5 Question 3 b)Find algebraically the exact solutions to the equations: (2)^x (e)^(3x+1)=10Give your answer to (b) in the form (a+lnb)/(c+lnd)where a, b, c and d are integers. (-1+ln5)/(1.5+ln1) (-1-ln10)/(3-ln2) (-1+ln10)/(3+ln2) (-1+ln10)/(4+ln2) Question 4 a) Figure 1 shows a sketch of part of the graph y=f(x), where F(x) = 2|3 – x| + 5, x≥ 0.Figure 2 shows a sketch of part of the graph y=g(x), where G(x) = (x+9)/(2x+3) , x≥ 0.(a)Find the value of fg(1) 6/7 2 7 -7 Question 4 b)(b) State the range of ( g ) g is greater than 0 & less than or equal 3 g is greater than 0.5 & less than or equal 3 g is greater than 0 & less than 3 g is greater than or equal 0 & less than or equal 3 Question 4 c)Find g^(-1) (x) and its domain (9-3x)/(2x-1) 0.5 (9+x)/(2x-1) 2 (2x+3)/(x+9) 0 (9+3x)/(2x+1) 1/3 Question 4 d)Given that the equation f(x)= k, where k is a constant, has exactly two roots, state the range of possible values of k. K is greater than 9 & less than or equal 11 K is greater than 1 & less than or equal 11 K is greater than 5 & less than or equal 11 K is greater than 10 & less than or equal 11 Question 5F(x) = 2x/(x^2+3) ,x ϵ R Find the set of values of x for which f’(x) >0 0 -√3 -√6 -3 Question 6 a) i.Given that a and b are constants and that 0 < a < b (a) State if the following graph is true or false , and if false draw the correct one. (i) y = | 2x + a | True False Question 6 a) ii.(a) State if the following is true or false , and if false draw the correct graph. (ii) y = | 2x + a | - b True False Question 6 b)Solve for x, the equation | 2x + a | - b = 1/3 x , giving any answers in terms of a and b x=3/5(b-a) & (-3)/7(a+b) x=7/3(b-a) & (-5)/3(a+b) x=(-3)/5(b-a) & (-3)/7(a+b) x=(-7)/3(b-a) & 5/3(a+b) Question 7 a)F(x) = sec x + 3x -2 , (-π)/2 < x < π/2(a) Select the correct interval in which there is a root in f(x)=0 [-0.2, -0.4] [0.2, -0.4] [0.2, 0.4] [0.2, -0.2] Question 7 b)Express the equation F(x) in its simplest form using f(x)=0 x= 2/3 - 1/(3 cosx ) x= 2/3 + 1/(3 cosx ) x= 2/3 - 1/(3 sinx ) x= 2/3 + 1/(3 sinx ) Question 7 c)The solution of f(x)=0 is α , where α=0.3 to 1 decimal place.Starting with x˳=0.3, use your obtained iterative formula from part (b) to calculate the values of x1 , x2 ,and x3 giving your answers to 4 decimal places. (in radians) x1=0.3177, x2= 0.3158, x3= 0.5160 x1=-0.3177, x2=- 0.3158, x3= 0.5160 x1=0.3177, x2= 0.3158, x3= 0.3160 x1=0.31, x2= 0.39, x3= 0.4 Question 7 d)State the value of α correct to 3 decimal places 0.318 0.316 0.516 0.322 Share: Sara Magdy Ali Next post P1 Quiz 1 You may also like Annual dish parties Marathon Important Classes
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