Class Test (Chapter 1 to 3)

Q1) Solve the simultaneous equations

[5]

Q2) a)Express (1+√3 )−(13

4+√3 )2

in the form of a+b√3 , where a and b are integers to be determined. [3]

b) Given that

9n+2−32 n+2

25=2a3b

, where a and b are integers, find the value of a and express b in terms of n. [2]

Q3) Solve the following equations

a)

35 x

(27x )x=1

9[4]

b) 22 y+1+32=16 ( 2y ) [4]

Q4) Find the range of values of m such that the line y = mx + 3 does not meet the circle with equation x2 + y2 – 2x – 1 = 0 [6]

Q5) The roots of the equation x2

- ( q – 5 )x =

q2 are α and α + 5. Find the

possible values of q. [5]

Q6) The roots of the quadratic equation 3 + 2x−x2=0 are α andβ

a. State the value of α+β and of αβ . [2]

b. Find the quadratic equation in x whose roots are αβ2

and α2 β [4]

Q7) (a) Find the range of values of x for (4 x−5)2≥49 . [2]

(b) Find the range of values of m for which the function

4 x+4m+( x−m)2is positive for all real values of x. [4]

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Q8) The cubic polynomial f(x) is such that the coefficient of x3 is 3 and the roots of f ( x )=0 are –1, 0 and k. It is given that f(x) has a remainder of 30 when divided by x – 2. (i) Find the value of k. [4](ii) Hence, find the remainder when f(x) is divided by x – 3k. [2]

Q9) (a) Factorise f ( x )=2 x3+3 x2−8x+3 completely. [4]

(b) Solve the equation 2 x3+3 x2=8x−3 . [2]

(c) Hence, find the real values of y if 2(2 y)3+3(2y )2−8(2 y)+3=0 . [3]

Q10) Express

x3−22x3−x2

in partial fractions. [4]

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