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OLEVEL PURE MATHEMATICS

MOCK TEST-1

TOTAL MARKS: 100

TIME: 2HOURS

ALL QUESTIONS ARE OF EQUAL CREDITS

SECTION A

1. X2 + 2x 8=(X+1)2+k(a) Find the value of constant(b) Deduce the minimum value of X2 + 2x 82. Find the set of values of the constant p for which the X 2 + px 2p = 3x 6 has real roots.3.Given that and are the roots of the equation X2 + 5x 4 = 0, form an equation with integer

coefficients whose roots are 2 and

2.

4.The equation X2 + 2x 8 = 0 has roots and . Without solving the equation,(a) Find the value of 2+ 2.(b) Hence show that 2+2= 6

(c) Hence or otherwise , form a quadratic equation with integer coefficients which has roots (2+

)and (

2+

)

5. Given that the equation X2 - 2x 3 = p ,where p is a constant, has a repeated root, find thevalue of p.

6. Given that p is a positive integer , find the smallest value of p for which the equation X2 + px +3= 0 has real roots.

7. Find out the minimum value of 5X2 + 7x 3 and the value of x at which it occurs.8. Given that x1 and x2 satisfy the equation (lnx)2 - 2lnx 5 = 0

(a) Show that lnx1 + lnx2 = 2(b) Deduce the value of x1x2 .

9. f(x) = 5X2 - 15x +7. The equation f(x)= 0 has roots and .(a) Without solving the equation , write down the value of + and the value of .(b) The axis of symmetry of the curve with equatin y=f(x) has equation x=k. use your answer to

part (a) to find the value of k.(c) Hence find the minimum value of f(x).

10.The equation X2 - 5x- 3 =0 has roots and . Calculate(a) 2+ 2(b)( -)2(c) 3+ 3(d) 3- 3 (e) Find the value of 3.

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SECTION B

1. Solve the equation iog3(5x+12) + log3x = 2.2. Solve the equation: 4xlog3x 3log3x +16xlog910 12log9 10 = 03. Evaluate log3 7 + log3 9 log3 21.4. Solve the simultaneous equations 3log2x + 4log3y = 10 , log2x log3y = 15. Find the exact value of (a) log7(

) + log7(

)(b)(125)

(

)

6. Find the exact solution of the equation

- = 4.

7. Solve 8= 16.8. Solve the equation log53 + log56 + log59 +log512 +log515 = 1 + log5x + log5x29. Solve the simultaneous equations 8log9x - 9log27y = 8 , log3x + 8log81y = 1310. The temperature, C, of a hot drink t minutes( t0) after it has been made is given by

= 20 + 40e-0.05t

(a)Find ,in C, the temperature of the drink at the instant at which it is made.(b)Calculate,C to 3 significant figures, the temperature of the drink 10 minutes after

it was made.

(c) Calculate, to the nearest whole number, the value of t when the temperature ofthe drink is 40C

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