Dunearn Prelim 2009 Am P1

Class

Number

Name : Name of your A.Maths Teacher: Mr. ______________________________ DUNEARN SECONDARY SCHOOL DUNEARN SECONDARY SCHOOL DUNEARN SECONDARY SCHOOL DUNEARN SECONDARY SCHOOL

DUNEARN SECONDARY SCHOOL DUNEARN SECONDARY SCHOOL DUNEARN SECONDARY SCHOOL DUNEARN SECONDARY SCHOOL

DUNEARN SECONDARY SCHOOL DUNEARN SECONDARY SCHOOL DUNEARN SECONDARY SCHOOL DUNEARN SECONDARY SCHOOL

DUNEARN SECONDARY SCHOOL DUNEARN SECONDARY SCHOOL DUNEARN SECONDARY SCHOOL DUNEARN SECONDARY SCHOOL

DUNEARN SECONDARY SCHOOL DUNEARN SECONDARY SCHOOL DUNEARN SECONDARY SCHOOL DUNEARN SECONDARY SCHOOL

DUNEARN SECONDARY SCHOOL Prelim Examination 2009 Add. Mathematics (4038/01) Paper 1 Secondary 4 Express & 5 Ruby Friday, 4 Sep 2009

0800 - 1000hrs

2 hours

INSTRUCTIONS TO CANDIDATES Write your name, class and register number in the spaces at the top of this page. Answer all questions. Write your answers on the writing paper provided. All working must be shown. Omission of essential working will result in loss of marks. Do not use any highlighters, correction fluid or correction tape for the paper.

INFORMATION FOR CANDIDATES Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 80. The use of an electronic calculator is expected where appropriate. You are reminded of the need for clear presentation in your answers. PARENT’S SIGNATURE

FOR EXAMINER'S USE

80 Setter: Mr Venkat

This question paper consists of 4 printed pages, including this cover page

Page 1 of 4

Mathematical Formulae 1.

ALGEBRA

Quadratic Equation 2

For the equation ax  bx  c  0

 b  b 2  4ac x 2a Binomial expansion  n n n (a  b) n  a n    a n1b   a n 2 b 2  ........   a n r b r  ...  b n , 1  2 r n n! n(n  1)........(n  r  1) where n is a positive integer and     r!  r  r!(n  r )! 2. TRIGONOMETRY Identities 2 sin A  cos 2 A  1 sec 2 A  1  tan 2 A cos ec 2 A  1  cot 2 A sin( A  B )  sin A cos B  cos A sin B cos( A  B )  cos A cos B  sin A sin B tan A  tan B 1  tan A tan B sin 2 A  2 sin A cos A

tan( A  B ) 

cos 2 A  cos 2 A  sin 2 A  2 cos 2 A  1  1  2 sin 2 A 2 tan A 1  tan 2 A 1 1 sin A  sin B  2 sin  A  B  cos  A  B  2 2 1 1 sin A  sin B  2 cos  A  B sin  A  B  2 2 1 1 cos A  cos B  2 cos  A  B  cos  A  B  2 2 1 1 cos A  cos B  2 sin  A  B sin  A  B  2 2 a b c   sin A sin B sin C 2 a  b 2  c 2  2bc cos A tan 2 A 

Formulae for ABC



1 ab sin C 2

Page 2 of 4

Answer all the questions 1.

(a)

(b)

2

Max.Mark: 80

Using the matrix method solve the simultaneous equations 5x + 2y = 3 2x = 5 + 3y Using the substitution y = 3x, find the values of x such that 9x – 10(3x+1) + 81 = 0

[4]

[4]

(a)

Find x if lg(2x -1) = 1 + lgx – lg(x +3)

[4]

(b)

2 5 The curve y = abx passes through the points (0,5) and  ,  . Find the 3 4 positive value of a and of b.

[4]

3.

Answer the whole of this question on a sheet of graph paper. The table below shows the experimental values of two variables x and y.

x y

1 1.19

2 0.87

3 0.69

4 0.57

5 0.48

m xn where m and n are unknown constants. Draw a graph of y against xy and use the graph to estimate

It is known that x and y are related by an equation of the form y 

4.

(a) (b)

5.

(a) (b)

(i)

the value of m and of n,

(ii)

the value of x when y  0.75 .

[8]

The expressions x3 + ax2 – x + b and x3 + bx2 – 5x + 3a have a common factor (x + 2). Find the value of a and of b. Given that the first three terms, in ascending powers of x, in the binomial expansion of (3 + ax)5 are 243 – 810x + bx2, find the value of a and of b. Calculate the coordinates of the points on the curve y = 2x3 - 3x2 – 9x + 1 at which the tangents to the curve are parallel to y – 3x = 4. Differentiate the following with respect to x. (i) tan3(3x – 1) (ii) (x2 – 1) cos 2x

[5] [5]

[5] [2] [3]

Page 3 of 4

6.

(a)

Given that the roots of the equation 2x2 -5x - 6 = 0 are  and , (i) find the value of 2 + 2.

[3]

2 2 and   2 Find the range values of k for which 2x + 4x + 3 > k, for all real values of x. (ii) form an equation whose roots are

(b)

7.

8.

(a) (b)

(a)

(b)

[4] [4]

Solve |2x – 7| = |x – 3| 4  2x Express in partial fractions. ( x  1)( x 2  7) 4  2x Hence, find the partial fractions of ( x  1)( x 2  7)

[4] [5] [2]

Find all the angles which satisfy each of the following equations. (i) 2(cos x + 5 sin x ) = 3 sin x, where 0 º  x  360 º (ii) 6 sin x = 7 + cos 2x, where 0 º  x  360 º (iii) cos x + cos 3x = 0, where 0 º  x  180 º

[3] [4] [4]

Given that x is in radians and that x > 12, find the least value of x such that 5 tan (3x + 2) = 12

[3]

END OF PAPER

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