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Module 5 Paper1 Higher Non Calculator Specimen Paper (non-coursework) Mock exam 2009 1hr 15mins PowerPoint PPT Presentation


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Module 5 Paper1 Higher Non Calculator Specimen Paper (non-coursework) Mock exam 2009 1hr 15mins. 1. In the diagram AB is parallel to CD. (a) State the value of x. Give a reason for your answer. Answer:- 130 degrees Reason:- Corresponding angle. 2 Marks.

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Module 5 Paper1 Higher Non Calculator Specimen Paper (non-coursework) Mock exam 2009 1hr 15mins

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Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

Module 5

Paper1

Higher

Non Calculator

Specimen Paper (non-coursework)

Mock exam 2009

1hr 15mins


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

1. In the diagram AB is parallel to CD.

(a) State the value of x. Give a reason for your answer.

Answer:- 130 degrees

Reason:- Corresponding angle

2 Marks

(b) State the value of y. Give a reason for your answer.

Answer:- 130 degrees

Reason:- Alternate angle or vertically opposite

2 Marks

( c) Find the value of z

Answer:- 50 degrees

1 Mark


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

2. Javed says that the triangle and parallelogram shown have the same area.

Is he correct?

You MUST show your working.

Triangle area = ½ x 4 x 12

= 24cm2

Parallelogram area = 8 x 3

= 24cm2

He is correct

4 Marks


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

3 (a) The nth term of a sequence is 5n-2

Write down the first three terms of the sequence

5 (1) – 2 = 3

5 (2) – 2 = 8

5 (3) – 2 = 13

Answer:- 3, 8, 13

2 Marks

(b) Matchsticks are used to make this pattern of triangles

Find an expression for the number of matchsticks needed to make Pattern n

Answer:- 2n + 1

2 Marks

+2

How many complete triangles can be made with 40 matchsticks?

2n + 1 = 40

2n = 39

n = 19.5

19 complete triangles

n 2n + 1

2 Marks


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

4. (a) Complete the table of values for y = x2 + x

Needs to be a smooth curve

2

2 Marks

6

(b) Draw the graph of y = x2 + x for values of x from -4 to +3

x

x

(c ) Write down the values of x where the line y = 5 crosses the graph

Y = 5

x

Answer : 1.8 and -2.8

x

2 Marks

(d) What happens top the value of y between x=-1 and x=0?

x

x

2 Marks

x

x

Answer: It is negative

1 Mark


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

Simplify

(a) 2(q + 3) + 3(q – 4)

2q + 6 + 3q - 12

2 Marks

= 5q - 6

(b) x2 X x5

Answer: x7

1 Mark

(c)

1 Mark

Answer: y3


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

6.

(a) Describe fully the single transformation that takes shape A onto shape B

Reflection in the line y = 2

2 Marks

(b) Triangle C is rotated onto triangle D.

(i) Write down the angle of rotation.

Answer 180º

(ii) Write down the coordinates of the centre of rotation

Answer ( 3, 0 )

2 Marks


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

6 (c)

Draw the new position of shape L

2 Marks


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

7. (a) In triangle ABC, angle B = 90º, AB = 9cm and AC = 15cm

Calculate the length of BC

152 = 92 + BC2

225 – 81 = BC2

BC2 = 144

BC =√ (144)

3 Marks

BC = 12 cm


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

7(b) In triangle DEF , angle E = 90º, DF = 10cm and angle F = 70º

hypotenuse

opposite

adjacent

Use the table of data to work out the length of EF

Given Hypotenuse

Need to find Adjacent

Use COSINE

Cos 70º =

Cos 70º=

10 x 0.342 = EF

3 Marks

EF = 3.42 cm


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

8(a) Expand and simplify (x + 3)(x – 4)

x2 + 3x - 4x - 12

x2 - x - 12

2 Marks

(b) Factorise fully 6a2 – 9ab

3(2)aa - 3(3)ab

3a(2a – 3b)

2 Marks

(c) Factorise x2 – 7x + 10

Hence solve x2 - 7x + 10 = 0

( x - 2 ) ( x - 5 )

Either (x – 2) = 0

Or (x - 5) = 0

3 Marks

x = 2 and x = 5


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

The line AB has equation 2x – 5y = 10

Show that the gradient of AB is

Need to write it in the form y=mx+c

Rearrange: 2x – 10 = 5y

÷ each side by 5

Gradient m is

2 Marks

9(b) A second line PQ has equation 2y = 6 - 5x.

Jade says that the line PQ is parallel to the line AB. Is she correct? You MUST show your working.

Divide both sides by 2

Jade is wrong

Gradient is

y = 3 -

2 Marks


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

10. The diagram shows two containers. One container is a hemisphere of radius 6cm. The other container is a cone of radius 5cm and height 18cm.

(a) Show that the volume of the hemisphere is 144π

Volume of a sphere is π r3

Which container has the larger volume?

Volume of a hemisphere is π r3

Volume of a cone is πr2h

V = π x 5 x 5 x 18

V = π x 6 x 6 x 6

V = 144π

V = 150π

The cone has the larger volume

5 Marks


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

11. Prove that (n+3)2 – (n-2)2 = 5(2n+1)

Multiply out

(n + 3)(n + 3) - (n – 2)(n – 2)

n2 + 3n + 3n + 9 - (n2 - 2n - 2n + 4)

n2 + 6n + 9 – n2 + 4n - 4

10n + 5

Factorise

5( 2n + 1) Hence shown

3 Marks


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

12. OABC is a parallelogram.

OA = p and OC = q

T is a point outside the parallelogram such that AT = 2p + 3q

(a) Find in terms of p and q, expressions for the following vectors. Give your answer in its simplest form.

OB = OA + AB

2 Marks

= p + q

Explain what your answers to part (a) tell you

BT = BA + AT

= -q + 2p + 3q

2 Marks

They are in a straight line and the length of BT is twice the length of OB

= 2q + 2p

2 Marks


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

13. The diagram shows the graph of y = cos x for 0º ≤ x ≤ 360º

One solution of the equation cos x = 0.809 is x = 36º

Work out the other solution in this range.

Other solution is 360 – 36 = 324º

Write down the number of solutions in the same range for each equation.

(i) 2cos x = -0.6

(ii)cos 2x = -0.6

cos x = -0.3

4 solutions

3 Marks

2 solutions


Module 5 paper1 higher non calculator specimen paper non coursework mock exam 2009 1hr 15mins

Find the values of a and b such that

x2 – 8x + 21 = (x – a) 2 + b

x2 – 8x + 21

= ( x - 4 )2 + 5

a = 4 and b = 5

2 Marks

Hence or otherwise write down

(i) The minimum value of x2 - 8x + 21

Minimum value is the coordinate (4,5)

(ii) The equation of the line of symmetry of x2 - 8x + 21

Answer : x = 4

2 Marks


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