1

2008 practice (June 2006) 43005 1HQuestion 1 equivalent fractions

Question 2 single power of 2

Question 3 bearings from a map

Question 4 perimeter; equilateral triangle in regular hexagon

Question 5 area of triangles

Question 6 volume from plan and elevations

Question 7 multiply out and simplify

Question 8 nth term of a sequence

Question 9 transformations; rotation; translation; vector

Question 10 algebra; expand; factorise; change the subject

Question 11 show some algebra

Question 12 simultaneous equations

Question 13 similar triangles; find lengths of sides

Question 14 vectors

Question 15 prove triangles congruent

Question 16 algebraic identity; simplify algebraic fraction

Question 17 draw graph of exponential function

Grade boundaries

2

2008 practice (June 2006) 43005 1H

1720

925

85100

35 25

40

1 Here is a list of fractions.

Which two fractions in the list are equivalent?

You must show your working

Simplify any which will …

85100

= 5 x 175 x 20

= 1720

2540

=5 x 55 x 8

= 58

Answer 1720

and 85100

3 marks

3

2008 practice (June 2006) 43005 1H

2 Write as a single power of 2

(a) 22 x 23

(b) 28 ÷ 22

… when multiplying power numbers add the indices

Answer = 25 1 mark

1 mark

… when dividing power numbers subtract the

indices

Answer = 26

4

2008 practice (June 2006) 43005 1H

3. The diagram shows the map of a bay and four ports P,Q , R and X.

(a)A ship sails due west to X from P.

Write down the three-figure bearing of X from P.

1 mark

bay

land land

P

North

North

North

R

X

Q

2700

5

2008 practice (June 2006) 43005 1H

2 marks

1 mark

(b) A boat sails to P from Q.

Measure and write down the three figure bearing of P from Q

back bearing is 180 + 110 = 2900

bay

land land

P

North

North

North

R

X

Q

0650

(c) A yacht sails to P from R on a bearing of 1100

Work out the three figure bearing of R from P.

6

2008 practice (June 2006) 43005 1H

4. A regular hexagon is made from 6 equilateral triangles as shown.

The perimeter of the hexagon is 54 centimetres.

Work out the perimeter of one of the equilateral triangles

3 marks

Perimeter = 54cm one edge is 9 cm

9 cm

9 cm9 cm

Perimeter = 27 cm

7

2008 practice (June 2006) 43005 1H

5 (a) The diagram shows a right angled triangle.

Work out the area of the triangle.

State the units of your answer.

3 marks

3 cm5 cm

4 cmArea of triangle = ½ base x height

Area = ½ x 4 x 3 = 6 cm2

1 of the marks is for correct units cm2The 5 cm

measurement is a

distractor!Do not use it.

8

2008 practice (June 2006) 43005 1H

5 (b) Three triangles are shown, A, B and C

Here are four statements

1. Triangle A has the greatest area.

2. Triangle B has the greatest area.

3. Triangle C has the greatest area.

4. All three triangles have the same area.

Which statement is correct?

Give a reason for your answer. 2 marks

3 cm5 cm

4 cm 4 cm 4 cm

3 cm 3 cm

A B C

Number 4

The base = 4cm and the height = 3cm on each triangle

9

2008 practice (June 2006) 43005 1H6. A room is in the shape of a cuboid.

The diagrams show the plan view, front elevation and side elevation

Calculate the volume of the room.

3 marks

plan view

5m

6m

front elevation

6m

3m 3m

5m

side elevation

cuboid room

look down on the plan

look straight at the side elevation

look straight at the front elevation

Volume = length x width x height

= 6 x 5 x 3 = 90m3

10

2008 practice (June 2006) 43005 1H7 (a) multiply out 6(3p + q)

(b) multiply out -2(2p + 3q)

(c) multiply out and simplify 6(3p + q) – 2(2p + 3q)

1 mark

1 mark

1 marktimes 3p +q

6

6(3p + q) on the grid

18p

6q

= 18p + 6q

times 2p +3q

-2

-2(2p + 3q) on the grid

-4p -6q

= -4p - 6q

= 18p + 6q – 4p – 6q = 18p + 6q – 4p – 6q = 14p

11

2008 practice (June 2006) 43005 1H8 (a) Here is a table about squares.

Complete the table for n squares

2 marks

1 mark

(b) Here is a sequence of numbers. 5 9 13 17

Write down an expression for the nth term.

Goes up in 4s first term 5 is 4 x 1 + 1

nth term is = 4n + 1

Number of squares Total number of sides

1 4

2 8

3 12

4 16

5 20

n …4n

12

2008 practice (June 2006) 43005 1H

9 (a) The diagram shows the rotation of shape A to shape B.

OX and OY are perpendicular.

Work out the angle of rotation.

2 marks

20°

20°O X

YA

B

20°

20°O X

YA

B

50°20°

20°O X

YA

B

70°

Angle of rotation = 70o

13

2008 practice (June 2006) 43005 1H

1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

x

y

C

9. (b) (i) Translate the shaded shape C by the vector

1 mark

4

–1

(ii) Write down the translation vector that would return C back to its original position.

–4

1

2 marks1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

7

8

9

x

y

C

This means move the

shape 4 to the right

and 1 down

4

–1

14

2008 practice (June 2006) 43005 1H

10 (a) Expand 2x(x2 – 4)

(b) Factorise y2 – 4y

(c) Make x the subject of the formula y = 3 + x

2 marks

2x times x2 = 2x3

2x times - 4 = - 8x

Answer = 2x3 - 8x

y x y – 4 x y = y ( y – 4 )

1 mark

1 mark

Take 3 from both sides

y – 3 = x

swap sides x = y – 3

15

2008 practice (June 2006) 43005 1H

4 marks

11 Show clearly that (n - 2)(n + 3) + (6 - n) = n2

(n - 2)(n + 3) = n2 -2n +3n -6

= n2 + n - 6

adding 6 – n to this answer gives n2 + n – 6 + 6 - n

= n2

16

2008 practice (June 2006) 43005 1H12 There are 70 bags of sugar on a shelf.

There are x bags that weigh 1 kg.

There are y bags that weigh 2kg.

(a) Write down an equation connecting x and y

(b) the total weight of the bags is 96kg

Use algebra to work out the values of x and y.

You must show your working.

x + y = 70 x + 2y = 96

Subtract from y = 26

x + 26 = 70 x = 44

44 + 52 = 96

4 marks

x + y = 70

1 mark

Use y = 26 in

Check x=44 and y=26 in

17

2008 practice (June 2006) 43005 1H13 The diagram shows three similar triangles

(a) Work out the value of x.

(b) Work out the value of y.

2 marks

3 marks

x

2 cm 6 cm

9 cmy

15 cm

The centre triangle is an enlargement scale factor 3 of the smallest triangle … So x = 3cm

The largest triangle is an enlargement scale factor 2.5 of the centre triangle …

So y = 22.5 cm

x3

x 2.5

18

2008 practice (June 2006) 43005 1H14 The diagram shows two vectors

Label the points C, D, E and F

OA = a and OB = b

a

b

C

AO

B

OC = 2b OD = a + b BE = 3b EF = 2a – 2b

D

E

F

1 mark 1 mark 1 mark 1 mark

19

2008 practice (June 2006) 43005 1H

15. The diagram shows a rhombus ABCD.

The diagonals intersect at X.

Prove that triangle ABX is congruent to triangle CDX

Rhombus all sides equal

and diagonals bisect at 900

A B

X

D C

Angle AXB = angle CXD = 900

AB = CD = equal sides of rhombus

AX = CX = bisected diagonal AC triangle AXB triangle CXD RHS

4 marks

20

2008 practice (June 2006) 43005 1H

16 (a) You are given the identity

x2 – ax + 144 ( x – b)2

Work out the values of a and b.

(x - b)2 = x2 – 2bx + b2

so x2 – ax + 144 x2 – 2bx + b2

To be identical 144 = b2 and a = 2b

which makes b = 12 and a = 24

3 marks

21

2008 practice (June 2006) 43005 1H

16 (b) Simplify x

2 – 4x +4

x2 – 4

Factorise the top and the bottom - remember difference of two squares

x

2 – 4x +4

x2 – 4

= (x – 2)(x – 2)(x – 2)(x +2)

Cancel common factors (x - 2)

x

2 – 4x +4

x2 – 4

= x – 2x +2

3 marks

22

2008 practice (June 2006) 43005 1H

17 (a) Complete the table of values for y = 12 x

x 0 1 2 3 4

y

when x =0 y = 12 0

= 1

when x =1 y = 12 1

= 12

when x =2 y = 12 2

= 14

when x =3 y = 12 3

= 18

when x =4 y = 12 4

= 116

12 1

4 1

8 1

16 1

23

2008 practice (June 2006) 43005 1H15 (b) Draw the graph of

for values of x from 0 to 4

y = 12 x

x1 2 3 4

y

18

14

38

12

58

34

78

1

98

x1 2 3 4

y

18

14

38

12

58

34

78

1

98

(c) Use your graph to estimate the value of

12

12

1

2

12 = 28

40 = 7

10

2 marks

2 marks

24

2008 practice (June 2006) 43005 1H

Total: out of 70 a rough guide

grade D C B A A*

score 16 26 36 46 56