2009 Practice Calc

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Edexcel GCSE Mathematics A (Linear) - 1387 Paper 4 – (Calculator)

Higher Tier Practice for Monday 1st June 2009 Time: 1 hour 45 minutes

Materials required for examination Ruler graduated in centimetres and millimetres, protracto protractor, compasses, pen, HB pencil, eraser eraser, calculator. Tracing paper may be used.

Items included with question papers Formulae sheet.

Instructions to Candidates In the boxes above, write your Centre Number and Candidate Number, your surname, initial(s) and signature. Check that you have the correct question paper. Answer ALL the questions in the spaces provided in this question paper. Supplementary answer sheets may be used.

Information for Candidates The total mark for this paper is 117.. The marks for the various parts of questions are shown in round brackets, e.g.: (2). This paper has 30 questions. Calculators may be used.

Advice to Candidates Work steadily through the paper. Do not spend too long on one question. Show all stages in any calculations. If you cannot answer a question, leave it and attempt the next one. Return at the end to those questions you have left out.

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Formulae Sheets EDEXCEL GCSE Mathematics Formulae Sheet Higher Tier

Volume of prism = area of cross section × length

Volume of sphere = 43 πr 3 Surface area of sphere = 4πr 2

Volume of cone = 13 πr 2 h Curved surface area of cone = π rl

In any triangle ABC Sine Rule

C

a b c = = sin A sin B sin C 2

2

Cosine Rule a = b + c – 2bc cos A Area of triangle =

1 2

b b

2

ab sin C

A

a c

B

The Quadratic Equation The solutions of ax2 +bx+c = 0 where a ≠ 0, are given by x =

− b ± (b 2 − 4ac ) 2a

Answer ALL TWE6TY FIVE questions. Write your answers in the spaces provided. You must write down all stages in your working.

1.

Use your calculator to work out

10.8 × 31.6
3.8

(a) Write down all the figures on your calculator display. ………………………….. (2) (b) Give your answer to part (a) correct to 3 significant figures. …………… (1)

2.

Isam, Zubayr and Aicha shared 66 marbles in the ratio 5:4:2 Work out how many marbles each of them gets.

Isam gets …….... Zubayr gets …… Aicha gets …….. (3 Marks) 3.

A man collected some information about the ages of people who went to the cinema. This information is shown in the stem and leaf diagram. 1 2 3 4

1 3 0 1

2 3 2 1

3 5 2 4

3 9 6 8

9 6

7

Key 1|1 means 11 years old

(a) Find the median.

……………. years old (2)

At another cinema the oldest person is 50. The youngest is 15. The median age of the people is 22, the lower quartile is 17, and the upper quartile is 35. Draw a box plot for this information.

(3)

4.

The diagram shows a cylinder cylinder. The radius of the circle face of the cylinder is 6cm. The height of the cylinder is 8cm. 6cm

Diagram 6OT accurately drawn 8cm

Work outt the surface area of the cylinder. Correct to 2 decimal places.

…………. cm2 (4)

5.

Shown below are some patterns made from smiley faces (☻)

Pattern number 1

Pattern number 2

Pattern number 3

Write down a formula for the number of smiley faces in terms of the pattern number, n.

………………. (2)

6.

C 27 cm 22 cm

B

y

D

7 cm

A (a) Calculate the length of side AD. Give your answer correct to three significant figures.

………….. cm (3) (b) Calculate the size of the angle marked y. Give your answer to one decimal place.

…………. ° (3)

7.

w, x, y and z represent lengths. π and 5 are numbers that have no dimensions. State whether the following expressions could be a lengt length, area, volume or neither.

 

5πy2

wπxy

wx + yz

π(x +y)

5(z + w)3

5πwy2

(2)

8.

(a) Expand and simplify (2x + 3)(x - 1) (b) Simplify (r4)6

(c) Simplify

………………….. (1) ………………….. (1)

 

(d) Calculate 6 

(e) Factorise 9 – S18

………………….. (1) ………………….. (1) ………………….. (1)

9.

As part of a survey, 20 people were asked for their age (in completed years) and the distance they travel to work (to the nearest km). The results are shown in the scatter diagram below.

(a) What correlation does this graph show? ………………………….. (1) (b) Amir is the youngest person to take part in the survey. How old is he? …………….. (1) (c) Sehifa travels further than anyone else. How far does she travel? …………….. (1)

10.

PQ is parallel to RS. OSQ and ORP are straight lines. (a) (i) Write down the value of x. x = …………. (ii) Give a reason for your answer. ………………………………………………………………………………………………… ………………………………………………………………………………………………….. (2) (b) Work out the value of y.

y =…………. (2)

11.

The equation y3 – 8y = 136 has a solution between 5 and 6. Use trial and improvement to find the solution correct to one decimal place. You must show ALL your working.

y=……………… (4) 12.

Construct the perpendicular bisector of line RS. You MUST show all your construction lines.

R

S

(2)

22.4 cm

13.

18.7cm

7.7 cm

A spindle is made up of a cylinder and two identical cones at each end. The height of each cone is 18.7cm. The length of the cylinder is 22.4cm. The diameter of the cylinder is 7.7 cm. (a) Calculatee the total surface area of the spindle, correct to three significant figures.

……………….cm2 (4) (b) Calculate the total volume of the spindle, correct to three significant figures.

……………….cm3 (4)

14.

The diagram shows a solid lid plastic brick cut in the form of a prism. The cross section of the prism is a trapezium. The vertical height between the two parallel sides of the trapezium is 42cm and the length of the prism is 127 cm.

26 cm

42 cm

127 cm 34 cm

prism. (a) Find the volume of the prism

……………… cm3 (3) (b) The prism is made out of a plastic that has a density of 8.45 grams per cm3. Find the mass of the prism and give your answer in kilograms kilograms.

……………..kg (2)

15.

(a) In a sale, the price of mountain bikes is reduced by 281⁄2%. A mountain bike costs £45.76. How much did it cost before the sale?

£……………. (3) (b) A mountain bike loses 13% of it value after each year of use. If it is worth £45.76 at the beginning of the first year how much will it be worth after 4 years of use?

£………….. (4)

16.

The table shows the heights of 30 children in a class. Height, h, (cm) 140 < h ≤ 144 144 < h ≤ 148 148 < h ≤ 152 152 < h ≤ 156 156 < h ≤ 160 160 < h ≤ 164

No. of students 4 5 8 7 5 1

Calculate an estimate for the mean height of a child.

……………….cm (3)

17.

The diagram shows a trapezium. The perpendicular height of the trapezium zium is h cm. The lengths of the two parallel sides of the trapezium are 3h cm and 50 cm. The area of the trapezium is 350 cm2.

3h cm

h cm

50 cm

(a) Show that 3h2 + 50h = 700

(2) (b) Solve the equation for h,, correct to 2 decimal places.

…………………. (3)

18.

(a) Reflect triangle Q in the line y = x. Label the triangle R. (2) (b) Enlarge triangle Q, scale factor 2, from the origin. (2) 19. The graph shows the speed of a car in kilometres per hour (km/h).

(a) What is the speed of the car after 10 seconds? ……………..km/h (1) (b) After 30 seconds, the car travels at a steady speed of 60 km/h for 1 minute. Continue the t graph by drawing a line AB to show this. (1) (c) Draw a straight line from B to the point C (110,0). (1) (d) What does the graph between B and C tell you about what the car is doing? ……………………………… ………………………………………………… ……………… ……………………………… ………………………………………………… ………………. (1)

20.

Solve the simultaneous equations below. 6 +  = 1 3 + 2 = −

x = ……………. y = ……………. (4)

21.

Over a six month period in 2008, the average monthly value of FTSE on the London stock exchange changed as shown below. May 6200

June 6000

July 5550

August 5300

September October 5600 4000

Calculate the three point moving averages for this information.

……..………. ……..………. ……..………. ……..………. (4)

22.

A 10 dirham note is a 143 × 70 mm. A 100 dirham note is 153 × 75 mm.

Show working to prove the two notes are NOT mathematically similar.

(2) 23.

BE is parallel to CD. AB = 9 cm, AE = 6 cm, BC = 3 cm, CD = 7 cm. (a) Calculate the length of BE.

…………cm (2) (b) Calculate the length of ED.

…………cm (2)

24.

(a) Show that 127 − 8 = 6

(b) Show that



!

(3)

= 32

(2)

25.

Express the recurring decimal 2.06 as a fraction, give your answer in its simplest form.

………………. (3)

26.

The diagram shows to vectors a and b. RS = a + 2b On the grid draw the vector RS RS. (2) 27.

X

A

B

a O

c

C

OABC is a trapezium. OC is parallel to AB. OA = a, OC = c, AB = 2 OC,, X is on point AB so that AX:XB = 3:1 Express XC in terms of a and c.

XC = ……………… (3)

28.

The diagram shows a pyramid. The apex of the pyramid is V. Each of the sloping edges is of length 6 cm. The base of the pyramid is a regular hexagon with sides of length 2 cm. O is the centre of the base.

(a) Calculate the height of V above the base of the pyramid, correct to 3 significant figures.

……………. cm (2) (b) Calculate the size of angle DVA, correct to 3 significant figure figures.

……………. ° (3)

(c) Calculate the size of angle AVC, correct to 3 significant figures.

……………. ° (4)

The diagram shows a tetrahedron. AD is perpendicular to both AB and AC. AB = 10 29. cm, AC = 8 cm, AD = 5 cm, Angle BAC = 90°.

(a) Calculate the size of BDC, correct to one decimal place.

……………..° (6)

(b) Work out the surface area of the tetrahedron.

……………cm3 (5)

30.

Make b the subject of the formula: " =

#.$ %&

(%(&)

b= …………………… (4) _____________________________________________________________________ TOTAL FOR PAPER: 117 MARKS E6D