L3 Assessment AoN

L3 DiagnosticAssessment

Application of Number

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basic & keySKILLBUILDER Application of Number

Diagnostic Assessment Level 3

Equipment Needed:

Pen, Pencil, Ruler

A scientific calculator. (Your tutor/teacher will tell you whether you may use a calculator and for which questions.)

= 3.14

Area of rectangle = length x width

Area of triangle = base x height

Area of circle = x radius 2

Perimeter = distance all round a flat object.

Volume of a cuboid = Length Width Height

Volume of a cylindrical shape = Area of the end shape Length

A net is a shape which can be cut out and folded to make a 3-dimensional shape.

Mean = the sum of a set of data divided by the number of pieces of data.

Median = the middle value of a set of data.

Mode = the most frequently occurring value in a set of data.

NB

You may be asked to use separate answer papers which do not contain the questions. Remember to:

indicate clearly the number of the question answered; copy diagrams and charts carefully.

Level 3: Diagnostic Assessment Application of Number © West Nottinghamshire College 20042



SECTION ONE

Complete the following:

1 or of a cake Which is larger?

2 or of a pizza Which is larger?

3 + = a) b) c) d)

4 - = a) b) c) d)

5 = a) b) c) d)

6 = a) b) c) d)

7 Ninety one people went on a coach trip to France, of them were over 26 years

old. How many were 26 years old or less?

In an election to choose a learner representative it was found that of the

learners voted for Omar, voted for Scott and the remainder voted for

Lindsey.

8 What fraction of the learners voted for Lindsey?

a) b) c) d)

9 If 136 learners voted for Lindsey, find the total number of learners who voted in the election.




10

10

10

11 In a sale all goods are reduced by 15%. A microwave oven costs £170 in the sale. Calculate the original price of the microwave.

£_________

12 A CD player is priced at £60 plus VAT. Calculate the VAT at 175% on the price.

a) £10.50 b) £60.50 c) £105 d) £22.75

13 A restaurant bill for £45 became £48 after a service charge was added. What is the percentage rate of the service charge? Express your answer to one decimal place.

a) 93.8% b) 6.3% c) 3.5% d) 6.7%

Express the ratio in its simplest form:

14 12p to £240 _______ : ________

Divide the following into the ratio shown:

15 329 ml in the ratio 27:20

a) 189 ml to 140 ml b) 140 ml to 189 ml

c) 270 ml to 59 ml d) 105 ml to 224 ml

16 Sharon, Sanjit and Jonathan pay into a lottery syndicate. Each week Sharon pays in £2. Sanjit pays in £3 and Jonathan pays in £4. Any winnings are to be divided in the same ratio as their contribution. One week their numbers are chosen and Sanjit’s share of the winnings is £240. Calculate their total winnings.

£__________


Fractions Decimals Percentages

a) b)


c) 0.45 d)


e) f) 35%

4

Formula

Value = Investment x (1 + )n

where n = number of years



SECTION TWO

17 The population of Great Britain is approximately 58,123,000. Express this number in standard form.

a) 5.8123 x 107 b) 5.8123

c) 58,123 x 107 d) 58.123 x 107

18 The coefficient of expansion for steel is 0000012. Express this number in standard form.

a) 12 x 10-5 b) 0.000012

c) 0.12 x 10-5 d) 1.2 x 10-5

19 The following value is expressed in standard form. Covert it to ordinary numbers. The distance from the earth to the sun is 1.5 108 kilometres.

a) 120,000,000 km b) 6,485,776 km

c) 150,000,000 km d) 15,000,000 km

20 The following value is expressed in standard form. Convert it to ordinary numbers. The thickness of a sheet of A4 paper is 4 10-5 m.

____________m

21 Wesley took a joint of beef from the freezer. The temperature of the beef was –18 C. Twenty minutes later he measured the temperature of the beef to be +5 C.

By how many degrees had the temperature risen?

____________oC

22 John invests £2000 for 5 years. The rate of compound interest is 7%. How much will he have at the end of the 5 years?

£___________




23 Work out 62 +

a) 77.67 b) 387 c) 41 d) 53.67

24 The formula v = u + at can be used to calculate the velocity of an object where:

v = velocity of the object in m/su = initial speed in m/st = time in secondsa = acceleration in m/s2

Calculate the velocity (v) when u = 7, a = -98 and t = 05.

a) 34.3 b) 2.1 c) 15.6 d) 8.4

25 The cost of hiring a bouncy castle is £30 fixed charge plus £7.50 per day. Using the following letters:

f = fixed charged = number of daysr = rate per dayc = total cost

Form an equation to calculate the total cost of hiring the bouncy castle.

a) c = f + r + d b) c = d + fr

c) c = f + rd d) c = fd + r

Rearrange the following formula to make the letter shown in brackets the subject:

26 P = 6K + 3 (for K)

a) K = b) K = 6P - 3 c) K = d) K = - 3

27 C = (F - 32) (for F)

a) F = - 32 b) F = + 32

c) F = (C + 32) d) F = - 32




The diagram shows the floor plan of a lounge (not drawn to scale).

B

Calculate the following. (Give your answers to two decimal places.)

28 The perimeter of the room. ____________m

29 The floor area. ____________m2

30 The volume, if the height is 24 m. ____________m3

31 A direction arrow has the dimensions shown in the diagram. Find the area of the sign.

a) 38,400 mm2 b) 36,000 mm2 c) 84,000 mm2 d) 18,000 mm2


A

24 m54 m Lounge

61 m

20 m

Reception

420 mm

300 mm

80 mm 200 mm



The diagram below shows the plan of a circular ornamental fishpond with a paved surround. Calculate:

32 The perimeter of the pond to 2 decimal places. __________m

33 The area of the paved surround.

a) 7.65 m2 b) 12.5666 m2 c) 4.909 m 2 d) 15.328 m2

34 The volume of water in the pond if the depth is 750 mm.

a) 4.712 m3 b) 15.348 m3 c) 367.9688 m3 d) 3.68 m3


Paved Surround

POND

Radius 2 m

Radius125 m

= 3.14



The drawing is a plan of a rectangular kitchen drawn to scale 1:50.

35 One of the windows of the kitchen is 1800 mm wide and 1200 mm high. Calculate the length of the line to be drawn on the plan which represents the width of the window.

__________ mm

36 On the plan the scale length of the kitchen measures 108 mm. Calculate the actual length of the kitchen (in metres).

__________ m

37 On the plan the scale width of the kitchen is 72 mm. Will a worktop 3.4 m long fit along this width?

Yes/No

A survey was carried out to find the approximate number of hours that 20 people spent watching television per week. The results are shown below:

10 11 19 15 25 22 7 9 29 2314 12 21 29 28 17 13 8 15 29

From the table calculate the following measures in respect of the number of hours spent watching television.

38 The mean a) 12.54 b) 17.80 c) 20.85 d) 24.31

39 The median a) 10 b) 16 c) 23 d) 29

40 The lower quartile a) 11 b) 21 c) 5 d) 8

41 The upper quartile a) 15 b) 19 c) 25 d) 9

42 The interquartile range a) 10 b) 11 c) 14 d) 13


Kitchen



SECTION THREE

The following grouped frequency table shows the number of marks obtained by 40 people in a recent examination.

Marks Frequency Midpoint Midpoint Frequency

1 - 10 2 5·5 11·0

11 - 20 9 15·5 139·5

21 - 30 15 25·5 382·5

31 - 40 11 35·5 390·5

41 - 50 3 45·5 136·5

Use the table to calculate the following:

43 the maximum range;

44 the modal marks gained in the test;

a) 15 b) (41 – 50) c) 40 d) (21 – 30)

45 the estimated mean number of marks;

a) 26.5 b) 3.2 c) 25.5 d) 78.3

46 the median marks gained in the test.

a) 15 b) 25.5 c) (1 – 50) d) (21 – 30)




The scatter graph below shows the heights and shoe sizes of 20 people. Each dot represents one person.

47 Pick the answer which best describes the graph.

The scatter graph shows that for these 20 people:

a) there is no link between height and shoe size;b) taller people in general take a larger shoe size;c) taller people tend to have a smaller shoe size;d) people with larger shoe sizes are generally shorter.

48 A group of 72 people were asked to state their favourite type of entertainment. It is intended to represent this information in the form of a pie chart. Some of the information is shown in the table below. Complete the missing values.

Entertainment Number of people Angle Sector

Cinema/Theatres 12 a) 108o

b) 12o

c) 60o

d) 72o

Clubs/Discos a) 12b) 15c) 21d) 24

105o




Abdul has, after necessary expenditure, £12.40 to spend per week. The pie chart below shows how he allocates his spending.

Estimate what fraction of his money is spent on:

49 Magazines and Videos;

a) b) c) d)

50 Newspapers.

a) b) c) d)




From the graph determine:

51 the month in which sales figures for both products were equal;

a) Feb b) Aug c) Apr d) Oct

52 the month in which the difference between sales was at a maximum;

a) Jul b) Mar c) Jun d) Dec

53 the maximum difference between sales;

a) £58 b) £580 c) £5800 d) £58,000

54 the two months between which product B experienced the greatest increase in sales.

a) May and Jun b) Jan and Feb

c) Nov and Dec d) April and May




The distribution of the weights of a sample of people is represented in the frequency polygon shown below.

Using the frequency polygon find:

55 The number of females in the sample __________ females

56 The range of the weights of the males __________ kg

57 Who has the highest modal weight, male or female? __________

58 In triangle ABC (not to scale), angle B = 90, AB = 8 mm and BC = 12 mm. Find the length AC.

a) 14.4 mm

b) 8.9 mm

c) 20 mm

d) 4 mm


A

B C

8 mm

12 mm






59 In triangle ABC (not to scale), angle A = 90, AC = 5 mm, and BC = 14 mm. Calculate the length of AB.

a) 9 mm

b) 14.9 mm

c) 13.1 mm

d) 19 mm

60 Triangle ABC is a right – angled triangle. If AC = 12 mm and BC = 10 mm calculate the size of angle x. Give your answer to 1 d.p.

x = __________0

61 Triangle ABC (not to scale) is a right-angled triangle. If angle B = 35 and BC = 15 mm, find the length of AC.

A C

a) 8.6 mm

b) 10.5 mm

c) 15.5 mm

d) 12.3 mm


5 mmA C

B

14 mm

B

10 mm

A

CB

12 mmx

35o



62 Give an estimate to the following calculation:

43 × 7349 × 9·72

a) 70,000 b) 700,000 c) 7,000,000

63 The total cost of a coach trip to Rome for a group of 39 people was £18,452.54. By rounding off each figure to one significant figure, estimate the cost of each ticket.

a) £4000 b) £2250 c) £400 d) £500

64 Jack often weighs himself on digital scales, his weight varies between 76·6 and 76·9 kg. Which answer is appropriate if he is asked how much he weighs?

a) 76·8149 kgb) 76·8 kgc) 76·615 kgd) 77 kg


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L3 Assessment AoN