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National 5

N5 Applications

Unit Test

Preparation Booklet 1

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Exercise 1

Calculate the area of each triangle below:

(a) (b) (c)

Exercise 2

Find the lengths AB, EF and PR in each of the three questions above in Exercise 1.

Exercise 3

(a) Three ships, Arran (A), Bigga (B) and Callanish (C) are positioned as shown below.

Arran is 155km from the Callanish. The Callanish is on a bearing of 065° from the Bigga.

The Bigga and Callanish are also 150km from each other.

What is the bearing of the Callanish from Arran? Give your answer to the nearest degree.

69⁰

230m

m

35⁰

16cm 42⁰

147m

12m

7m

16cm

A

C B D

F E

R

Q

P

B

150 km

C

A

N

65°

155 km

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(c) A boat sailed south from port to the Island of Raasay

for a distance of 63 km.

It then sailed on a bearing of 060°.

The boat is now 72km from port.

Calculate the boat’s bearing from port.

Give your answer to the nearest degree

(b) Three oil rigs are situated in the North Sea.

Beaumont is 57km north of Indio and is 66km

from Thermal.

Thermal is on a bearing of 070° from Indio.

Calculate the bearing of Thermal from Beaumont.

Give your answer to the nearest degree.

57 km

Beaumont

N

66 km

Thermal

N

Port

Boat

Raasay

Indio

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Exercise 4

The diagrams below show 4 directed line segments s, t, u and v.

Draw the resultant vector of;

(See worksheet)

(a) s + t (b) 2t + u (c) v + 3s (d) 4u + 2v

Exercise 5

(a) State the coordinates of each vertex of the cuboid.

s t u v

G

O x

C B

A

E

D

F

z y

12

3

5

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(b) The roof of a house is constructed from two congruent isosceles triangles and two

congruent trapezia as illustrated in the diagram. State the coordinates of each corner of

the roof.

(c) State the coordinates of each vertex of the square-based pyramid shown in the diagram

Q

R

T

S

(20, 8, 6)

24

16

O

P

x

z y

N

Q

M 8 O

y

x

9

z

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Exercise 6

(a) The forces acted on a body are represented by three vectors u, v and w as given below.

u = v =

Find the resultant force.

(b) The forces acted on a body are represented by three vectors p, q and r as given below.

p =

q =

Find the resultant force.

(c) The forces acted on a body are represented by three vectors a, b and c as given below.

a =

b =

Find the resultant force.

Exercise 7

Vector a = , vector b =

, vector c =

and vector d =

Calculate;

(a) (b) (c)

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Exercise 8

(a) A house which cost £43,000 four years ago appreciates in value by 1.5%. Calculate the

value of the house after 5 years.

(b) A piano costs £3000, its value depreciates by 18% each year. Calculate the value of piano

after 5 years.

(c) A boat is worth £20,000, unfortunately its value depreciates by 9% each year. Calculate

its value after 11 years.

Exercise 9

Calculate the exact area of the following shapes;

(a) square of length 5

cm (b) rectangle (c) triangle

Exercise 10

(a) A food processor has been reduced to £120 with 20% off in the sale.

What was the original price?

(b) The value of a bungalow has appreciated by 6% in a year. It is now valued at £180,000.

What, to the nearest pound, was its value last year?

(c) A tree has grown by 15% over the course of a year. It is now 12m tall.

What, to nearest whole number, was the tree’s height last year?

12 cm

10

cm

6

cm

4

cm

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Exercise 11

(a) In a bakery, a sample of six fruit loaves is selected and the weights, in grams, are

recorded.

395 400 408 390 405 402

(i) For the above data find the mean and standard deviation.

(ii) New methods are introduced to ensure more consistent weights.

Another sample is taken and the mean and standard deviation are found to be 400 grams and 5.8

grams respectively.

Are the new methods successful? Give a valid reason for your answer.

(b) A new central heating system is installed in a house. Sample temperatures, in

degrees Celsius, are recorded below.

19 21 23 21 19 20

(i) For this sample data, calculate the mean and the standard deviation.

The target temperature for this house is 20°C. The system is judged to be operating effectively if the

mean temperature is within 0.6°C of the target temperature and the standard deviation is less than

2°C.

(ii) Is the system operating effectively?

Give 2 valid reasons for your answer.

(c) Two groups of six students are given the same test.

(i) The marks for Group A are

73 47 59 71 48 62

Calculate the mean and standard deviation for Group A.

(ii) In Group B, the mean is 60 and the standard deviation is 29.8.

Compare the results of the two groups and give 2 valid comparisons.

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Exercise 12

( a) A weed killer is applied to plants under laboratory conditions. The increase in length (xcm)

before it died was charted against the number of days (y) it took to die.

(i) Determine the y-intercept and the gradient of the line.

(ii) Use these values to determine the equation of the straight line.

(iii) Using you equation, estimate how long it would take for a plant with increase of 10cm to

die.

(b) The scatter diagram shows the heights and masses of some horses. The scatter diagram also

shows a line of best fit.

1 2 3 4 5 6 7

1

2

3

4

5

6

7

8

9

10

x

y

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(i) Determine the y-intercept and the gradient of the line.

(ii) Use these values to determine the equation of the straight line.

(iii) The height of the horse is 163cm, use your equation to determine the mass.

(c) The number of hours spent on math homework each week and the final exam grades for twelve

students in Mr. Dylan's algebra class are plotted below.

(i) On your worksheet draw a line of best fit.

(ii) Determine the y – intercept and gradient of the line.

(iii) Use these values to determine the equation of the straight line.

(iv) Using your equation, which exam grade is the best prediction for a pupil who

spends 4 hours on maths homework each week, to nearest whole number?

The End

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Worsheet for N5 Applications Preparation Booklet

Exercise 4

Exercise 12 (c)

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Answers

Exercise 1

a) 39.2m2 b) 73.4cm2 c) 9983.8m2

Exercise 2

a) 11.5m b) 9.6cm c)155.7m

Exercise 3

a) 1190 b)1240 c)1090

Exercise 4

Exercise 5

a) B(12,0,0), C(12,3,0), D(0,3,0), E(0,0,5), F(12,0,5), G12,3,5), H(0,3,5), O(0,0,0)

b) O(0,0,0), Q(24,0,0), R(24,16,0), S(0,16,0), T(4,8,6)

c) M(8,0,0), N(8,8,0), P(0,8,0), Q(4,4,9), O(0,0,0)

Exercise 6

a)

b)

Exercise 7

a) 26 b) 5 c)√424

a)

b)

c)

d)

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Exercise 8

a) £46,323.21 b) £1112.22 c) £7087.37

Exercise 9

a) 30 ¼ cm2 b) 76

cm2 c) 46

cm2

Exercise 10

a)£150 b) £16981 c) 10m

Exercise 11

a)i) mean = 4.2, standard deviation = 6.6

ii) Yes successful, although mean is the same the standard deviation is lower therefore there is more

consistency in weight.

b)i) mean = 20.5, standard deviation = 1.52

ii) 19 < 20.5 < 20.6 mean is within the range, 1.52 < 2 standard deviation is within the range

Yes the system is operating effectively.

c)i) mean = 60, standard deviation = 11.02

ii) Although the mean is the same for both groups, the standard deviation for Group A is lower,

meaning that Group A have better test results as there is less variation in their results.

Exercise 12

a)i) c = 4.2, m = 1.8 ii) y = 1.8x + 4.2 iii) 22.2 days

b)i) c = 400, m =

ii) y =

x + 400 iii) 507

kg

c)i) see diagram ii) c = 65, m =

iii) y =

x +65 iv) 74%

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Gryffe High School

Gryffe High School

Gryffe High School

Gryffe High School

Gryffe High School

Gryffe High School

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