PLC Papers - WordPress.com€¦ · · 2017-05-05PiXL PLC 2017 Certification Trigonometry 3 Grade...

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PiXL PLC 2017 Certification

Bearings 1 Grade 4

Objective: Measure and use bearings (including the 8 compass point bearings).

Question 1.

On what bearing are the following directions?

(a) North

(b) South East

(c) North West

(d) South (Total 4 marks)

Question 2.

What angles are between the following compass points?

(a) North West to South West

(b) South to North East

(c) South to South East

(d) North West to South East (Total 4 marks)

Question 3.

Abi and Jake are in an orienteering race.

Abi runs from checkpoint A to checkpoint B, on a bearing of 065° Jake is going to run from checkpoint B to checkpoint A.

Work out the bearing of A from B.

(Total 2 marks)

Total /10


Bearings 3 Grade 4


Question 1.

(a) Town A is on a bearing of 0450from B. What is the bearing of B from A?

(b) Amy looks on a bearing of 3000 to Blake. What is the bearing from Blake to Amy?

(c) X is on a bearing of 1740 from Y. What is the bearing from X to Y?

(Total 6 marks)

Question 2.

The scale diagram shows the positions of two towns, A and B. The scale is 1cm:15km

(a) Measure and write down the bearing of town B from town A.

(b) What is the real distance from town A to town B? Give your answer in km.

(Total 4 marks)

Total /10


Bearings 2 Grade 4


Question 1.

On what bearing are the following directions?

(a) North East

(b) South West

(c) North

(d) South East (Total 4 marks)

Question 2.

What angles are between the following compass points?

(a) North West to South

(b) South to North West

(c) South to South West (Total 3 marks)

Question 3.

The diagram shows the position of two boats, B and C.

Boat T is on a bearing of 060° from boat B. Boat T is on a bearing of 285° from boat C.

In the space above, draw an accurate diagram to show the position of boat T.

Mark the position of boat T with a cross (×). Label it T.

(Total 3 marks)

Total /10


Bearings 4 Grade 4


Question 1.

(a) Town A is on a bearing of 1450from B. What is the bearing of B from A?

(b) Amy looks on a bearing of 3200 to Blake. What is the bearing from Blake to Amy?

(c) X is on a bearing of 1620 from Y. What is the bearing from X to Y?

(Total 6 marks)

Question 2.

The scale diagram shows the positions of two towns, A and B. The scale is 1cm:20km

(a) Measure and write down the bearing of town A from town B.

(b) What is the real distance from town A to town B? Give your answer in km.

(Total 4 marks)

Total /10


Trigonometric Ratios 1 Grade 5

Objective: Know and use the trigonometric ratios for right-angled triangles

Question 1

ABC is a right angled triangle. BC = 14 m and the angle ACB is 32o Calculate the length of AB. Give your answer to 1 decimal place.

…..………………. (3) (Total 3 marks) Question 2 ABC is a right angled triangle.

AB = 12 cm, AC = 27 cm Calculate the angle BAC. Give your answer correct to the nearest degree.

…..……………. (Total 3 marks) (3)


Question 3 ABCD is a rectangle.

AD = 12 m and the diagonal BD makes an angle of 28o with AB. Work out the length of the diagonal BD. Give your answer correct to 3 significant figures

………….. …. (4) (Total 4 marks)

Total /10


Trigonometry 3 Grade 5


Question 1

This is a funicular railway in Portugal. The track length is 274m and the station at the top of the hill is 116m higher than the station at the bottom. What is the angle between the track and the horizontal ground? Give your answer to the nearest degree.

….………………. (3) (Total 3 marks) Question 2 A ladder is placed against a vertical wall. The bottom of the ladder is 1.5 m from the base

of the wall on horizontal ground. The ladder makes an angle of 65o with the ground. How high up the wall does the ladder reach? Give your answer to 2 significant figures.

…………………. (Total 3 marks) (3)


Question 3 A ship travels on a bearing of 063o for an unknown distance. At the end it is exactly 8

miles North of its original position. How far has the boat travelled? Give your answer correct to 3 significant figures

…………………. (4) (Total 4 marks) Total /10


Venn Diagrams 1 Grade 4

Objective: To design and use Venn diagrams to calculate probability.

Question 1.

Here is a Venn diagram.

50 students are asked if they have a dog or cat.

• 29 have a dog. • 30 have a cat. • 8 have a dog, but not a cat.

(a) Complete the Venn diagram.

(3)

(b) A student is chosen at random.

What is the probability that this student has a cat and a dog?

..............................................

(1)

(Total 4 marks)


Question 2.

100 students were asked in a survey whether they used texts or social media.

• 35 students said they only use texts.

• 29 students said they only use social media.

• 21 students said they use both texts and social media.

(a) Put this information on the Venn diagram.

(1)

(b) One of the students in the survey is chosen at random.

What is the probability that this student uses social media?

..............................................

(2)

(Total 3 marks)


Question 3.

ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

A = {multiples of 3}

A ∩ B = {3, 9, 12}

A ∪ B = {1, 2, 3, 6, 7, 9, 10, 11, 12, 14, 15}

Draw a Venn diagram for this information.

(3)

(Total 3 marks)

Total /10




Question 1.

Jessica asks 25 people in her school if they like History or Geography.

The Venn diagram shows her results.

(a) What does the number 1 on the diagram represent?

…………………………………………………………………………………………………………………

………………………………………………………………………………………………………………….

(1)

(b) A student is chosen at random.

What is the probability that the student likes Geography?

.............................................

(1)

(c) Jessica’s friend Anna says ‘The Venn diagram shows that 12 people like History.’

Explain why Anna is not correct.

…………………………………………………………………………………………………………………

………………………………………………………………………………………………………………….

(1)

(Total 3 marks)

8 12 4

1

H G


Question 2.

Last year there were 38 students in a class.

Of these students, 18 studied French, 11 studied Spanish and 4 studied both French and Spanish.

(a) Put this information on the Venn diagram.

(1)

(b) One of the students in the class is chosen at random.

What is the probability that this student did not study French or Spanish?

..............................................

(2)

(Total 3 marks)

French Spanish


Question 3.

ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,}

A = {prime numbers}

A ∩ B = {2, 5, 11,}

A ∪ B = {1, 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17}

(a) Draw a Venn diagram for this information.

(3)

(b) What is the probability of A ∩ B?

..............................................

(1)

(Total 4 marks)

Total /10




Question 1.

Lucas asked 50 people which flavour crisps they liked from plain, beef and salt and vinegar.

All 50 people like at least one of the flavours.

17 people like all three flavours.

15 people like plain and beef but do not like salt and vinegar.

22 people like beef and salt and vinegar.

26 people like plain and salt and vinegar.

38 people like beef.

2 people like salt and vinegar only.

Lucas selects at random one of the 50 people.

(a) Work out the probability that this person likes plain flavoured crisps.

.............................................

(4)

(b) Given that the person selected at random from the 50 people likes plain flavoured crisps, find the probability that this person also likes exactly one other flavour.

..............................................

(2)

(Total 6 marks)


Question 2.


(a) Write down the numbers that are in set:

(i) A ∪ B

.......................................................

(ii) A ∩ B

.......................................................

(2)

One of the numbers in the diagram is chosen at random.

(b) Find the probability that the number is in set Aʹ.

.......................................................

(2)

(Total 4 marks)

Total /10

A B

1

3

4

8

2

10

6

7

5 9




Question 1.

119 people chose the courses they wanted at a charity dinner.

72 chose starters.

103 chose main.

80 chose dessert.

40 chose starter, main and dessert.

25 chose main and dessert.

22 chose starter and main.

9 chose starter and dessert.

(a) Work out the probability that a person chosen at random chose main course only.

.............................................

(4)

(b) Given that the person selected at random from the 119 people had a dessert, find the probability that this person also had a main course.

..............................................

(2)

(Total 6 marks)


Question 2.


(a) Write down the numbers that are in set:

(i) X ∪ Y

.......................................................

(ii) X ∩ Y

.......................................................

(2)

One of the numbers in the diagram is chosen at random.

(b) Find the probability that the number is in set Yʹ.

.......................................................

(2)

(Total 4 marks)

Total /10

X Y

21

34

14

88

12

10

63

79

25 19




Question 1

ABC is a right angled triangle. AC = 11 cm and the angle ACB is 67o Calculate the length of AB. Give your answer to 1 decimal place.

…….………………. (3) (Total 3 marks) Question 2 ABC is a right angled triangle.

AB = 9 cm, BC = 12 cm Calculate the angle ACB. Give your answer correct to the nearest degree.

…………………. (Total 3 marks) (3)


Question 3 ABCD is a rectangle.

AD = 13 m and the diagonal BD makes an angle of 74o with BC. Work out the length of the diagonal BD. Give your answer correct to 3 significant figures

………………. (4) (Total 4 marks) Total /10




Question 1

An aeroplane is 5000m from touchdown measured along the ground. Its angle of decent is 25o below the horizontal. How high is it above the ground? Give your answer to the nearest metre.

………………………. (3) (Total 3 marks) Question 2 A buoy is 12 km east and 5 km north of a lighthouse. Find the bearing of the buoy from the

lighthouse.

….……………. (Total 3 marks) (3)


Question 3 The diagram shows the side of a house. Find the

angle x between the two sloping edges of the roof. Give your answer to the nearest degree.

………….…. (4) (Total 4 marks) Total /10


Cumulative Frequency 1 Grade 6

Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data) Question 1

The grouped frequency table shows information about the weekly wages of 80 factory workers.

(a) Complete the cumulative frequency table.

(1)

(b) On the next page, draw a cumulative frequency graph for your table.

(2)


(c) Use your graph to find an estimate for the median.

…………………………………… (1)

(d) Use your graph to find an estimate for the interquartile range.

…………………………………… (2)

(e) Use your graph to find an estimate for the number of workers with a weekly wage of more than £530.

…………………………………… (2)

(Total 8 marks)

0

10

20

30

40

50

60

70

80

90

0 100 200 300 400 500 600 700 800

CU

MU

LAT

IVE

FR

EQ

UE

NC

Y

WEEKLY WAGE, £


Question 2

The cumulative frequency graph shows information about the times 80 swimmers take to swim 50 metres.

(a) Use the graph to find an estimate for the median time.

…………………………………… (1)

(b) Use the graph to find an estimate for the lower quartile..

…………………………………… (1)

(Total 2 marks)

Total marks /10



Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous

data) Question 1

The table below shows information about the heights of 60 students.

(a) On the grid, draw a cumulative frequency graph for the information in the table.

(3)

0

10

20

30

40

50

60

140 150 160 170 180 190 200

CU

MU

LAT

IVE

FR

EQ

UE

NC

Y

TIME, T SECS


(b) Find an estimate

(i) for the median,

........................................................................................................................................................

(ii) for the interquartile range.

........................................................................................................................................................

(3)

(Total 6 marks)


Question 2

The table shows information about the lengths, in seconds, of 40 TV adverts.

(a) Complete the cumulative frequency table for this information.

(1)


(b) On the grid, draw a cumulative frequency graph for your table. (2)

(c) Use your graph to find an estimate for the median length of these TV adverts.

……………………… seconds (1)

(Total 4 marks)

Total marks /10

0

5

10

15

20

25

30

35

40

45

0 10 20 30 40 50 60 70

CU

MU

LAT

IVE

FR

EQ

UE

NC

Y

TIME, T SECS



Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data) Question 1

The table below shows the times it takes a group of boys to run 150m.

Boys time, secs Frequency

0 < x ≤ 5 0

5 < x ≤ 10 2

10 < x ≤ 15 7

15 < x ≤ 20 16

20 < x ≤ 25 9

25 < x ≤ 30 2

Totals 36

The cumulative frequency graph below shows the times it takes a group of girls to run 150m.

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35

CU

MU

LAT

IVE

FR

EQ

UE

NC

Y

TIME, SECS


(a) Which is the quicker gender at running 150m. Explain your answer.

……………………………………….

(1)

…………………………………………………………………………………………………………………………………………………………………….

…………………………………………………………………………………………………………………………………………………………………….

…………………………………………………………………………………………………………………………………………………………………….

…………………………………………………………………………………………………………………………………………………………………….

(5)

b) Were the boys or the girls more consistent in their running speeds, explain your reasons for your answer

…………………………………………………………………………………………………………………………………………………………………….

…………………………………………………………………………………………………………………………………………………………………….

…………………………………………………………………………………………………………………………………………………………………….

…………………………………………………………………………………………………………………………………………………………………….

(4)

Total for question - 10

marks

Total marks /10



Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous

data) Question 1

The cumulative frequency below shows the scores of two classes (X and Y) in a maths assessment which is out of 90

marks.

a) (i) Which set do you think is the Higher set?

………………………………………….

(1)

(ii) Explain your answer

………………………………………………………………………………………………………………………………………………………………………

………………………………………………………………………………………………………………………………………………………………………

………………………………………………………………………………………………………………………………………………………………………

(2)

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80 90 100

CU

MU

LAT

IVE

FR

EQ

UE

NC

Y

TEST SCORES

Class X

Class Y


b) Which class is more consistent? Explain your answer.

………………………………………………………………………………………………………………………………………………………………………

………………………………………………………………………………………………………………………………………………………………………

………………………………………………………………………………………………………………………………………………………………………

(4)

c) The pass mark for the test was 63%. How many students in total (from both classes) failed?

………………………………………….

(3)

Total marks /10


Pythagoras’ and Trigonometry 2D and 3D 4 Grade 7

Objective: Solve problems using Pythagoras's theorem and trigonometry in general 2-D triangles and 3-D figures

Question 1.

ACDEF is a tent.

The base is 2.2m wide and 3.6m long.

The ends are isosceles triangles.

The ends are at an angle of 80o to the base.

Angle AEB and angle DFC is 70o.

M is the midpoint of AB.

What is the maximum height inside the tent?

.............................................

(Total 3 marks)

Question 2.

Ed wants to fence his new triangular shaped paddock ABC

He knows the widest part is 5m.

He knows the longest part is 8m.

He knows the two diagonal sides are the same length.

Fencing costs £3.99 per metre.

What will be the cost of fencing the paddock?

.............................................

(Total 2 marks)

Diagram NOT drawn accurately

8m

5m A C

B



2.2m

Question 3.

Ben is 1.62m tall.

The tent he is considering buying is a square based pyramid.

The length of the base is 3.2m.

The poles AE, CE, AE and BE are 2m long.

Ben wants to know if he will be able to stand up in the middle of the tent. Explain your answer clearly.

..............................................

(3)

What will be the angle between the poles and the base of the tent?

..............................................

(2)

Total /10

2m



Standard trigonometric ratios 1 Grade 7

Objective: Know and derive the exact values for Sin and Cos 0, 30, 45, 60 and 90 and Tan 0, 30, 45 and 60 degrees.

Question 1.

A right angled triangle has the dimensions as shown in the diagram.

Using the diagram, or otherwise, state the exact values of:

(a) Sin 60

(b) Cos 60

(c) Tan 60

(d) Sin 30

(e) Cos 30

(f) Tan 30

(Total 6 marks)

Question 2.

Using the triangle shown, or otherwise, find the exact values of:

(a) Sin 45

(b) Cos 45

(c) Tan 45

(d) Sin 90

(Total 4 marks)

Total /10

1

2 √3

1

1

√2




Question 1.

A right angled triangle has the dimensions as shown in the diagram.

Using the diagram, or otherwise, state the exact values of:

(a) Sin y

(b) Cos y

(c) Tan y

(d) Sin x

(e) Cos x

(f) Tan x

(Total 6 marks)

Question 2.

State the values of:

(a) Tan 0

(b) Cos 90

(Total 2 marks)

Question 3.

The relationship Sin 30 = Cos 60, can be found for other values of sin and cos. What must the angles add up to for this relationship to work?

(Total 2 marks)

Total /10

4

x

3 5

y




Question 1.

Use the triangle to write cosθ in terms of x and hence,

Or otherwise, work out the value of x.

(Total 6 marks)


Question 2.

ABC is a right angled triangle and P is a point on AB.

Tan� = 23. Work out the length of BC

(Total 4 marks)

Total /10




Question 1.

Show that angle x is 60 0.

(Total 6 marks)


Question 2.

Use the triangle shown to prove that sin60=√32 .

(Total 4 marks)

Total /10




Question 1.

ABC is an isosceles triangle

BC = 24cm

Vertical height = 20cm

Calculate the length of AC. Give your answer correct to one decimal place.

..............................................

(Total 2 marks)

Question 2.

ABCDEFGH is a cuboid

AE = 5cm

AB = 6cm

BC = 9cm

(a) Calculate the length of AG. Give your answer correct to 3 significant figures.

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

(b) Calculate the size of the angle between AG and the face ABCD.

Give your answer correct to 1 decimal place.

..............................................

(3)

(Total 4 marks)

Diagram NOT drawn

accurately

20cm

24cm

A C

B



Question 3.

The diagram shows a square based pyramid.

The square base has sides 18cm.

(a) Calculate the length of the diagonal AB.


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

(b) If ∠VBA = 58o, calculate the vertical height VC.


..............................................

(3)

(Total 4 marks)

Total /10

Diagram NOT drawn

accurately

18cm





Question 1.

The diagram represents a cuboid ABCDEFGH.

Its height is 2.5metres and its width is 4 metres.

Angle GHF = 62o

(a) Calculate the length of the diagonal HF. Give your answer to one decimal place.

..............................................

(2)

(b) Calculate the angle CHF. Give your answer to one decimal place

..............................................

(2)

(Total 4 marks)

Question 2.

ABC is an isosceles triangle.

AC = 18cm

Vertical height = 14cm

Calculate angle BCA to 1dp.

..............................................

(2 marks)

14cm

18cm A C

B


Diagram NOT drawn

accurately


Question 3.

ABCDE is a square based pyramid.

The base has sides 9cm.

The vertical height of the pyramid is 8cm.

(a) Calculate the length of AC. Give your answer correct to one decimal place.

..............................................

(1)

(b) Calculate the length of AE. Give your answer correct to one decimal place.

..............................................

(1)

(c) Calculate the size of angle EAC.

..............................................

(2)

Total /10

Diagram NOT drawn

accurately




Question 1.

A piece of land is the shape of an isosceles triangle with sides 7.5m, 7.5m and 11m.

Turf can be bought for £11.99 per 5m2 roll.

How much will it cost to turf the piece of land?

..............................................

(Total 3 marks)

Question 2.

ABCDEFGH is a cuboid shaped cardboard box.

Length = 18cm

Width = 12cm

Height = 6cm

(a) Calculate AC the diagonal length of the base of the box.

..............................................

(1)

(b) Harry the Magician has promised to post his spare magic wand to a friend. His spare magic wand is 22cm long. Explain whether or not he could use this box to post the wand.

..............................................

(2)

(Total 3 marks)

12cm

18cm

6cm


Question 3.

ABCDEF is a wedge shaped skate ramp.

AB = 3m

BC = 4m

FC = 2m

(a) If Owen wants to skate from corner E at the top of the ramp to corner B at the bottom,

what is the shortest distance he can travel?

..............................................

(2)

(b) The angle of elevation of the ramp enables a judge to categorise its difficulty.

Category A ramps have an angle of elevation less than 20o.

Category B ramps have an angle of elevation between 20o and 30o inclusive.

Category C ramps have an angle of elevation greater than 30o.

Explain what type of ramp ABCDEF is.

..............................................

(2)

(Total 4 marks)

Total /10

3m

2m

4m

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PLC Papers - WordPress.com€¦ · · 2017-05-05PiXL PLC 2017 Certification Trigonometry 3 Grade...

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