Mathematics – Main Paper – Year 11 – Track 3 – 2018 Page 1 of 12

DEPARTMENT FOR CURRICULUM,

RESEARCH, INNOVATION AND LIFELONG LEARNING

Directorate for Learning and Assessment Programmes

Educational Assessment Unit

Annual Examinations for Secondary Schools 2018

YEAR 11 MATHEMATICS TIME: 1h 40min

Main Paper

Question 1 2 3 4 5 6 7 8 9 10 11 12 13 Total

Main Non Calc

Global

Mark

Mark

DO NOT WRITE ABOVE THIS LINE.

Name: _____________________________________ Class: ________________

Calculators are allowed but all necessary working must be shown.

Answer ALL questions.

Table of Formulae

Curved Surface Area of Right Circular Cone πrl

Surface Area of a Sphere 4𝜋𝑟2

Volume of a Pyramid/Right Circular Cone 1

3 base area × perpendicular height

Volume of a Sphere 4

3𝜋𝑟3

Solutions of 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0 𝑥 = −𝑏±√𝑏2−4𝑎𝑐

2𝑎

Track 3

Page 2 of 12 Mathematics – Main Paper – Year 11 – Track 3 – 2018

1. Dale, a mechanic, earns money by servicing cars. He pays a monthly sum to cover his

expenses. The graph shows the profit made against the number of services each month.

a) What is the number of services Dale needs to do to make a profit of €500?

Ans: _________ services

b) How much is the monthly sum?

Ans: €_________

c) Show that the gradient of the line is 20.

d) What does the gradient of this graph represent?

______________________________________________________________________

e) How many services must Dale do to make a profit of €2000?

Ans: ________ services

(6 marks)

– 200

4

– 400

Profit (€)

Number of

Services

200

400

600

0 10 20 30 40 50

Mathematics – Main Paper – Year 11 – Track 3 – 2018 Page 3 of 12

2. a) Use your calculator to evaluate (2

3)

3

2, giving your answer correct to 2 decimal places.

Ans: ____________

b) Fill in the blanks with integers.

(27)−2

3 = (1

)

2

3

= 1

( √

)

= 1

9

(4 marks)

3. An electronic weighing scale rounds up weight to the nearest gram.

For breakfast, Waylen and Melanie measure some cereal on the balance.

Waylen measures 40 g while Melanie measures 30 g.

a) Write down the lower and upper bounds of the weight of Waylen’s cereal.

Lower bound: _________ g; Upper bound: _________ g

b) During April, Waylen and Melanie have breakfast everyday.

What is the total maximum weight of cereal they have altogether in April?

Ans: __________ g

(4 marks)

Name: ________________________________ Class: ______________ Track 3

Page 4 of 12 Mathematics – Main Paper – Year 11 – Track 3 – 2018

4. The table shows the acceptable amount per litre of some cells and substances found in the

male human blood.

Type of cell or substance Acceptable

amount per litre

White Blood Cells 3.8 × 109

Red Blood Cells 4.2 × 1012

Platelets 150 × 109

Grams of Creatinine 5 × 10−3

Grams of Haemoglobin 120

a) Express the number of white blood cells in ordinary form.

Ans: ___________________________

b) Is the number of platelets in standard form? Explain.

______________________________________________________________________

c) Anthony’s blood test shows he approximately has 820 000 000 000 red blood cells.

Is this amount greater than the acceptable level? Explain.

______________________________________________________________________

______________________________________________________________________

Bernard’s and Paul’s blood tests show they have the acceptable amounts for every item.

Bernard donates ½ a litre of blood. Paul donates 0.7 litre of blood.

d) i) How much grams of haemoglobin does Bernard’s donation contain?

Ans: __________ g

ii) How much grams of creatinine do Bernard’s and Paul’s donations contain altogether?

Give your answer in standard form.

________________________ g

(8 marks)

Mathematics – Main Paper – Year 11 – Track 3 – 2018 Page 5 of 12

5. Solve these simultaneous equations.

2𝑥 − 𝑦 = 3

𝑥𝑦 − 2𝑥 = 12

Ans: 𝑥 = _________; 𝑥 = _________

𝑦 = _________; 𝑦 = _________

(6 marks)

6. a) Underline a possible equation for this sketch.

A) 𝑦 = 𝑥3 − 2𝑥2

B) 𝑦 =1

𝑥+ 2

C) 2𝑥 + 3𝑦 = 2

b) i) Solve the equation 𝑥2 + 5𝑥 − 6 = 0.

Ans: 𝑥 = ________ or 𝑥 = ________

ii) On the axes below, sketch the graph 𝑦 = 𝑥2 + 5𝑥 − 6, indicating clearly the points

of intersection with both axes.

(6 marks)

Name: ________________________________ Class: ______________ Track 3

x

y

x

y

x

Page 6 of 12 Mathematics – Main Paper – Year 11 – Track 3 – 2018

7. a) ABC is a right-angled triangle.

Work out the length of BC, correct to the nearest centimetre.

Ans: __________ cm

Pawlu cuts a piece of wood using triangle ABC as its cross-section. He plans to put it underneath a

statue as a support. The statue is to be placed on a downhill.

The diagram above shows that Pawlu’s piece of wood is not a good support. He cuts another piece

of wood using triangle BCD as its cross-section. Points A, C and D lie on a straight vertical line.

62 cm

18 cm

A

x

B

C

Diagram NOT

drawn to scale

Diagram NOT

drawn to scale

62 cm

18 cm

A

60°

B

C

D

Base of statue

Mathematics – Main Paper – Year 11 – Track 3 – 2018 Page 7 of 12

b) Work out the length of BD.

Ans: ____________ cm

c) Work out the length of CD.

Ans: ____________ cm

(9 marks)

Page 8 of 12 Mathematics – Main Paper – Year 11 – Track 3 – 2018

8.

ABCD and PQRS are the top faces of two cubes. The ratio of their areas is 16 : 49.

a) Calculate BD : QS, the ratio of the diagonals of the cube’s faces.

Ans: _____:_____

b) The volume of the larger cube is 2000 cm3. What is the volume of the smaller cube?

Ans: ________________ cm3

(4 marks)

9.

a) Explain why triangles ABC and PQR are similar.

b) Another triangle XYZ is similar to the above triangles. The lengths of its sides are

15.6 cm, 20.8 cm and 31.2 cm.

What is the scale factor of enlargement from triangle PQR to triangle XYZ?

Ans: _______

(5 marks)

Diagrams NOT

drawn to scale A B

C D

P Q

R S

B

A

C

117°

9 cm

4.5 cm 6 cm

Diagrams NOT drawn to scale

Q P

R

117°

6 cm

3 cm

4 cm

Mathematics – Main Paper – Year 11 – Track 3 – 2018 Page 9 of 12

10. The time taken for a group of boys and a group of girls to run 100 m is recorded.

The box plot below shows the distribution of the boys’ times.

a) Write down the median time.

Ans: __________ seconds

b) Calculate the range.

Ans: __________ seconds

For the girls’ group, the information below is available.

c) On the diagram above, draw the box plot for the distribution of the girls’ time.

d) Underline the correct answer.

i) The fastest runner is a (boy, girl).

ii) The slowest girl is (slower, faster) than the slowest boy.

(7 marks)

lowest time: 16 seconds median: 28 seconds lower quartile: 23 seconds

interquartile range: 8 range: 24

seconds

Boys

0 5 10 15 20 25 30 35 40 45 50

Page 10 of 12 Mathematics – Main Paper – Year 11 – Track 3 – 2018

11. This table shows the time taken by the employees of a company to travel from home to their

workplace. Below the table there is a histogram for the same data.

Both the table and the histogram are incomplete.

Time, t minutes 0 < t < 5 5 < t < 15 15 < t < 35 35 < t < 40

Frequency 15 38 12

Frequency Density 3 3.8 0.6

a) Complete the table and the histogram.

b) Estimate the probability that an employee chosen at random is one who takes less than 10

minutes travelling.

Ans: ____________

(6 marks)

0

Time (minutes)

5

1

2

3

10 15 20 25 30 35 40

Fre

qu

ency

Den

sity

4

Mathematics – Main Paper – Year 11 – Track 3 – 2018 Page 11 of 12

12.

a) A pyramid has a perpendicular height of 1

𝑥+4 m and a rectangular base 3 m by 2 m.

A cuboid measures 1 m by 3 m by 1

𝑥 m. The total volume of both shapes is 1 m3.

Show that 2

𝑥+4 +

3

𝑥 = 1.

b) Solve the equation 2

𝑥+4 +

3

𝑥 = 1 and hence calculate the height of the pyramid.

Ans: __________ m

(8 marks)

Diagrams NOT drawn to scale.

All dimensions are in metres.

1

3

1

𝑥

1

𝑥 + 4

2

3

Page 12 of 12 Mathematics – Main Paper – Year 11 – Track 3 – 2018

13.

ABC is a triangle where BAC = 𝑥. Triangles PAB and QAC are equilateral.

a) Write down the value of PAB.

Ans: _______°

b) i) Join the points P and C with a straight line. Similarly, join Q and B.

Show that triangles PAC and QAB are congruent.

ii) Which angle is equal to AQB? Explain why.

___________________________________________________________________

___________________________________________________________________

(7 marks)

END OF EXAMINATION

Diagram NOT drawn to scale

P

x

Q

A

B

C