year 11 mathematics time: 1h 40min main paper...mathematics – main paper – year 11 – track 3...
Post on 25-Mar-2021
3 Views
Preview:
TRANSCRIPT
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
top related