DIRECTORATE FOR QUALITY AND STANDARDS IN EDUCATION Department of Curriculum Management Educational Assessment Unit Annual Examinations for Secondary Schools 2015

FORM 3 MATHEMATICS TIME: 30 minutes Non Calculator Paper

Question 1 2 3 4 5 6 7 8 Total

Mark

DO NOT WRITE ABOVE THIS LINE

Name: _____________________________________ Class: _______________

Instructions to Candidates Answer ALL questions.

This paper carries a total of 25 marks.

Calculators and protractors are NOT ALLOWED.

Track 3

Page 2 of 4 Mathematics – Non Calculator Paper – Form 3 Secondary – Track 3 – 2015

1. a) i. Write 4–1 as a fraction. Ans: ________________

ii. Work out + 4–1

Ans: ________________

b) Work out

Ans: ________________

[6 marks]

2. Shade the odd one out:

[1 mark]

3. The diagram shows a

scale drawing of the position of a ship, S, before it starts its journey towards the harbour, H.

a) Which of the following is the best estimate of the bearing of the ship from the harbour? Underline the correct bearing.

052 085 128 245

b) To reach the harbour the ship sails 40 km West and then 30 km North. Finish off the diagram to show this information with all the measurements shown.

c) What is the straight line distance between the harbour, H, and the starting position of

the ship, S?

Ans: _____________ km

[3 marks]

1 9  16 20 25 36 

H

S

Mathematics – Non Calculator Paper – Form 3 Secondary – Track 3 – 2015 Page 3 of 4

0

y

x

4. Write these numbers in their correct position.

[2 marks]

5. This is the graph of the line y = 2x – 3. 

a) Another line has the equation 3x + y = 2.

A(2 , a), B(0 , 2) and C(2 , 4)

are points lying on this line.

Find the missing coordinate of point A.

a = _________

b) On the same axes, plot points A, B and C and join the line.

c) Use your graphs to solve simultaneously the equations y = 2x – 3 and 3x + y = 2.

Ans: x = ______ , y = ______

[3 marks]

6. Find the value of x.

Ans: x = ________

[2 marks]

x

54

0 1 2 

3    4 =+  + 5

Page 4 of 4 Mathematics – Non Calculator Paper – Form 3 Secondary – Track 3 – 2015

7. a) The angles of a triangle are in the ratio 6 : 5 : 7. Find the size of the largest angle.

Ans: ___________

b) A train takes 6 hours to cover a certain distance at a speed of 30 km/h.

How long would it take to cover the same distance at a speed of 40 km/h?

Ans: _____ h _____ min

[4 marks]

8. a) Find the value of x. x + 5 = 45

Ans: x = __________

b) Expand (x + 5)2.

Ans: ___________________

c) Use your answers in (a) and (b) to find the value of 452. Show all your working.

Ans: ___________________

[4 marks]

END OF PAPER

Mathematics – Main Paper – Form 3 Secondary – Track 3 – 2015 Page 1 of 12

DIRECTORATE FOR QUALITY AND STANDARDS IN EDUCATION Department of Curriculum Management Educational Assessment Unit Annual Examinations for Secondary Schools 2015

FORM 3 MATHEMATICS TIME: 1h 30min Main Paper

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

Non Calc

Global Mark

Mark

DO NOT WRITE ABOVE THIS LINE

Name _____________________________________ Class _______________ 1. Anna has to guess how many stickers her brother Paul has left to finish his album.

Paul gives her some hints in the diagram below:

4 5 6 7 8 9 10 11

a) Anna writes the information in a different way. Tick the correct version.

(A) 6 stickers < 10 .

(B) 6 stickers 10 .

(C) 6 < stickers < 10 .

(D) 6 < stickers 10 .

b) What is the probability that Anna guesses the correct number of missing stickers?

Ans: ___________

c) Paul helps her further and suggests that the number of missing stickers is prime.

How many stickers does he need to finish the album? Ans: ________ stickers

[3 marks]

CALCULATORS ARE ALLOWED BUT ALL NECESSARY WORKING MUST BE SHOWN. 

ANSWER ALL QUESTIONS. 

Track 3 

Page 2 of 12 Mathematics – Main Paper – Form 3 Secondary – Track 3 – 2015

2. Bernice is working out the following calculation:

3.25 × 5.869

a) She rounds the numbers to one significant figure and starts off with a rough estimate. What is her estimate?

Ans: _________

b) Use your calculator to work out the calculation.

Ans: ____________

c) Bernice’s estimate is slightly different from the calculator answer. Express this difference as a percentage of your answer in (b). Give your answer correct to 2 significant figures.

Ans: _____________ %

d) Bernice works out the above calculation

on her calculator and gets the following

answer.

She checks her working and finds that

she had keyed in a different calculation.

Tick the incorrect calculation that she keyed in, thus getting the above answer.

3.25 × 5.689 . 

2.35 × 5.869 .

2.35 × 5.896 .

[6 marks]

Mathematics – Main Paper – Form 3 Secondary – Track 3 – 2015 Page 3 of 12

Name: ____________________________________              Class: _______________ 

  Track 3

3. This is a table of values for the graph y = x2 – 4x + 1.

x –2 –1 0 1 2 3 4 5

y 13 6 1 2 3 2 1 6

a) Plot the graph using values of x from –2 to 5.

b) Write down the coordinates of the minimum point of the graph.

Ans: ( ____ , ____)

c) Use your graph to find the values of x when y = 0.

Ans: x = ________________

[5 marks]

-3 -2 -1 O 1 2 3 4 5 6

-4

-2

2

4

6

8

10

12

14

0 x

y

Page 4 of 12 Mathematics – Main Paper – Form 3 Secondary – Track 3 – 2015

4. 22 students are carrying out an experiment to check the weight of 22 bags of sweets. The weight shown on each bag is 1 kg. Each student is given a bag and has to weigh it as accurately as possible, using one of the following scales.

A B C

a) Which of the above scales should the students use? Explain your choice, giving reasons why they should not use the other two.

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

b) One of the bags weighs 0.96 kg.

On the scale that you chose in (a), draw the correct hand to show this weight.

c) After the experiment, the students compiled the following frequency table. Fill in the missing entries in the table and use the information to draw a bar chart.

 

d) Fill in the blanks:

From their experiment the students concluded that when you buy one of these bags of

sweets, the probability that it has at least the weight as stated on the bag is __________.

[7 marks]

Bag

s 14

12

10

8

6

4

2

0

940 960 980 1000 1020 1040

grams

Weight (grams) Frequency940 w < 960 2 960 w < 980 5 980 w < 1000 1000 w < 1020 6 1020 w < 1040 1

Total 22

Mathematics – Main Paper – Form 3 Secondary – Track 3 – 2015 Page 5 of 12

Name: ____________________________________              Class: _______________ 

  Track 3 

5. a) Sarah needs to find the volume of a cylinder.

i. Underline the formula that Sarah should use. 2rh r2h 2r2h

ii. Find the volume of the cylinder when r = 3.6 cm and h = 8.92 cm. Give your answer correct to 2 decimal places.

Ans: Volume = ______________ cm3

b) Sarah uses the formula S = 180n – 360 to find the sum of the interior angles of any polygon with n sides.

i. Make n the subject of the formula.

Ans: ________________

ii. The sum of the interior angles of a given polygon is 1800. Calculate the number of sides n.

Ans: n = ____________ sides

[6 marks]

Page 6 of 12 Mathematics – Main Paper – Form 3 Secondary – Track 3 – 2015

6. Diana is buying some items online. Postage is charged at a fixed rate, for any amount of items shipped. All the items have the same price. The following graph shows the total cost of buying different quantities of these items.

a) Diana notices that the y-intercept of the graph is 8. Calculate the gradient of the graph.

Ans: Gradient = ________________

b) Use the values in (a) to fill in the blanks:

The graph shows that each item that Diana is buying costs €_______ and postage is charged

at a fixed rate of €________.

Diana uses a spreadsheet to calculate the total cost of the items that she buys. She fills cell B1 with the fixed postage cost.

c) Highlight the formula that she inputs in cell G4 to calculate the cost of 6 items.

= G3+8 = G3*B1+7 = B1+(7*G3) = B1+(8*G3)

0 1 2 3 4 50

10

20

30

40

50

Tot

al C

ost

(€)

Quantity

Mathematics – Main Paper – Form 3 Secondary – Track 3 – 2015 Page 7 of 12

d) Find the total cost of buying 25 items.

Ans: Total Cost = €__________

e) Write down an expression, in terms of n, for the total cost of buying n items.

Ans: _____________

[7 marks]

7. Grandma gives Vanessa and her sister Sharon different amounts of pocket money.

Let €x be the amount of pocket money that Vanessa gets and €y the amount that Sharon gets.

a) Sharon writes down the following equation: x – 20 = y.

Briefly explain what you understand by this equation.

__________________________________________________________________________

b) If grandma gives Sharon €22 less, Vanessa would then have twice as much as Sharon. Underline the equation that represents this information.

x – 22 = 2y x = 2y – 22 x = 2(y – 22)

c) Solve the simultaneous equations in (a) and (b) to find how much money Vanessa and Sharon each gets from grandma.

Ans: Vanessa = €_______

Sharon = €_______

[5 marks]

Page 8 of 12 Mathematics – Main Paper – Form 3 Secondary – Track 3 – 2015

8. The diagram below shows a scale drawing of a toy train, using a 1 cm grid. Every 1 cm on the drawing represents 5 cm of the actual toy. The curved lines are circles or part of a circle.

a) The shaded part of the scale diagram represents one of the train’s carts. Work out the area of this part of the scale drawing, correct to 3 significant figures.

Ans: Area= _________ cm2

Scale  1 cm : 5 cm 

D

Cart

Mathematics – Main Paper – Form 3 Secondary – Track 3 – 2015 Page 9 of 12

b) The circle with diameter D cm, represents the large wheel of the toy train. Calculate, correct to 2 decimal places, the circumference of the large wheel of the actual toy train.

Ans: Circumference = _________ cm

c) The toy train is driven on a railway track, 2.4 m long. How many whole revolutions does the large wheel make to cover the distance of the railway track?

Ans: __________ revolutions

[7 marks]

9. a) Write 0.000406 in standard form.

Ans: __________________

b) Solve 6x – 2(x + 7) = 10

     

 

Ans: x = _____________

c) Simplify 5e2f × 4e4g

Ans: _________________

[4 marks]

Page 10 of 12 Mathematics – Main Paper – Form 3 Secondary – Track 3 – 2015

10. a) Kieran has a part-time job. He earns €3.70 an hour. Here’s a list of the hourly pay rates of his friends:

€3.60 €4.50 €4.25 €3.40 €4.01 €4.25 €4.25 €3.90

i. Work out the mean, median and mode of his friends’ hourly pay rates.

Ans: Mean = €____________

Median = €____________

Mode = €____________

ii. Kieran’s employer offers him a 9% increase on his hourly rate. Will this give Kieran an hourly rate above his friends’ mean? Show all your working.

Yes No .

iii. Which of the following should Kieran use to try to negotiate the highest pay rise possible?

Mean Median Mode .

b) Amanda invested €1750 at a rate of simple interest of 3.5% p.a. Calculate the interest that she received after 4 years.

Ans: €__________________

[10 marks]

Mathematics – Main Paper – Form 3 Secondary – Track 3 – 2015 Page 11 of 12

11. A PC LOGO turtle is given the following commands to draw the diagram ABCD below.

LT 90 FD 80 RT 90 FD 39 RT 84 FD 89 HOME

 a) Write down the value of angle x. Ans: x = ___________

b) Draw line AC and use Pythagoras’ theorem to find the length of AC, in turtle steps.

Ans: AC = __________ turtle steps

c) Circle the mistake in the following attempt to find BCA.

Tan BĈA =adj

opp = 

80

39 = 0.4875 BCA = 26

d) Work out the correct value of BCA, giving your answer to the nearest degree.

 

  

 

 Ans:  BCA = __________ 

e) In isosceles ACD, find the value of DAC.

 

 

 Ans:  DAC = __________

[9 marks]

x

B

C D

A

Page 12 of 12 Mathematics – Main Paper – Form 3 Secondary – Track 3 – 2015

12. a) Fill in the blanks using the following algebraic expressions:

i. __________ (5x2 – y) = 20x2 – __________

ii. (2x – 1)(2x + 1) = __________

iii. 36x2y – 9xy = 9xy (___________)

iv. (__________)(3x – 1) = 12x2 – 10x + 2

b) A teacher asks the class to find an expression for the shaded area in the diagram.

i. Janet works out the shaded area as a2 – b2. Explain how she obtains this answer. ___________________________________

___________________________________

___________________________________

___________________________________

James divides the shape in 2 rectangles as shown in the diagram. He writes the following expression for the shaded area:

_____ (a – b) + _____ (a – b)

ii. Fill in the blanks in the expression above.

iii. Show that Janet’s and James’ algebraic expressions are equivalent.

[6 marks]

 

a

a

b

b

4y 4x – 1 4x – 2 4x2 – 1 4

a

a

b

b