form 3 mathematics time: 30 minutes non calculator paper

DIRECTORATE FOR QUALITY AND STANDARDS IN EDUCATION Department of Curriculum Management

Educational Assessment Unit

Annual Examinations for Secondary Schools 2014

FORM 3 MATHEMATICS TIME: 30 minutes

Non Calculator Paper

Name: _____________________________________ Class: _______________

Question 1 2 3 4 5 6 7 8 9 Total

Mark

Instructions to Candidates

Answer ALL questions.

This paper carries a total of 25 marks.

Calculators and protractors are NOT ALLOWED.

Track 3

of 4 Mathematics – Non Calculator – Form 3 Secondary – Track 3 – 2014

1. a) Water on Earth covers an area of about 361 000 000 km2.

Write this number in standard form.

Ans ______________

b) Work out the following, giving your answers as mixed numbers.

i.

Ans ______________

ii.

Ans ______________

[5 marks]

2. A LOGO turtle is given the following commands to draw a triangle.

PD LT90 FD40 RT90 FD30 HOME

a) Draw a rough sketch of the triangle.

Label all the sides of the triangle with their lengths in turtle steps.

b) Calculate the perimeter of the triangle.

Ans ______________t.s.

[3 marks]

Mathematics – Non Calculator – Form 3 Secondary – Track 3 – 2014 of 4

3. Calculate the annual simple interest on €1600 invested at a rate of 4% p.a.

Ans ______________

[2 marks]

4. A line passes through the points A (3, 5) and B (–1, 1).

a) Work out the gradient of the line.

Ans ______________

b) Underline the correct answer:

Which of the following is the equation of the line AB?

(A) y = 3x + 5 (B) y = 2 – x (C) y = x + 2 (D) y = 1 – x

[3 marks]

5. Fill in with >, < or = a) 91 1

9

b) 360 6

2

c) 3

2 × 3

5 3 3

7

d) 50% 2–1

[4 marks]

6. Underline the correct answer:

An estimate for the circumference of a circle with diameter 13.8 cm is :

(A) 42 cm (B) 72 cm (C) 84 cm

[1 mark]

of 4 Mathematics – Non Calculator – Form 3 Secondary – Track 3 – 2014

7. A pencil case has blue, red and black pens only.

The probability of picking up a blue pen from the

pencil case is

and that of picking up a red pen is

.

What is the probability of picking up a black pen?

Ans ______________

[2 marks]

8. A farmer has enough hay to feed 12 cows for 10 days.

He buys 3 more cows. How many days will the same hay last?

Ans ___________ days

[2 marks]

9. Calculate the value of x.

°

Ans x = __________

[3 marks]

END OF PAPER

50° x°

Mathematics – Main – Form 3 Secondary – Track 3 – 2014 Page 1 of 10

DIRECTORATE FOR QUALITY AND STANDARDS IN EDUCATION Department for Curriculum Management

Educational Assessment Unit

Annual Examinations for Secondary Schools 2014

FORM 3 MATHEMATICS TIME: 1h 30min

Main Paper

Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total

Main

Non

Calc Global

Mark

Mark

DO NOT WRITE ABOVE THIS LINE

Name _____________________________________ Class _______________

1. This Speed/Time graph illustrates the journey of a car between a set of traffic lights and

a zebra crossing.

a) What is the maximum speed reached? Ans: ____________m/s

b) For how long does the car move at constant speed? Ans: ____________sec

c) How long does the car take to brake? Ans: ____________sec

d) How long does it take to drive from the traffic lights to the zebra crossing?

Ans: ____________sec

[4 marks]

spee

d (m

/s)

15

10

5

0 20 40 60 80 100

Time (seconds)

CALCULATORS ARE ALLOWED BUT ALL NECESSARY WORKING MUST BE SHOWN.

ANSWER ALL QUESTIONS.

Track 3

of 10 Mathematics – Main – Form 3 Secondary – Track 3 – 2014

2. During a survey, 20 students were asked about the number of hours that they spend

watching TV daily.

Stu

den

ts

8

7

6

5

4

3

2

1

0 1 2 3 4

Number of hours watching TV

a) Complete the bar chart above to show all the information collected.

b) Find the probability that a student chosen at random does not watch TV.

Ans: ______________

c) Find the mean number of hours that students spend watching TV daily.

Ans: __________ h

[6 marks]

3. The supermarket Buy 4 Less is offering a discount of €15 with every €80 spent.

The supermarket Best Deal is offering a discount of 16% on the total bill.

Emily’s shopping bill is €83.95. At which supermarket would she get the best offer?

Ans: ______________

[2 marks]


4. a) i. Round each of the following numbers correct to 1 significant figure:

21.83 ___________________

9.53 ___________________

98.1 ___________________

ii. Hence find an estimate for:

1.98

)53.9(83.21 2

Ans: ______________

iii. Now work out the above using your calculator and give your answer correct to

3 decimal places.

Ans: ______________

iv. Was the rough estimate a good approximation to the actual answer?

Explain your reasoning.

b) A group of friends shared a restaurant bill equally among them.

They worked out the calculation on their mobile calculators and rounded the answer

correct to 2 decimal places.

Explain why they chose to correct the answer to 2 decimal places and not to 2

significant figures.

[6 marks]

Name: ____________________________________ Class: _______________

Track 3


5. John is playing a computer game. John has to jump over obstacles.

When he jumps over an obstacle successfully he is awarded 3 points.

When he hits the obstacle or misses it, a point is subtracted from his total.

Let x be the number of obstacles that John jumps over successfully and y the number of

obstacles that he hits or misses.

a) There are 22 obstacles in one game. Write an equation to show this information.

Ans: ______________

b) At the end of the game John writes the equation 3x – y = 42.

What does this equation tell you?

c) Solve the equations in (a) and (b) simultaneously to find the number of obstacles

that John jumps over successfully.

Ans: ________ obstacles

d) John draws the graphs of

equations in (a) and (b).

Explain how you can use

these graphs to check that

your answer in (c) is correct.

[5 marks]

x

y

-2 O 2 4 6 8 10 12 14 16 18 20 22 24

-2

2

4

6

8

10

12

14

16

18

20

22


2x + 5

6. a) Expand: i. 5x(x + 2y) ii. (x + 3)(x – 1)

Ans: _______________ Ans: __________________

b) Factorise and simplify:

Ans: __________________

c) i. Write and simplify an expression for the perimeter of ΔABC.

Factorise your answer.

Ans: __________________

ii. Amanda notices that ΔABC above is an isosceles triangle with AB = BC.

Write an equation and solve it to find x.

Ans: x = _______________

[9 marks]

Name: ____________________________________ Class: _______________

Track 3

3x – 11

B

C

A

9x

3x2 + 2xy

5xy


7. Look at these patterns.

Pattern 1 Pattern 2 Pattern 3

a) Draw the next two patterns.

b) Write the next 3 terms of the sequence of the number of circles used in each pattern.

Ans: 4 , 7 , ______, ______, ______

c) Find a formula for the nth

term of this sequence.

Ans: _________________

d) Calculate the total number of circles needed to make the 25th

pattern.

Ans: ____________ circles

[7 marks]

8. The angles in a triangle are in the ratio 5 : 3 : 1.

a) What type of triangle is it? Ans: ______________

b) Calculate the biggest angle of this triangle.

°

Ans: _____________

[3 marks]


9. Beans come in cylindrical tins of radius of 6.5 cm and height 12 cm.

a) Calculate the volume of a tin.

Give your answer correct to 3 significant figures.

Ans: _____________ cm3

b) The curved part of the cylindrical tin is all covered with a label.

Find the area of the label, giving your answer correct to the nearest cm2.

Ans: _____________ cm2

[4 marks]

10. a) The formula for the sum of the Interior Angles of any polygon is 180n – 360, where

n is the number of sides.

Use this formula to complete the following table:

Shape

Sum of Interior Angles 180° 360°

b) Use your answer in (a) to find the angle marked x in the polygon below.

°

Ans: x = _____________

[4 marks]

125°

117°

95° 176°

x


11.

a) Underline the correct answer.

The curve above is the graph of :

(A) y = x + 5 (B) y = x2 – 5x + 5 (C) y = 5 – x

3

b) What is the minimum value of the graph? Ans: ________________

c) Underline the correct answer.

Which of the following is the equation of the line of symmetry of this graph?

(A) y = x (B) y = 2.5 (C) x = 2.5

d) Use your graph to find the values of x when y = 2.

Ans: x = ___________ , ___________

[5 marks]

0 1 2 3 4 5 x

y

5

4

3

2

1

1

2


12. Amanda uses the formula below to find the simple interest on a sum of money.

I = 100

PTR

a) Make T subject of the formula.

Ans: T = ___________

b) Amanda deposits a sum of €2565 at a rate of interest of 3.5% p.a.

After how many years will Amanda gain a simple interest of €718.20?

Ans: ______________ years

[4 marks]

13. A flagpole AB is held in a vertical

position with 2 cables of equal length,

attached to its top and at points X and Y

on the ground.

The cables are 8.3 m long and points X

and Y are 5.8 m away from each other.

Calculate the angle at A, between the two

cables. Give your answer correct to the

nearest degree.

°

Ans: ______________

[5 marks]

A

Y

X

B


14. Ship A is 18.2 km South of lighthouse L.

Ship B is to the East of lighthouse L and on a bearing of 042° from A.

Work out the distance, correct to 1 decimal place, of ship B from

lighthouse L.

Ans: ___________ km

[3 marks]

15. A courtyard 10 m wide and 12 m long has a spotlight in

each of its 4 corners.

Each spotlight lights up a sector of radius 8 m, as shown.

a) When only one of the spotlights is on, what percentage

of the courtyard is lit?

Give your answer correct to 3 significant figures.

Ans: ___________ %

b) Calculate the distance between any two spotlights which are diagonally opposite

each other. Give your answer correct to 3 significant figures.

Ans: ___________ m

c) When all the 4 spotlights are on, is the whole courtyard lit? Explain your answer.

[8 marks]

L

North

form 3 mathematics time: 30 minutes non calculator paper

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