YEAR 9 MATHEMATICS TIME: 30 minutes Non Calculator Paper

[Pages:14]DIRECTORATE FOR QUALITY AND STANDARDS IN EDUCATION Department of Curriculum Management Educational Assessment Unit

Annual Examinations 2017

Track 3

YEAR 9

MATHEMATICS Non Calculator Paper

TIME: 30 minutes

Question 1

2

3

4

5

6

7 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. All necessary working must be shown.

1. a) Tick () the numbers that are in standard form.

6.2 ? 105

82.3 ? 104

8.0 ? 103

0.42 ? 102

3.75 ? 101

b) Write one of the numbers that you selected as an ordinary number.

Ans: _______________ = ___________________

Standard Form

Ordinary Number

[3 marks]

2. Mark invests 5 000 for 2 years at a simple interest rate of 2.5% p.a. Work out the interest that he receives after 2 years.

Ans: ______________ [2 marks]

3. a) John uses 300 g of ham to prepare sandwiches for a party of ten children. How much more ham does he need if the guests are increased to 18 children?

Ans: _________ grams

b) 4 workers can paint a fence in 3 hours. If everyone works at the same rate, how long will it take 6 workers to paint the same fence?

Page 2 of 4

Ans: _________ hours [5 marks]

Mathematics ? Non Calculator Paper ? Year 9 ? Track 3 ? 2017

4. a) Factorise completely 15x2 ? 10xy2

Ans: _______________

152 ? 102

b) Simplify

5

Ans: _______________

152 ? 102

c) Hence or otherwise find the value of

5

when x = 2 and y = 3.

Ans: _______________ [5 marks]

5. a) Write 32 as a fraction.

b)

Work out

+

,

giving

your

answer

as

a

mixed

number.

Ans: _________

c) Evaluate i) 140 53?55

ii) 56

Mathematics ? Non Calculator Paper ? Year 9 ? Track 3 ? 2017

Ans: _________ Ans: _________

Ans: _________ [6 marks]

Page 3 of 4

6. A 5 cm B

12 cm

a) Write down the length of AC. Ans: AC = ___________ cm

b) If AC = 2x + 5, work out the value of x. C

7. This is the graph of y = 3x ? x2. y

Ans: x = ____________ [3 marks]

0

x

y = 3x ? x2

Use your graph to solve the equation 3x ? x2 = ?3. Ans: x = _________ or __________ [1 mark]

END OF NON CALCULATOR PAPER

Page 4 of 4

Mathematics ? Non Calculator Paper ? Year 9 ? Track 3 ? 2017

DIRECTORATE FOR QUALITY AND STANDARDS IN EDUCATION Department of Curriculum Management Educational Assessment Unit

Annual Examinations 2017

Track 3

YEAR 9

MATHEMATICS Main Paper

TIME: 1h 30min

Question 1

2

3

4

5

6

7

8

9

Total Non Global Main Calc Mark

Mark

DO NOT WRITE ABOVE THIS LINE

Name: _____________________________________

Class: _______________

Calculators are allowed but all necessary working must be shown. Answer ALL questions.

1. Two dice, one 4-sided and another 6-sided, are tossed. The numbers obtained are multiplied.

a) Fill in the possibility space to show all the products obtained.

4-sided dice

6-sided dice

?

1

2

3

4

5

6

2

2

4

6

8

10 12

3

3

12

5

5

15

30

7

7

35

b) Work out the probability that the two dice give a square number as a product. Ans: ______________

c) What is the probability of obtaining a product which is an even multiple of 3? Ans: ______________ [3 marks]

Mathematics ? Main Paper ? Year 9 ? Track 3 ? 2017

Page 1 of 10

2. Thea uses the formula S = 180n ? 360 to find the sum, S, of the interior angles of a polygon with n sides. a) i) Make n the subject of the formula.

Ans: n = ______________ ii) The interior angles of Thea's regular polygon add up to 1440?.

Show that her polygon is a decagon (10 sides).

b) Thea creates a tessellation pattern around her regular decagon, using regular pentagons. Part of her pattern is shown below. i) Work out the value of each interior angle x.

? Ans: x = __________

ii) Use Thea's formula for the sum, S, of the interior angles of a polygon, to calculate the value of angle y.

Page 2 of 10

? Ans: y = __________ iii) Explain why it was possible for Thea to create this tessellation. ___________________________________________________ ___________________________________________________

[8 marks]

Mathematics ? Main Paper ? Year 9 ? Track 3 ? 2017

Name: ____________________________________

Class: _____________

3. John is forming patterns with black and white circles as shown below.

Track 3

Pattern 1

Pattern 2

Pattern 3

Pattern 4

a) Draw the 4th Pattern. b) Fill in the following table.

Pattern number 1

2

3

4

5

Black Circles 2

White Circles 2

Total number of circles 4

c) Fill in the blanks. In the 8th Pattern John will use _______ black circles and_______ white circles, that is a total of ______ circles in all.

d) Write down the nth terms for the following sequences. i) The number of black circles used ____________________ ii) The number of white circles used ____________________ iii) The total number of circles used ____________________

e) John notices that the total number of circles is always even. Explain why this happens.

____________________________________________________________________

____________________________________________________________________

[10 marks]

Mathematics ? Main Paper ? Year 9 ? Track 3 ? 2017

Page 3 of 10

4. Ship S is sailing 75 km away from Harbour H, on a bearing of 036?. Tanker T is 48 km away from Harbour H on a bearing of 306?. a) Fill in all the above details in the rough sketch below to show the positions of the ship S and the tanker T.

N

H

? b) Fill in the blanks. The bearing of harbour H from tanker T is___________ .

c) Explain why THS = 90?.

d) Calculate HST.

e) Work out the distance between the tanker and the ship.

? Ans: _____________

Page 4 of 10

Ans: __________ km [10 marks]

Mathematics ? Main Paper ? Year 9 ? Track 3 ? 2017

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