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Name: ___________________

Newcastle Mathematics Association

STAGE 5⋅1

MATHEMATICS COMPETITION

2019

Time allowed – 75 minutes. Directions to Candidates

:

Attempt all questions. Board-approved calculators are allowed. Section 1

• Section 1 is worth 40 marks. • Section 1 consists of 40 multiple choice questions worth 1 mark each. • Please answer all questions on the multiple choice answer sheet provided by circling the

correct answer. Section 2

• Section 2 is worth 30 marks. • Section 2 consists of 30 short answer questions worth 1 mark each. • Please answer all questions in the spaces provided.

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2019 Stage 5⋅1 Mathematics Competition Paper

Section 1

• Section 1 is worth 40 marks. Instructions:

• Section 1 consists of 40 multiple choice questions worth 1 mark each. • Please answer all questions on the multiple-choice answer sheet provided by circling the

correct answer. ________________________________________________________________________ 1. Name the type of graph shown below.

(A) Column graph (B) Travel graph (C) Pie graph (D) Bar graph ________________________________________________________________________ 2. Evaluate 32 . (A) 4 (B) 6 (C) 8 (D) 16 ________________________________________________________________________

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3. Simplify 𝑥 + 2𝑎 + 2𝑥 + 4𝑎. (A) 6𝑎 + 2𝑥2 (B) 6𝑎 + 3𝑥 (C) 8𝑎2 + 2𝑥2 (D) 12𝑎2𝑥2 ________________________________________________________________________ 4. Round 419 correct to the nearest ten. (A) 410 (B) 420 (C) 400 (D) 500 ________________________________________________________________________ 5. A marble is selected from a bag containing 3 red, 4 blue and 5 green marbles. What is the probability of drawing out a purple marble?

(A) 0 (B) 712

(C) 1 (D) 13

______________________________________________________________________________ 6. Which of the following is the net of a rectangular prism? (A) (B)

(C) (D) 7. Write 12⋅25% as a decimal. (A) 12⋅25 (B) 1⋅225 (C) 0⋅1225 (D) 0⋅01225 ______________________________________________________________________________

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8. For the following stem-and-leaf display, what is a possible value for the missing number (∆ ). Stem Leaf

5 1 2 3 5 6 ∆ 6 0 1 2 3 5 6 7 7 0 1 2 2 3 6 8 9 8 2 2 3 9 0 1 2

(A) 56 (B) 57 (C) 5 (D) 7 ______________________________________________________________________________ 9. What fraction of the following shape is shaded?

(A) 1 (B) 14

(C) 18

(D) 116

______________________________________________________________________________ 10. Classify DBA∠ as shown below.

(A) Acute (B) Obtuse (C) Right (D) Straight ______________________________________________________________________________ 11. Solve: 4x 1 11− = (A) x 2= (B) x 3= (C) x 4= (D) x 5= ______________________________________________________________________________ 12. Write 23:59h in am/pm time. (A) 11:59 am (B) 11:59 pm (C) 00:59h (D) 12:59h ______________________________________________________________________________

A

B C D

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13. Write . x 34 56 10 as a basic numeral. (A) 4⋅5 (B) 45⋅6 (C) 456 (D) 4560 ______________________________________________________________________________ 14. Given that a : b = 7 : 8 and b : c = 8 : 9 then what is a : c ?

(A) 7 : 8 (B) 8:8 (C) 1 : 1 (D) 7:9 _____________________________________________________________________________ 15. The weather forecast for Sydney for one week from 13th July 2019 is shown below. Which day has the largest temperature range?

(a) Monday (B) Tuesday (C) Wednesday (D)Thursday

______________________________________________________________________________ 16. Calculate the Perimeter of the following shape.

(A) 40 m2 (B) 14 m (C) 14 m2 (D) 28 m ______________________________________________________________________________ 17. Using the formula I = PRN, calculate the simple interest earned on an investment of $100 000 over 5 years at 3% p.a.

(A) $3 000 (B) $15 000 (C) $103 000 (D) $115 000 ______________________________________________________________________________ 18. Students were asked to arrange the measurements 5mL, 0⋅5L, 50mL, 5L in descending order. Which arrangement is correct? (A) 5mL, 0⋅5mL, 50mL, 5L (B) 5L, 0⋅5L, 50mL, 5mL (C) 5mL, 50mL, 0⋅5L, 5L (D) 5L, 50mL, 0⋅5L, 5mL ______________________________________________________________________________

10 m

4 m

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19. Meghan is paid $250 000 p.a. Calculate her income per fortnight. (A) $20 833⋅33 (B) $4 807⋅69 (C) $9 615⋅38 (D) $5 208⋅33 ______________________________________________________________________________

20. The following table is the NRL ladder for the 2019 NRL season on 12th July 2018

Note: P = Played W = Win D = Draw L = Loss

What percentage of games played have the Knights won? (A) 46⋅67 % (B) 53⋅33% (C) 0⋅4667% (D) 0⋅5333%

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21. Expand ( )2x x 5− . (A) 2x (B) 210x− (C) 22x 10x− (D) 2 22 10x x− ______________________________________________________________________________ 22. Cadbury Fruit and Nut chocolate comes in a 50g pack at $1/each, and a 350g pack at $4.50/each. How many extra grams of chocolate do you get by buying the 350g pack in preference to six of the 50g pack?

(A) 50g (B) 100g (C) 150g (D) 250g ______________________________________________________________________________ 23. Which of the following statements IS NOT true? (A) x m n m na a a += (B) 0a 1= (C) m n m na a a ÷÷ = (D) ( )m n mna a=

_____________________________________________________________________________________________________________________

24. Find the length of the unknown side in the diagram below (to the nearest metre).

(A) 41 m (B) 841 m (C) 20⋅5 m (D) 29 m ______________________________________________________________________________ 25. At a local supermarket, a 375g jar of Sanitarium Natural Crunchy Peanut Butter costs $4.05 what is the price per 100 grams?

(A) $0⋅0405 (B) $0⋅0108 (C) $1⋅08 (D) $4⋅05

21 m

x 20 m

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26. The graph below shows Lithium Carbonate (used in batteries) prices from 2000 to 2024(estimated)

What is the best way to describe the trend in lithium prices? (A) declining (B) fairly constant (C) there is no trend (D) steadily increasing _____________________________________________________________________________ ______________________________________________________________________________ 27. Choose the best name for the following shape: (A) Parallelogram (B) Rectangle (C) Rhombus (D) Kite

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28. Find the median of 4, 5, 5, 5, 7, 8, 9, 10 (A) 5 (B) 6 (C) 7 (D) 8 ______________________________________________________________________________ 29. Two coins are tossed at the same time.

What best describes the chance of having two tails landing facing up?

(A) Certain (B) Even chance (C) Better than an even chance (D) Less than an even chance ______________________________________________________________________________ 30. What is the correct simplification of: 5 59x 4x− ? (A) 0 (B) 5 (C) 513x (D) 55x ______________________________________________________________________________

Red

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31. The travel graph below is of Dan’s walking trek.

How long did Dan rest for in total? (A) ½ hour (B) 1 hour (C) 1⋅5 hours (D) 2 hours ______________________________________________________________________________ 32. How many digits in the following phone number are odd?

0415 044 133

(A) 3 (B) 4 (C) 5 (D) 6 ______________________________________________________________________________ 33. The following is the net of a:

(A) Circle (B) Cylinder (C) Cone (D) Sphere _____________________________________________________________________________

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34. KFC have Colonel’s table meal deals for those who download and use their app.

This normally costs $12⋅20. When paying full price, 4 meals costs $48⋅80. How many more meals can you buy using the Colonel’s table meal deal for $48⋅80?

(A) one (B) two (C) three (D)four ________________________________________________________________ 35. How many sixes (6) must be added together to get a number more than 30 but less than 39? (A) 5 (B) 6 (C) 7 (D) 8 ______________________________________________________________________________ 36. Find the value of a - b + c if a = 5, 2b = − , and c = 3. (A) 6 (B) 4 (C) 10 (D) 0 ______________________________________________________________________________ 37. Some test scores are recorded below:

Class scores Frequency 50 5 51 7 52 9 53 2

The total frequency for this set of scores is (A) 206 (B) 23 (C) 5⋅75 (D) 51⋅75 ______________________________________________________________________________

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38. Find the area of the following shape: (A) 660 cm2 (B) 330 cm2 (C) 132 cm2 (D) 40260 cm2 ______________________________________________________________________________ 39. A store is having a “5% off everything” sale. Calculate the sale price of an item that has an original price of $100.

(A) $5⋅00 (B) $105⋅00 (C) $95⋅00 (D) $90⋅25 ______________________________________________________________________________ 40. Movie session times can be found on the Internet…

The movie Avengers Endgame runs for 181 minutes.

Write this time in hours and minutes. (A) 1 hr 81 mins (B) 2 hrs 21 mins (C) 3 hours (D)3 hrs 1 min ______________________________________________________________________________

End of Section 1

61 cm

60 cm

11 cm

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2019 Stage 5⋅1 Mathematics Competition Paper

Section 2

• Section 2 is worth 30 marks. Instructions:

• Section 2 consists of 30 short answer questions worth 1 mark each. • Please answer all questions in the spaces provided.

___________________________________________________________________________

1. Using a dot, mark the position of the fraction 79100

on the number line below.

______________________________________________________________________________ 2. Find the missing number ( )∆ in the pattern below: 7 x 103 = 7000 7 x 102 = 700 7 x 101 = 70 7 x 100 = ( )∆ 7 x 10-1 = 0.7 7 x 10-2 = 0.07 7 x 10-3 = 0.007 ___________________________________________________________________________ 3. Find the size of x in the diagram below.

30o

x

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4. Evaluate: . .2 97 1 9913− correct to 2 decimal places.

______________________________________________________________________________

5. Write the reciprocal of 56

.

______________________________________________________________________________ 6. Write “two million, five hundred and ten thousand, and eighty-eight” as a numeral. ______________________________________________________________________________ 7. Arrange the following set of scores in ascending order.

555, -0⋅5, 0⋅55, 0⋅555, 55 ______________________________________________________________________________ 8. The following advertisement appears at a supermarket during a sale.

How much will a block of Cadbury’s Chocolate that normally costs $5 be while the sale is on?

______________________________________________________________________________ 9. How many faces does the following rectangular pyramid have?

______________________________________________________________________________

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10. The Hugh Jackman ‘The man. The music. The show’ tour is selling tickets from $57⋅10 for the ‘cheap seats’ to $699 for the ‘Diamond VIP reception’ tickets. How many ‘cheap seats’ could you get for the price of one ‘Diamond VIP reception’ ticket?

______________________________________________________________________________ 11. Complete the rule for the table of values below. Tip: the equation is of the form y = mx + b

x 0 1 2

y 2 5 8

y =

_____________________________________________________________________________

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12. The following graph shows the height of males aged 2 to 20 in the U.S.A. If a 10-year-old boy is 150cm tall, how tall would we expect him to be when he is 20 years

old? (answer to the nearest cm)

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13. Find the volume of the shape below.

_____________________________________________________________________________ 14. There are 16 truffles in a Lindt 200g truffle pack. The pack costs $14⋅17, what is the cost per truffle? (to the nearest cent)

_____________________________________________________________________________

30 cm2

15 cm

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15. If the following shape is cut across the dotted line, name the shapes that are formed.

____________________________________________________________________ 16. The new Sydney Metro train system (M) is shown below. Travelling from Chatswood to Castle Hill, how many stops are there after Chatswood

(including Castle Hill)

_____________________________________________________________________ 17. Expand and simplify: 5(a - 1) + 7(2a + 5) ____________________________________________________________________________

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18. The heights of 20 students (in cms) were recorded below.

168, 168, 169, 169, 169, 169, 172, 172, 173, 173 174, 180, 180, 181, 182, 184, 189, 187, 191, 192

Find the value of A in the grouped frequency distribution table below.

Class Frequency (f) 160-69 A 170-79 5 180-89 7 190-99 2

Total = 20 A= ………. ______________________________________________________________________________ 19. Use your calculator to find the value of cos 22⋅5o to 3 decimal places. ____________________________________________________________________________ 20. Two congruent shapes are shown below. Insert one of the words listed in the box to make the statement true.

Rotated, Reflected or Translated Both shapes are congruent because Shape A can be to create shape B. ________________________________________________________________________

Shape A Shape B

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21. A Rubix cube is a cube made up of smaller cubes. How many smaller cubes make up one Rubix cube?

________________________________________________________________________ 22. In a magic square, the numbers in every row, column and diagonal have the same total. Find the missing numbers in the magic square below (only positive numbers are needed), if each row, column and diagonal has a total equal to 15. Note – each number from 1 to 9 can be used only once.

2 6

9 5

______________________________________________________________________________ 23. Write the smallest four-digit number that can be formed from the digits 9, 0, 3, 5. ______________________________________________________________________________ 24. In a class, two-thirds of the students walk to school, the rest take the bus. If twenty students walk to school, how many students are in the class altogether? ____________________________________________________________________________

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25. 290 mL of water is to be poured into the cylinder below. Draw a line on the cylinder below to show the level the water would reach.

______________________________________________________________________________ 26. Susan and Philip share $720 000 in the ratio 3:2. How much money will Susan receive? ______________________________________________________________________________ 27. Name the type of angles (marked x and y in the diagram) formed by the parallel lines and transversal below:

______________________________________________________________________________

x

y

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28. What do you have to do to a Kite to turn it into a Rhombus? ______________________________________________________________________________

29. Complete the following statement: “The smallest side in a triangle is opposite the ____________ angle. ______________________________________________________________________________

30. A metal container holding a toxic chemical initially contained 5 Litres but has now expanded to 5⋅29 Litres due to gases building up. The 5 Litre container allowed for 10% expansion. Explain whether the container is still safe.

End of Section 2 and Test