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NAPLAN-style Numeracy Practice Test 1 (Year 9) — Answers

Answer sheet with worked solutions for the Year 9 number practice test.

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Year 9 · Mathematics · Number

NAPLAN-style Numeracy Practice Test 1 (Year 9) — Answers

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Part A — Index Laws

1.Simplify: 6x3 × 3x2[1 mark]

Answer: 18x5

6 × 3 = 18; add the indices: 5

2.Simplify: (x4)4[1 mark]

Answer: x16

Multiply the indices: 4 × 4 = 16

3.Simplify: 5x7 × 5x7[1 mark]

Answer: 25x14

5 × 5 = 25; add the indices: 14

Part B — Scientific Notation

4.Write 9,100 in scientific notation.[1 mark]

Answer: 9.1 × 103

Move the decimal point 3 places.

5.Write 1.4 × 103 as an ordinary number.[1 mark]

Answer: 1,400

6.Write 2.4 × 105 as an ordinary number.[1 mark]

Answer: 240,000

Part C — Expanding Brackets

7.Expand and simplify: (x − 2)(x − 9)[2 marks]

Answer: x2 − 11x + 18

  1. x × x = x2
  2. x × −9 + −2 × x = −11x
  3. −2 × −9 = 18
8.Expand and simplify: (x + 2)(x + 3)[2 marks]

Answer: x2 + 5x + 6

  1. x × x = x2
  2. x × 3 + 2 × x = 5x
  3. 2 × 3 = 6
9.Expand and simplify: (x − 2)(x − 2)[2 marks]

Answer: x2 − 4x + 4

  1. x × x = x2
  2. x × −2 + −2 × x = −4x
  3. −2 × −2 = 4

Part D — Solving Linear Equations

10.6(x − 2) = −36[2 marks]

Answer: x = −4

  1. Expand: 6x − 12 = −36
  2. Add 12: 6x = −24
  3. Divide by 6: x = −4
11.3x + 6 = 2x + 14[2 marks]

Answer: x = 8

  1. Subtract 2x from both sides: x + 6 = 14
  2. Subtract 6: 1x = 8
  3. Divide by 1: x = 8
12.5x − 2 = 4x − 6[2 marks]

Answer: x = −4

  1. Subtract 4x from both sides: x − 2 = −6
  2. Add 2: 1x = −4
  3. Divide by 1: x = −4

Part E — Pythagoras' Theorem

13.A right-angled triangle has shorter sides of 8 cm and 15 cm. Find the length of the hypotenuse.[2 marks]

Answer: 17 cm

  1. c2 = 82 + 152
  2. c2 = 64 + 225 = 289
  3. c = √289 = 17
14.A right-angled triangle has shorter sides of 12 cm and 16 cm. Find the length of the hypotenuse.[2 marks]

Answer: 20 cm

  1. c2 = 122 + 162
  2. c2 = 144 + 256 = 400
  3. c = √400 = 20

Part F — Percentage of an Amount

15.A jacket costs $450. It is reduced by 4% in a sale. What is the sale price?[2 marks]

Answer: $432.00

  1. Discount: 4% of 450 = 18
  2. 450 − 18 = 432.00
  3. (Or: 96% × 450 = 432.00)
16.A jacket costs $600. It is reduced by 45% in a sale. What is the sale price?[2 marks]

Answer: $330.00

  1. Discount: 45% of 600 = 270
  2. 600 − 270 = 330.00
  3. (Or: 55% × 600 = 330.00)
17.A jacket costs $290. It is reduced by 15% in a sale. What is the sale price?[2 marks]

Answer: $246.50

  1. Discount: 15% of 290 = 43.5
  2. 290 − 43.5 = 246.50
  3. (Or: 85% × 290 = 246.50)

Part G — Ratio

18.Simplify the ratio 8 : 64[1 mark]

Answer: 1 : 8

  1. HCF of 8 and 64 is 8
  2. Divide both parts by 8
19.Simplify the ratio 2 : 16[1 mark]

Answer: 1 : 8

  1. HCF of 2 and 16 is 2
  2. Divide both parts by 2
20.Divide $24 in the ratio 1 : 3.[2 marks]

Answer: $6 and $18

  1. Total parts: 1 + 3 = 4
  2. One part: 24 ÷ 4 = 6
  3. 1 × 6 = 6 and 3 × 6 = 18

Part H — Area and Perimeter

21.A rectangle is 7 cm long and 13 cm wide. Find its area.[2 marks]

Answer: 91 cm2

  1. A = length × width = 7 × 13
  2. = 91 cm2
22.A triangle has a base of 14 m and a perpendicular height of 4 m. Find its area.[2 marks]

Answer: 28 m2

  1. A = ½ × base × height = ½ × 14 × 4
  2. = 28 m2

Part I — Mean, Median, Mode and Range

23.Data: 26, 45, 45, 33, 23, 16, 26, 45. Find the (a) mean, (b) median, (c) mode and (d) range.[2 marks]

Answer: mean 32.38; median 29.5; mode 45; range 29

  1. Mean: 259 ÷ 8 = 32.38
  2. Ordered: 16, 23, 26, 26, 33, 45, 45, 45 → median 29.5
  3. Mode: 45
  4. Range: 45 − 16 = 29
24.Data: 15, 1, 3, 30, 29, 22. Find the (a) mean, (b) median, (c) mode and (d) range.[2 marks]

Answer: mean 16.67; median 18.5; mode no mode; range 29

  1. Mean: 100 ÷ 6 = 16.67
  2. Ordered: 1, 3, 15, 22, 29, 30 → median 18.5
  3. Mode: no mode
  4. Range: 30 − 1 = 29

Part J — Probability

25.A bag has 4 red, 1 blue and 5 green marbles. One is chosen at random. What is the probability it is green?[2 marks]

Answer:

  1. Total marbles: 10
  2. P(green) = 5/10 =
26.A fair six-sided die is rolled. What is the probability of rolling a multiple of 3?[2 marks]

Answer:

  1. Favourable outcomes: 2 out of 6
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