Test 6 Year 8 measurement 2024.docx

**Year 8 Mathematics 2024** **Topic: Measurement Test** **Test 6-- (10%)\ ** **Time Allowed** 50 minutes **First Name Surname\ ** **Marks** 57 marks +-----------------------------------------------------------------------+ | **[Assessment Conditions:] *(N.B. [Working out must be | | shown...

**Year 8 Mathematics 2024** **Topic: Measurement Test** **Test 6-- (10%)\ ** **Time Allowed** 50 minutes **First Name Surname\ ** **Marks** 57 marks +-----------------------------------------------------------------------+ | **[Assessment Conditions:] *(N.B. [Working out must be | | shown to gain full marks])*** | | | | +------------------------------------------------------------------+ | | | - Calculators: Allowed | | | | | | | | - Formula Sheet: Not Provided | | | | | | | | | | | | | | | | - Notes: Allowed (1 A4 Page, Single Sided) | | | | | | | | - Special Equipment Required: None | | | +------------------------------------------------------------------+ | +-----------------------------------------------------------------------+ **Question 1 *Circle the correct answer* (5 marks)** A. **The internal angle sum of a quadrilateral is always equal to;** a. [**90**^**∘**^]{.math.inline} **b.** [**180**^**∘**^]{.math.inline} **c.** [**270**^**∘**^]{.math.inline} **d.** [**360**^**∘**^]{.math.inline} B. **The internal angle sum of a triangle is always equal to;** C. **The number of sides equal in an equilateral triangle is;** D. **The number of sides equal in a scalene triangle is;** a. **0 b.** [**2**]{.math.inline} **c.** [**3**]{.math.inline} **d. *none of these*** E. **The number of right angles in a right angled triangle is:** a. **1 b.** [**2**]{.math.inline} **c.** [**3**]{.math.inline} **d. *none of these*** **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Question 2 (1, 2, 3 = 6 marks)** Determine the **perimeter** of each of the following. Show all working out. +-----------------------------------+-----------------------------------+ | a) | | | | | |  | | +===================================+===================================+ | b) | | | | | | c) | | | | | |  | | +-----------------------------------+-----------------------------------+ | | | +-----------------------------------+-----------------------------------+ **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ ** +-----------------------------------------------------------------------+ | Question 3 (2 marks) | | | | What is the area of the kite? | +=======================================================================+ | | +-----------------------------------------------------------------------+ | | +-----------------------------------------------------------------------+ | | +-----------------------------------------------------------------------+ **Question 4 (2, 3 = 5 marks)** Calculate the **circumference/perimeter** of the following shapes. Show all working out. Round answers to **2 decimal places** where needed. +-----------------------------------+-----------------------------------+ | a) | | | | | | b) | | | | | | \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ | | | _\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ | | | \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ | | | _\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ | | | \_\_\_\_\_\_\_\_\_ | | +-----------------------------------+-----------------------------------+ **Question 5 (4 marks)** Convert the following measurements to the units indicated a. **2000 m = \_\_\_\_\_\_\_\_\_\_\_\_\_ km** b. **460 cm = \_\_\_\_\_\_\_\_\_\_\_\_\_ m** c. **15 mm = \_\_\_\_\_\_\_\_\_\_\_\_\_ cm** d. **2.56 km = \_\_\_\_\_\_\_\_\_\_\_\_\_ m** **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Question 6 (2, 2, 2, 3 = 9 marks)** Calculate the **area** of the following shapes. Show all working out. Round answers to **2 decimal places** where needed. a) +-----------------------------------+-----------------------------------+ | b) | | | | | | c) | | | | | | d) | | | | | | \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ | | | _\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ | | | \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ | | | _\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ | | | \_\_\_\_\_\_\_\_\_ | | +-----------------------------------+-----------------------------------+ **Question 7** **(3 marks**) The figure shows a triangle with a piece removed. Calculate the shaded area**.** **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** +-----------------------------------+-----------------------------------+ | **Question 8** | **(5 marks)** | | | | | Farmer Jim wants to create a | | | grain trough; he draws up the | | | following plans. | | | | | |  | | | | | | a. What is the shape of the | | | drinking trough? | | | | | | b. How much grain can this | | | trough hold? | | +===================================+===================================+ | | | +-----------------------------------+-----------------------------------+ **Question 9 (3 marks)** This rhombus has an area of 12 cm^2^. Find the missing length, *y*. **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Question** **10 (1, 1, 1, 1 = 4 marks)** a. If there are two brushstrokes every 2cm, how many brushstrokes would be in 10cm? b. How many millilitres are in a 1.5 litre bottle of hand cleaner? c. How many millimetres are in 1m? d. How many metres are in 3500 mm? **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Question** **11 (4 marks)** **A wall is created by stacking equal-sized rectangular bricks on top of each other as shown. The end of each rectangle sits exactly half-way along the long side of the rectangle underneath it.**  **A 500 ml tin of white paint has been purchased to paint the wall. The instructions on the paint tin say this is enough to cover an area of 11500** [*cm*^2^. ]{.math.inline} a. **Use calculations to show if there is enough paint in the tin to cover one side of the wall.** b. **Each brick is 28cm by 16cm by 10cm. An ant walks on the ground around the wall shown, how far does he walk?** **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Question 12 (7 marks)** A farmer wishes to sow paddocks with three different types of seed with different costs. - Barley seeds are \$0.04 per square metre - Oat seeds are \$0.06 per square metre - Corn seeds are \$0.09 per square metre What will the total cost of the seed for the three paddocks with the dimensions shown? **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **End of Test** +-----------------------+-----------------------+-----------------------+ | | **Year 8 Mathematics | | | | 2024** | | | | | | | | **Topic: Measurement | | | | Test** | | | | | | | | **Test 6-- (10%)** | | | | | | | | **SOLUTIONS\ | | | | ** | | +=======================+=======================+=======================+ | **Time Allowed** | **First Name Surname\ | **Marks** | | | ** | | | 50 minutes | | 57 marks | +-----------------------+-----------------------+-----------------------+ +-----------------------------------------------------------------------+ | **[Assessment Conditions:] *(N.B. Sufficient working out | | must be shown to gain full marks)*** | | | | +------------------------------------------------------------------+ | | | - Calculators: Allowed | | | | | | | | - Formula Sheet: Not Provided | | | | | | | | | | | | | | | | - Notes: Allowed (1 A4 Page, Single Sided) | | | | | | | | - Special Equipment Required: None | | | +------------------------------------------------------------------+ | +-----------------------------------------------------------------------+ **Question 1 *Circle the correct answer* (5 marks)** A. **The internal angle sum of a quadrilateral is always equal to;** B. **The internal angle sum of a triangle is always equal to;** C. **The number of sides equal in an equilateral triangle is;** D. **The number of sides equal in a scalene triangle is;** a. **0 b.** [**2**]{.math.inline} **c.** [**3**]{.math.inline} **d. *none of these*** E. **The number of right angles in a right angled triangle is:** a. **1 b.** [**2**]{.math.inline} **c.** [**3**]{.math.inline} **d. *none of these*** +-----------------------------------+-----------------------------------+ | **Solution** | | +===================================+===================================+ | **D, B, C, A, A** | | +-----------------------------------+-----------------------------------+ | **Behaviours** | | +-----------------------------------+-----------------------------------+ | - Correct answer for each = 1 | | | mark | | +-----------------------------------+-----------------------------------+ **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Question 2 (1, 2, 3 = 6 marks)** Determine the **perimeter** of each of the following. Show all working out. +-----------------------------------+-----------------------------------+ | a) | | | | | |  | | +===================================+===================================+ | b) | +--------------+--------------+ | | | | **Solution** | | | | c) | +==============+==============+ | | | | \ | | | |  | | [**a)** **P* | | | | | | * **=** **1. | | | | | | 5** **+** ** | | | | | | 6** **+** ** | | | | | | 1.5** **+**  | | | | | | **6**]{.math | | | | | |.display}\ | | | | | | | | | | | | \ | | | | | | [ **=** **15 | | | | | | **mm | | | | | | ]{.math | | | | | |.display}\ | | | | | | | | | | | | \ | | | | | | [**b)** **P* | | | | | | * **=** **3. | | | | | | 9** **+** ** | | | | | | 4.6** **+**  | | | | | | **3.9** **+* | | | | | | * **4.6** ]{ | | | | | |.math | | | | | |.display}\ | | | | | | | | | | | | **=17cm** | | | | | | | | | | | | \ | | | | | | [**c)** **P* | | | | | | * **=** **7* | | | | | | * **+** **8* | | | | | | * **+** **3. | | | | | | 5** **+** ** | | | | | | 3.5** **+**  | | | | | | **3.5** **+* | | | | | | * **4.5**]{. | | | | | | math | | | | | |.display}\ | | | | | | | | | | | | \ | | | | | | [ **=** **30 | | | | | | m**]{.math | | | | | |.display}\ | | | | | +--------------+--------------+ | | | | **Behaviours | | | | | | ** | | | | | +--------------+--------------+ | | | | a. Correct | | | | | | answer = | | | | | | 1 | | | | | | | | | | | | b. Shows | | | | | | correct | | | | | | answer = | | | | | | 1 | | | | | | | | | | | | Shows | | | | | | correct | | | | | | units = | | | | | | 1 | | | | | | | | | | | | c. Shows | | | | | | working | | | | | | out with | | | | | | correct | | | | | | missing | | | | | | side | | | | | | (4.5) = | | | | | | 1 | | | | | | | | | | | | Shows | | | | | | correct | | | | | | answer = | | | | | | 1 | | | | | | | | | | | | Shows | | | | | | correct | | | | | | units = | | | | | | 1 | | | | | +--------------+--------------+ | +-----------------------------------+-----------------------------------+ **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ ** +-----------------------------------+-----------------------------------+ | Question 3 (2 marks) | | | | | | ------------------------------- | | | What is the area of the kite? | | | ------------------------------- | | +===================================+===================================+ | **Solution** | | +-----------------------------------+-----------------------------------+ | \ | | | [\$\$\\frac{\\mathbf{1}}{\\mathbf | | | {2}}\\mathbf{\\text{xy}}\$\$]{.ma | | | th | | |.display}\ | | | | | | \ | | | [**0.5** **×** **70**  **×** **80 | | | **]{.math | | |.display}\ | | | | | | \ | | | [**2800** **cm**^**2**^]{.math | | |.display}\ | | +-----------------------------------+-----------------------------------+ | **Behaviours** | | +-----------------------------------+-----------------------------------+ | - Displays correct working | | | calculation = 1 | | | | | | - Displays correct answer with | | | correct units = 1 | | +-----------------------------------+-----------------------------------+ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ **Question 4 (2, 3 = 5 marks)** Calculate the **circumference/perimeter** of the following shapes. Show all working out. Round answers to **2 decimal places** where needed. +-----------------------------------+-----------------------------------+ | a) | | | | | | +--------------+--------------+ | | | | **Solution** | | | | | +==============+==============+ | | | | \ | | | | | | [**a)** **πd | | | | | | **]{.math | | | | | |.display}\ | | | | | | | | | | | | \ | | | | | | [**π**  **×* | | | | | | * **16**]{.m | | | | | | ath | | | | | |.display}\ | | | | | | | | | | | | \ | | | | | | [**50.27** * | | | | | | *mm**]{.math | | | | | |.display}\ | | | | | | | | | | | | \ | | | | | | [**b)** **πd | | | | | | ** **×** **0 | | | | | |.5** **+** * | | | | | | *d**]{.math | | | | | |.display}\ | | | | | | | | | | | | \ | | | | | | [**π**  **×* | | | | | | * **26**  ** | | | | | | ×** **0.5**  | | | | | | **+** **26** | | | | | | ]{.math | | | | | |.display}\ | | | | | | | | | | | | \ | | | | | | [**66.84** * | | | | | | *cm**]{.math | | | | | |.display}\ | | | | | +--------------+--------------+ | | | | **Behaviours | | | | | | ** | | | | | +--------------+--------------+ | | | | a. Displays | | | | | | Use of | | | | | | diameter | | | | | | in | | | | | | calculat | | | | | | ion | | | | | | = 1 | | | | | | | | | | | | Displays | | | | | | correct | | | | | | answer | | | | | | with | | | | | | correct | | | | | | units = | | | | | | 1 | | | | | | | | | | | | b. Displays | | | | | | -- ½ in | | | | | | calculat | | | | | | ion | | | | | | = 1 | | | | | | | | | | | | Correct | | | | | | working | | | | | | calculat | | | | | | ion | | | | | | = 1 | | | | | | | | | | | | Correct | | | | | | answer | | | | | | with | | | | | | correct | | | | | | units = | | | | | | 1 | | | | | +--------------+--------------+ | | | | | | b) | | | | | | \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ | | | _\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ | | | \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ | | | _\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ | | | \_\_\_\_\_\_\_\_\_ | | +-----------------------------------+-----------------------------------+ **Question 5 (4 marks)** Convert the following measurements to the units indicated a. **2000 m = 2 km** --------------------------------- **Solution** ------------------------------ -- \ [As Shown ]{.math.display}\ **Behaviours** Correct answer 1 mark each --------------------------------- b. **460 cm = 4.6 m** c. **15 mm = 1.5 cm** d. **2.56 km = 2560 m** **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Question 6 (2, 2, 2, 3 = 9 marks)** Calculate the **area** of the following shapes. Show all working out. Round answers to **2 decimal places** where needed. a. +-----------------------------------+-----------------------------------+ | **Solution** | | +===================================+===================================+ | \ | | | [**a)** **area** **=** **L**  **× | | | ** **W**]{.math | | |.display}\ | | | | | | \ | | | [**5.4**  **×** **2.3** ]{.math | | |.display}\ | | | | | | \ | | | [**12.42** **cm**^**2**^]{.math | | |.display}\ | | | | | | \ | | | [**b)**  **area=** **πr**^**2**^] | | | {.math | | |.display}\ | | | | | | \ | | | [**π** **×** **9** **×** **9**]{. | | | math | | |.display}\ | | | | | | \ | | | [**254.47m**^**2**^]{.math | | |.display}\ | | +-----------------------------------+-----------------------------------+ | **Behaviours** | | +-----------------------------------+-----------------------------------+ | a. Displays correct calculation | 2 | | = 1 | | | | | | Displays correct answer with | | | correct units = 1 | | | | | | b. Displays correct calculation | | | = 1 | | | | | | Displays correct answer with | | | correct units = 1 | | +-----------------------------------+-----------------------------------+ b) c) +-----------------------------------+-----------------------------------+ | **Solution** | | +===================================+===================================+ | \ | | | [**c)** **area** **=** **0.5**bh] | | | {.math | | |.display}\ | | | | | | \ | | | [**0.5**  **×** **3.1**  **×** ** | | | 6.8**]{.math | | |.display}\ | | | | | | \ | | | [**10.54** **cm**^**2**^]{.math | | |.display}\ | | | | | | \ | | | [**b)**  **area=** **πr**^**2**^  | | | **×** **0.25**]{.math | | |.display}\ | | | | | | \ | | | [**π** **×** **76**  **×** **76** | | |   **×** **0.25**]{.math | | |.display}\ | | | | | | \ | | | [**4536.459** **mm**^**2**^     * | | | *∴** **4536.46** **mm**^**2**^]{. | | | math | | |.display}\ | | +-----------------------------------+-----------------------------------+ | **Behaviours** | | +-----------------------------------+-----------------------------------+ | a. Displays correct calculation | 3 | | = 1 | | | | | | Displays correct answer with | | | correct units = 1 | | | | | | b. Displays Correct portion of a | | | circle = 1 | | | | | | Displays correct calculation | | | = 1 | | | | | | Displays correct answer with | | | correct units = 1 | | +-----------------------------------+-----------------------------------+ d) **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Question 7** **(3 marks**) The figure shows a triangle a with a piece removed. Calculate the shaded area**.** +-----------------------------------+-----------------------------------+ | **Solution** | | +===================================+===================================+ | \ | | | [ **area** **triangle** **=** **0 | | |.5**bh]{.math | | |.display}\ | | | | | | \ | | | [**0.5**  **×** **15**  **×** **2 | | | 5**]{.math | | |.display}\ | | | | | | \ | | | [**187.5m**^**2**^]{.math | | |.display}\ | | | | | | \ | | | [**area**  **square** **=** **lw* | | | *]{.math | | |.display}\ | | | | | | \ | | | [**8**  **×** **8**]{.math | | |.display}\ | | | | | | \ | | | [**64m**^**2**^]{.math.display}\ | | | | | | \ | | | [**Triangle** **−** **Square** ** | | | =** **187.5** **−** **64**]{.math | | |.display}\ | | | | | | \ | | | [**123.5m**^**2**^]{.math | | |.display}\ | | +-----------------------------------+-----------------------------------+ | **Behaviours** | | +-----------------------------------+-----------------------------------+ | Correct area of triangle = 1 | 3 | | | | | Correct area of a square = 1 | | | | | | Correct final answer with correct | | | units = 1 | | +-----------------------------------+-----------------------------------+ **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** +-----------------------------------+-----------------------------------+ | **Question 8** | | | | | | Farmer Jim wants to create a | | | grain trough; he draws up the | | | following plans. | | | | | |  | | | | | | a. What is the shape of the | | | drinking trough? | | | | | | b. How much grain can this | | | trough hold? | | +===================================+===================================+ | **Solution** | | +-----------------------------------+-----------------------------------+ | a. [Triangular prism]{.math | | |.inline} | | | | | | b. **Volume =** | | | [**0.5bh** **×** **l**]{.math | | |.inline} | | | | | | \ | | | [                                 | | |                        **1.8m** * | | | *=** **1800**cm]{.math | | |.display}\ | | | | | | \ | | | [                                 | | |   **0.5**  **×** **50**  **×** ** | | | 40**  **×** **1800**]{.math | | |.display}\ | | | | | | \ | | | [                                 | | |          **1** **800** **000** ** | | | cm**^**3**^]{.math | | |.display}\ | | +-----------------------------------+-----------------------------------+ | **Behaviours** | | +-----------------------------------+-----------------------------------+ | a. **Correct answer = 1** | | | | | | b. **Correctly coverts m to cms | | | = 1** | | | | | | **Displays a knowledge of the | | | correct formula = 1** | | | | | | **Displays correct | | | substitution into formula = | | | 1** | | | | | | **Correct answer with correct | | | units = 1** | | +-----------------------------------+-----------------------------------+ **Question 9 (3 marks)** This rhombus has an area of 12 cm^2^. Find the missing length, *y*. +-----------------------------------+-----------------------------------+ | **Solution** | | +===================================+===================================+ | \ | | | [\$\$\\mathbf{Area | | | =}\\frac{\\mathbf{1}}{\\mathbf{2} | | | }\\mathbf{\\text{xy}}\$\$]{.math | | |.display}\ | | | | | | **12 =** [\$\\frac{\\mathbf{4\\ | | | \\ \\times \\ \\ y\\ | | | }}{\\mathbf{2}}\\mathbf{\\ \\ \\ | | | \\ \\ \\ \\ or\\ \\ \\ \\ \\ \\ | | | \\ \\ \\ 12 = 0.5\\ \\times 4\\ | | | \\times y}\$]{.math.inline} | | | | | | [**24** **=** **4**  **×** **y**  | | | ]{.math | | |.inline} [ or ]{.math.inline} | | | [**12** **=** **2**  **×** **y**] | | | {.math | | |.inline} | | | | | | [\$\\frac{\\mathbf{\\ | | | 24}}{\\mathbf{\\ \\ \\ \\ | | | 4}}\\mathbf{= \\ y\\ }\$]{.math | | |.inline} [ or ]{.math.inline} | | | [\$\\frac{\\mathbf{12}}{\\mathbf{ | | | 2}}\\mathbf{= | | | y}\$]{.math.inline} | | | | | | \ | | | [**6km** **=** **y**]{.math | | |.display}\ | | +-----------------------------------+-----------------------------------+ | **Behaviours** | | +-----------------------------------+-----------------------------------+ | **Displays a knowledge of the | | | correct formula = 1** | | | | | | **Displays correct substitution | | | into formula = 1** | | | | | | **Correct answer with correct | | | units = 1** | | +-----------------------------------+-----------------------------------+ **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Question** **10 (1, 1, 1, 1 = 4 marks)** a. If there are two brushstrokes every 2cm, how many brushstrokes would be in 10cm? b. How many millilitres are in a 1.5 litre bottle of hand cleaner? c. How many millimetres are in 1m? d. How many metres are in 3500 mm? +-----------------------------------+-----------------------------------+ | **Solution** | | +===================================+===================================+ | a. **5 brushstrokes** | | | | | | b. **1500 mls** | | | | | | c. **1000mm** | | | | | | d. **3.5m** | | +-----------------------------------+-----------------------------------+ | **Behaviours** | | +-----------------------------------+-----------------------------------+ | - Correct answer for each = 1 | | | mark | | +-----------------------------------+-----------------------------------+ **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Question** **11 (4 marks)** **A wall is created by stacking equal-sized rectangular bricks on top of each other as shown. The end of each rectangle sits exactly half-way along the long side of the rectangle underneath it.**  **A 500 ml tin of white paint has been purchased to paint the wall. The instructions on the paint tin say this is enough to cover an area of 11500** [*cm*^2^. ]{.math.inline} c. **Use calculations to show if there is enough paint in the tin to cover one side of the wall.** d. **Each brick is 28cm by 16cm by 10cm. An ant walks on the ground around the wall shown, how far does he walk?** +-----------------------------------+-----------------------------------+ | **Solution** | | +===================================+===================================+ | a. **Calculate area of the face | | | of one brick:** | | | [**Area** **=** **l**  **×**  | | | **w,**      ]{.math | | |.inline} | | | | | | \ | | | [ **16** **×**  **28** **cm**   * | | | *=** **448** **cm**^**2**^ ]{.mat | | | h | | |.display}\ | | | | | | \ | | | [**448cm**^**2**^  **×** **25** * | | | *bricks** **=** **11** **200** ** | | | cm**^**2**^]{.math | | |.display}\ | | | | | | \ | | | [**Answer** **:** **There** **is* | | | * **enough** **paint** **to** **c | | | over** **one** **side** **of** ** | | | the** **wall.**  ]{.math | | |.display}\ | | | | | | b. **Perimeter = 7 bricks long + | | | 10 cm wide + 7 bricks long + | | | 10cm.** | | | | | | \ | | | [**7**  **×** **28cm**  **×** **2 | | | ** **+** **20cm** **=** **412** * | | | *cm** **Perimeter**]{.math | | |.display}\ | | +-----------------------------------+-----------------------------------+ | **Behaviours** | | +-----------------------------------+-----------------------------------+ | a) | | | | | | Correctly calculates the area | | | front face of one brick. = 1 | | | | | | Correctly answers question, 'Yes' | | | or something appropriate. = 1 | | | | | | b) | | | | | | Correctly displays working for | | | finding perimeter. = 1 | | | | | | Correctly calculates the | | | perimeter of the fence along the | | | ground. =1 | | +-----------------------------------+-----------------------------------+ **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Question 12 (7 marks)** A farmer wishes to sow paddocks with three different types of seed with different costs. - Barley seeds are \$0.04 per square metre - Oat seeds are \$0.06 per square metre - Corn seeds are \$0.09 per square metre What will the total cost of the seed for the three paddocks with the dimensions shown? \ [Type equation here.]{.math.display}\ +-----------------------+-----------------------+-----------------------+ | **Solution** | | | +=======================+=======================+=======================+ | \ | \ | \ | | [**Oats−152**^**2**^] | [Barley ]{.math | [Corn ]{.math | | {.math |.display}\ |.display}\ | |.display}\ | | | | | \ | ***0.5*** | | [**152**  **×** **152 | [**400**  **×** **120 | [ **×** **108**  **×* | | =** **23104m**^**2**^ | ** **=** **48** **000 | * **400**  **=** **21 | |  ]{.math | m**^**2**^]{.math | 600m**^**2**^]{.math | |.inline} |.display}\ |.inline} | | | | | | \ | ***48 000*** | \ | | [**23104**  **×** **0 | [ **×** **0.04** ]{.m | [**21** **600**  **×* | |.06** ]{.math | ath | * **0.09**]{.math | |.display}\ |.inline} |.display}\ | | | | | | \ | \ | [  **=** **\$1944** ] | | [ **=** **\$1386.24** | [**=** **\$1920** ]{. | {.math | |  ]{.math | math |.inline} | |.display}\ |.display}\ | | +-----------------------+-----------------------+-----------------------+ | ***Cost*** | | | | | | | | \ | | | | [**1386.24**]{.math | | | |.display}\ | | | | | | | | \ | | | | [**1920**]{.math | | | |.display}\ | | | | | | | | \ | | | | [**+** **1944**]{.mat | | | | h | | | |.display}\ | | | | | | | | ***\$5250.24*** | | | +-----------------------+-----------------------+-----------------------+ | **Behaviours** | | | +-----------------------+-----------------------+-----------------------+ | **Oats: Correctly | | | | found total area = | | | | 1** | | | | | | | | **Correctly found | | | | total cost = 1** | | | | | | | | **Barley: Correctly | | | | found total area = | | | | 1** | | | | | | | | **Correctly found | | | | total cost = 1** | | | | | | | | **Corn: Correctly | | | | found total area = | | | | 1** | | | | | | | | **Correctly found | | | | total cost = 1** | | | | | | | | **Correctly found | | | | total cost = 1** | | | +-----------------------+-----------------------+-----------------------+ **\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **End of Test** -------------------------------------------------------------------------- **Grade Breakdown** --------------------------- -------- -------- -------- -------- ---------- **Questions** **A** **B** **C** **D** **MARKS\ TOTAL** **1** **5** **5** **2** **6** **6** **3** **2** **2** **4** **5** **5** **5** **4** **4** **6** **3** **6** **9** **7** **3** **3** **8** **4** **1** **5** **9** **3** **3** **10** **4** **4** **11** **4** **4** **12** **7** **7** **TOTAL MARKS breakdown** **7** **13** **27** **10** **57** **% breakdown** **A** **B** **C** **D** **12** **23** **47** **18** **100%** --------------------------------------------------------------------------