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Name: ___________________________________________ Mathletics Diagnostic Test Year 7 - National Curriculum 813 Number and Algebra Suggested Time: 90 minutes 83 marks Name: Teacher: Date: All questions are worth one mark. Sub-strand and content elaborations are based on Version 1.2 ACARA Australian National Mathematics Curriculum Year 7 | March 2011 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 1 - Number and Place Value ACMNA149 a Which of the following numbers is prime? A 28 B 58 18 D 13 C 157 D 13 C 3, 3, 11 D 2, 3, 3, 13 15 D 30 D 15 D 5 C b Which of the following numbers is composite? A 109 B 145 c What are the prime factors of 78? A 3, 9, 9 B 2, 3, 13 d What is the lowest common multiple of 3 and 5? A 12 B 20 C e What is the lowest common multiple of 3, 4 and 6? A 60 B 12 C 30 f What is the highest common factor of 136 and 30? A 4 B 2 C 9 ACMNA149 /6 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 2 - Number and Place Value ACMNA150 a What is the square of 2? Answer: b What is the square root of 121? Answer: c What is 3 2 ? Answer: d What is √ 144 ? Answer: e If 13 2 = 169 and 15 2 = 225, then the square root of 196 is most likely: Answer: f If 160 2 = 25600 and 162 2 = 26244, then the square root of 25921 is most likely: Answer: ACMNA150 /6 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 3 - Number and Place Value ACMNA151 a Which of the following demonstrates Distributive Law? A (a + b) + c = a + (b + c) B a x (b + c) = a x b + a x c C a+b=b+a b Which law best describes: a - c = c - a ? A Commutative Law C Distributive Law B Associative Law D These laws don't apply to subtraction c When can you not use associative law? A subtraction B addition d Which equation is correct? A (a + b) - c = a - (b + c) B (a - b) - c = a - (b - c) C (a + b) + c = a + (b + c) e Calculate 2 x (5 + 8) = Answer: f Calculate (2 x 5) x 8 = Answer: ACMNA151 /6 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 4 - Number and Place Value ACMNA280 a Which number has the highest value? A 99,241 B 84,067 C 82,976 D 84,067 C 96,649 D 101,951 b Which number has the lowest value? A 103,072 B 98,145 c Calculate 7324 + 932. Answer: d Calculate 3388 + 932. Answer: e Calculate 4845 - 960. Answer: f Calculate 5515 - 932. Answer: ACMNA280 /6 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 5 - Real Numbers ACMNA152 Use the fraction wall below to answer the following questions. a Which fraction is equivalent to 2/4? A 1 2 B 2 8 C 4 9 D 1 3 b Write at least two equivalent fractions for 2/4. Answer: c Find 1/5 + 2/5. Answer: d Find 3/6 + 5/10. Answer: ACMNA152 /4 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 6 - Real Numbers ACMNA153 1 3 a 9 24 A b 3 7 1 3 3 6 3 6 - 2 1/2 B 38 7 C 43 7 B 11 7 C 3 14 B 1 2/3 C 5/6 B 3 6 B 1/2 D 10 24 D 36 7 D 4 14 = 1 6 1 8 D 5/12 C 6 6 D 7 6 C 1 1/2 D = 2 6 5 8 A + C 8 24 = 2 1/2 A f 1 7 4 7 A e + B 11 24 = 40 7 A d 1 7 5 A c = = 5 ACMNA153 /6 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 7 - Real Numbers ACMNA154/155 a A b 2 4 A d A e 3 4 = 2+3 4+4 2 4 ÷ 3 4 2 4 x 3 5 ÷ 2-3 4-5 3 5 B 2÷4 4÷3 B 2÷5 4÷3 B 2x5 4x3 C 2x3 4x4 C 2÷3 4÷4 C 2x3 4x5 C 2÷3 4÷5 D 4x3 2x4 D 4x3 2x4 D 4x3 2x5 D 4x3 2x5 = 2+3 4+5 2 4 B 2÷4 4÷3 = 2x4 4x3 A c x = Express 25 millilitres as a fraction of 1 litre. Answer: f Express 10 minutes as a fraction of 1 hour. Answer: ACMNA154/155 /6 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 8 - Real Numbers ACMNA156/157 a Round 61.5311 to 2 decimal places. Answer: b Round 14.7513 to 3 decimal places. Answer: c Convert the fraction 16/100 to a decimal. Answer: d What percentage of 0.15 is 1? Answer: e Jackson is entitled to receive a 5% staff discount. If the original price was $100, how much is the discounted price? Answer: f Nicola wants to donate 15% of her savings to charity. If she has saved $90, how much is she wanting to donate? Answer: ACMNA156/157 /6 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 9 - Real Numbers ACMNA173 a If Sarah eats 3/10 of a cake and Matthew eats twice as much as Sarah, how much cake did Matthew eat? Answer: b Cindi needs to make lemonade for a school fundraiser. The ratio of lemons to water to sugar is 1:1:3 . If she has 35 lemons, how much water and sugar will she need? Answer: c For every 35 lemons, Cindi can sell 105 cups of lemonade for $1.50 per cup. How much money will she raise if she sells all of the lemonade? Answer: d It takes one person one day to dig a 5m x 5m x 5m hole. How long will it take 6 people, working at the same rate, to dig a 20m x 20m x 20m hole? Answer: ‽ answer might not be a whole number ACMNA173 /4 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 10 - Money and Financial Mathematics ACMNA174 a b c d Which is the best buy? Choose the item(s) with the best value for money. There may be more than one answer. A 440 grams of tinned tomatoes for $2. C 110 grams of tinned tomatoes for $4. B 300 grams of tinned tomatoes for $3. D 200 grams of tinned tomatoes for $1. Which is the best buy? Choose the item(s) with the best value for money. There may be more than one answer. A 2 kilograms of flour for $3. C 2.5 kilograms of flour for $5. B 4 kilograms of flour for $2. D 1.5 kilograms of flour for $4. Which is the best buy? Choose the item(s) with the best value for money. There may be more than one answer. A 250 litres of petrol for $300. C 400 litres of petrol for $400. B 800 litres of petrol for $100. D 600 litres of petrol for $200. Which is the best buy? Choose the item(s) with the best value for money. There may be more than one answer. A 170 bricks for $30. C 180 bricks for $20. B 150 bricks for $20. D 160 bricks for $30. ACMNA174 /4 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 11 - Patterns and Algebra ACMNA175 a A b A c d A e The 2 in 2a is referred to as a __________ variable formula C constant D pronumeral B 5a C 4+a D a a+a+a+a = 4a 4 (a + 5) + (7a + 8) = A (a + 8a) + (5 + 7) C 20a B 21a D (a + 7a) + (5 + 8) If a = 8, then 2a = 10 B 16 C 28 D 280 Which of the following equations does not describe a number pattern increasing by 5? A b = 5a + 2 f B B b = 19 + 5a C b=a+5 D b = 5a - 5 If the rule describing a number pattern is d = 4c - 5, what will the value of d be when c = 60? A 95 B 233 C 240 D 235 ACMNA175 /6 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 12 - Patterns and Algebra ACMNA176/177 a If speed = distance / time, calculate the speed when d = 144 and t = 4. speed (km/h) = s A b 0.03 km/h distance (km) = d B c A d A e A D 140 km/h 36 km/h If force = mass x acceleration, calculate the acceleration when F = 92 and m = 2. force (N) = F A C 576 km/h time (h) = t B 46 acceleration (m/s 2 ) = a mass (kg) = m C 0.02 D 184 17.83 D 19 g = 18 D g = 19 90 If y = mx + c, calculate 'y' when m = 2 and x = 6 and c = 7. 4.333 B Solve for g: g = 20.5 C 15 17g - 16 = 15g + 20 B C g = 21 Make B the subject of the formula B= A P+R B B= A P-R C P= A R - B= A R -P B D B= A R +P Which value for m makes 16m - 14 < 16 true? f A m = 5.5 B m=4 C m=0 D m=3 ACMNA176/177 /6 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 13 - Linear and non-linear relationships ACMNA178 a 6 5 Which are the correct co-ordinates of the point? 4 3 2 1 A (-5, 2) B (2, -5) C (2, 5) D (5, -2) 0 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 b 6 5 Which are the correct co-ordinates of the point? 4 3 2 A (-4, -4) B (-4, 5) C (-5, 4) D (5, -4) 1 0 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 13 - continued c Plot the point (-6,6) on the graph. 6 5 4 3 2 1 0 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 -6 d Plot the following points on the graph. x -4 -2 0 2 4 y -7 -5 -3 -1 1 20 15 10 5 0 -20 -10 0 10 -5 -10 -15 -20 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 20 6 Name: ___________________________________________ e Plot the following points on the graph. x -6 -4 -2 0 2 y 0 -2 -4 -6 -8 20 15 10 5 0 -20 -10 0 10 20 -5 -10 -15 -20 ACMNA178 /5 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 14 - Linear and non-linear relationships ACMNA179 Represent the following equation on the balance beam below, using boxes to represent 'x' and '2'. For example to represent x + 2 you would need to draw one x box and two one's boxes. eg: x + 2 = x 1 1 a Represent 4x + 3 = 7 on the balance below using boxes to show x and units of 1. b Draw what the other side of the balance would look like if you were to find x. x c Explain what you did to both sides of the balance to find x. Answer: © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 ? Name: ___________________________________________ Section 14 - continued ACMNA179 d Describe a strategy you could use to solve the following: "I'm thinking of a number. When I subtract 3 from my number, multiply the result by 8, then divide this result by 3, I get 16. What is my number?" Answer: e Using the following - substitute the values to choose the correct equation. c=9 a=3 b=3 f A 28 = c x b + a C 32 = (c x a) + b B 30 = (c x b) + a D 27= (c x b) + a Using the following - substitute the values to choose the correct equation. y=4 x=2 z = 12 A 5 = (z/y) + x C 7 = (z/y) + x B 3 = (z/y) + x D 2= (z/y) + x ACMNA179 /6 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 Name: ___________________________________________ Section 15 - Linear and non-linear relationships ACMNA180 The following questions refer to the graph below: Distance From Home (km) Travel Graph a b c d 20 15 10 5 0 1 2 3 4 5 6 Time (mins) At 3 minutes, how far is Sam from home? A can't tell C 5 km B 10 km D 15 km During which time frame was Sam not moving at all? A between 1 and 4 minutes C between 4 and 5 minutes B between 5 and 6 minutes D can't tell During which time frame was Sam travelling the fastest? A between 6 and 7 minutes C between 1 and 4 minutes B between 4 and 5 minutes D can't tell At how many minutes did Sam begin to travel back home? A at 4 minutes C at 5 minutes B at 6 minutes D can't tell © 3P Learning - Mathletics National Curriculum Assessment Series - 2011 7 Name: ___________________________________________ Section 15 - continued ACMNA180 The following questions refer to the graph below: Monthly evaporation compared with rainfall (mm) for open pan water storage 2000 1800 1600 1400 1200 1000 800 Evaporation 600 Rainfall 400 200 0 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 e In which year was there the most water retained in the water storage area? Explain your answer. Answer: f In which year was evaporation the greatest? Explain why you chose that year. Answer: ACMNA180 /6 © 3P Learning - Mathletics National Curriculum Assessment Series - 2011