YEAR 9 MATHEMATICS, 2011
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1 Answer ALL questions in the spaces provided in this booklet. Show ALL working. NAME: TEACHER: YEAR 9 MATHEMATICS, 2011 Algebra QUESTION AND ANSWER BOOKLET Answer ALL questions in the spaces provided in this booklet. Show ALL working. Achievement Curriculum Level 3 For Assessor s use only Curriculum Level 4 Curriculum Level 5 Total: / 50 ========================================================================= QUESTION ONE (b) 3x = 15 Luke has a certain number of lollies. We ll call it n. Write down how many lollies these people have, using the variable n. (c) 8 x = 2 (a) Jessica, who has twice as many as Luke. (b) Sam, who has six more than Luke. (c) Sean, who has 12 less than Luke. QUESTION TWO Solve the following equations (what is x?) (a) x + 4 = 8 QUESTION THREE If k = 3 and p = 4, what do these equal? (a) k + p (b) p 2 (c) 2k - p
2 QUESTION FOUR Simplify the following expressions: (a) m + m + m + m (b) e x e x e (c) y x 4 QUESTION FIVE Solve the following equations. Show your working. (a) 2n + 5 = 17 (b) x 4 +1 = 3 Write an algebra equation for each situation below AND then solve your equation to find the answer. (c) A number will give the answer 6 when it has been doubled. QUESTION SIX Expand the following sets of brackets. Simplify if possible. (a) 2(n + 5) (b) 3(k + h) (c) 2(y + 1) + 5(y + 3) QUESTION SEVEN Solve the following equations (a) 3m + 6 = m 10 (b) 2x = 3 (d) A number gives 12 when it is divided by 4 and the result increased by 2 (c) 2x 2 8 = 0
3 (d) -2(x + 1) = -6 QUESTION TEN Simplify the following expressions (a) 3x 2 x xy x 4 QUESTION EIGHT Expand and simplify the following: (a) x(x+3) 2(x + 1) (b) 4x(x + 5) + 3x(y 2) QUESTION NINE Factorise the following into brackets (a) 3x 18 (b) x 2 4 x (c) 10x 2 15xy (b) 3m x 2m (c) 16y 2 20y (d) 2p + 3p 2 + p p 2 QUESTION ELEVEN Given that x = -2, y = 4 and z = 0.6, calculate the following: (a) 4xy + yz (b) 2x z (c) x 2 y 3
4 NAME: TEACHER: YEAR 9 MATHEMATICS Measurement Answer ALL questions in the spaces provided in this booklet. Show ALL working. Achievement Achieved (20-32) For Assessor s use only Achieved with Merit (33-44) Achieved with Excellence (45-50) Total: / 50 Useful Formulae C = πd 2 A = πr 1 A = bh 2 1 A = ( a + b) h 2 Volume = base area x height A = bh A = bh QUESTION ONE Write down the measurements shown: (a) degrees (b) (c) mm L 60L 40L 20L mm L
5 (d) (i) Measure the height and width of this rectangle to the nearest centimetre. (e) Weight of a person (f) Volume (capacity) of petrol a car s tank can hold. Length = cm Width = cm (ii) Give the area of the rectangle Area = cm 2 QUESTION TWO What is the area of these shapes in squares? (a) QUESTION FOUR (a) How long is a television programme that starts at 18:00 and finishes at 19:25? (b) If I go to bed at pm and get up at 6.45am, how long do I spend in bed? squares QUESTION FIVE Complete the following metric conversions: (b) squares QUESTION THREE Next to each measurement, write the best unit to use from the choices in the box (a) Distance from Dunedin to Christchurch (b) Length of your thumb (c) Weight of a mouse (d) Volume (capacity) of a coke can m L g cm mm kg ml km (a) 6m = cm (b) 567 ml = L (c) 345 mm = cm (d) 0.45 kg = g QUESTION SIX Find the perimeter and area of each shape (a) 5m 12m Perimeter = Area =
6 (b) 4 cm 3.8 cm 3 cm 6.1 cm QUESTION EIGHT A soft-drink can is a cylinder. This means that it has a circular base and remains an even shape all the way up. Perimeter = Area = (c) 3 cm 10.4 cm Perimeter = 4.2 cm This particular soft-drink can is 11 cm high. The radius of its circular base is 6 cm. (a) Calculate the area of the can s circular base (b) What is the volume of this can in cm 3? Area = QUESTION SEVEN For each measurement that needs to be taken, write down an appropriate measuring instrument e.g. tape measure. (a) The temperature in the classroom after lunch (c) Bearing in mind that cm 3 are the same size as ml, how many of these cans could be filled from a 2L drink bottle? QUESTION NINE (b) The length of the edge of your text book (c) A friend s waist circumference (around the waist) (d) The weight of your schoolbag (e) The time taken to run 100m (a) Here are the measurements on a diagram for some new asphalt paths at the school. Give the area (on the diagram) of the new paths.
7 (b) The diagram of the paths (in Question a) is drawn to a scale of 1cm = 0.5m. Write the REAL lengths on this copy of the diagram. QUESTION ELEVEN (c) What is the REAL area of the paths? (d) The asphalt on the paths will be 15cm thick. What will the volume of the asphalt be? (Hint: you need to work with cm or m, not a combination of the two) QUESTION TEN A Toblerone packet is a triangular prism. This means that the triangular shape of the end stays constant the whole way down. This Toblerone packet is 25cm long. The triangular end is an equilateral triangle (all sides 4cm long). The height of the triangle is 3.5 cm. (a) What is the total area of the cardboard in the packet? (Do not count flaps or overlaps, just count faces). (b) If the chocolate completely filled the packet, what would the volume of the chocolate be? (a) Here is an unusual shape. Draw lines on this shape to show a way to break it into rectangle(s) and triangle(s). (b) Calculate the total area of the shape. Show all working
8 NAME: TEACHER: YEAR 9 MATHEMATICS, 2011 Angles QUESTION AND ANSWER BOOKLET Answer ALL questions in the spaces provided in this booklet. Show ALL working. Achievement Curriculum Level 3 For Assessor s use only Curriculum Level 4 Curriculum Level 5 Total: / 28 QUESTION ONE (a) What is the size of the angle being measured by the protractor below? (c) Label each of the following four angles using a word from the box below. (i) (ii) Angle = (b) What size angle is shown by this symbol? (iii) (iv) Angle = acute reflex right straight obtuse
9 QUESTION TWO Work out the size of A, the missing angle. (a) QUESTION THREE Work out the size of the missing angles. You do not have to give reasons for your answer. A = (b) 50 o A (a) A = A 85 o This is a square (b) A 72 o A A = A = (c) A 80 o 90o (c) A this is an isosceles triangle 65 o A = A = (d) 114 o (d) A A this is an equilateral triangle A = A =
10 QUESTION FOUR Work out the size of the missing angles and give a reason for each answer. (a) QUESTION FIVE These diagrams are not drawn to scale. Look at the sizes of the angles. If the diagram was drawn correctly, would the lines AB and PQ be parallel? Give a reason for each answer. A 128 o B (a) A P 60 o 60 o 60 o 60 o B Q Angle A = because Angle B = because Are lines AB and PQ parallel? Explain the reason for your decision (b) (b) B B 32 o Q 115 o A A 90 o 50 o 88 o Angle A = because Angle B = because P Are lines AB and PQ parallel? Explain the reason for your decision
11 NAME: TEACHER: YEAR 9 MATHEMATICS, 2011 Number QUESTION AND ANSWER BOOKLET Answer ALL questions in the spaces provided in this booklet. Show ALL working. Achievement Curriculum Level 3 For Assessor s use only Curriculum Level 4 Curriculum Level 5 Total: / 40 ========================================================================== QUESTION ONE (a) If the large square is worth one whole, give (b) What value is the arrow pointing at on this number-line? (c) Rewrite these numbers in order from smallest to largest: 2.7, 7.02, 2.07, 2.77, 2.72, 2.027, 20.7, (i) The decimal value of what has been shaded (ii) The fraction that has been shaded in its simplest form. (d) Complete this multiplication working: 3 x 24 = 3 x x = 60 + =
12 QUESTION TWO (a) Samantha wants to eat ¾ of her lollies and give the rest to a friend. She has 24 lollies. How many does she eat? (b) Pete sees a sign saying 25% off all skis. The skis he wants usually cost $480. How much will he save in the sale? (c) Darryl s dad says he can either have 3 10 of a cake or 28% of it. Which is the bigger amount? Explain your reasons QUESTION THREE (a) Fill in the gaps that would make these fractions equivalent: (b) Complete the table of equivalents Fraction Decimal % 26% % QUESTION FOUR (a) What is 58% of 14? (b) Tulip sends 480 texts a month. 300 of those are to her best friend. What percentage of her texts are to her best friend? (c) Hemi phone cost 56% more than Tulip s phone. If Tulip spent $180 on her phone, how much did Hemi s phone cost? 3 = 7 21 (d) Hemi normally sends 800 texts per month. His mother told him he needed to reduce this by 40%. How many texts does he need to reduce his monthly total by? = = QUESTION FIVE (a) Samara has two bank accounts. One is a savings account, which has $200 in it. One is a credit card account, which is $330 in debt. Write an integer (positive or negative number) that represents the amount of money Samara has.
13 (b) Complete the following integer skills questions: (i) = (ii) 5-1 = (iii) 6 x - 3 = (iv) (4 6) 2 x ( ) QUESTION SIX (a) If 3kg of oranges cost $12.60, what would 7kg of oranges cost? (b) Anabelle is saving for a trip to Australia. She gets $12 pocket-money per week, and is saving 30% of it. Her parents also say that they will give her $2 spending money for every $1 she can save. Annabelle wants to have $600 spending money. How long will it take her to save enough so that she gets at least this much? (b) Shelley ran 30 m in 5 seconds. (i) If she could keep this speed up, how long would it take her to run a kilometre? (ii) What would her speed be in kilometres per hour? QUESTION SEVEN (a) A supermarket is selling tinned beans for 40c off. This is a discount of 8%. How much did the beans originally cost?
14 Algebra Level 3 1a 1b 1c 2a 2b 2c 3a 3b 2n n + 6 n 12 x = 4 x = 5 x = Answer only (i.e. no x = ) is okay. Answer only (i.e. no x = ) is okay. Answer only (i.e. no x = ) is okay. 3c 2 Level 4 4a 4b 4c 5a 5b 5c 5d 4m e 3 4y n = 6 x = 8 e.g. 2n = 6, n = 3 e.g. n + 2 =12, n = 40 4 Mark for working, mark for answer Mark for working, mark for answer Mark for equation, mark for answer Mark for equation, mark for answer 6a 6b 6c 2n k + 3h 2y y + 15 = 7y + 17 Mark for expansion, mark for simplifying
15 Level 5 7a 7b 7c 7d 8a 8b 9a 9b 9c 10a 10b 10c 10d 11a 11b 11c 2m + 6 = -10 2m = -16 m = -8 2x + 4 = 15 2x = 11 x = 5.5 2x 2 = 8 x 2 = 4 x = 2 or -2 x + 1 = 3 x = 2 x 2 + 3x 2x 2 = x 2 + x 2 4x x + 3xy 6x = 4x x + 3xy 3(x 6) x(x - 4) 5x(2x 3y) 12x 3 y 6m 2 4y 5 3p + 2p = ( 2) = = -60 Mark for working, mark for answer Mark for working, mark for answer Mark for working, mark for answer (must have both x values) Mark for working, mark for answer Mark for expanding, mark for simplifying Mark for expanding, mark for simplifying Mark for each factor (if bracket contents correct) Mark for coefficient, mark for rest of term Mark for coefficient, mark for rest of term Mark for coefficient, mark for rest of term
16 Measurement Level 3 1a 1b 1c 1di 1dii 2a 2b 3a 3b 3c 3d 3e 3f 4a 4b 5 degrees 12 mm 72L 8cm, 3cm 24cm 2 33 squares 22 squares km cm or mm g ml kg L 1 hour 25 minutes (or 85 minutes) 8 ½ hours Level 4 Accept Does not matter which is designated length Or equivalent Must have both Only 1 required 1.25 not acceptable! Or equivalent 5a 5b 5c 5d 6a 6b P = 34cm, A = 60cm 2 P = 13.1cm, A = 5.7cm 2
17 6c 7a 7b 7c 7d 7e P = 29.2cm, A = 31.2cm 2 thermometer ruler tape measure scales stopwatch Level 5 8a 8b 8c 9a A = π 6 2 = 113 (nearest whole) 1243mL Only 1 whole can (e.g. 9x3 + 9x1) = 36 cm 2 Mark for working, mark for answer. Any rounding. Consistent with 8a Accept 1.6 or other consistent answer. Mark for working, mark for answer 9b 1.5m 2.5m 1.5m Mark for at least 2 correct, mark for all correct. 4.5m 9c 9 m 2 0.5m Mark for working, mark for answer 9d 10a 10b 1.35m 3 or cm 3 Answers will vary 22m 2 Mark for working, mark for answer Mark each for up to 2 individual area calculations, mark for answer. 11a rectangular faces triangular faces Marks given for individual areas (triangle, rectangle). Third mark for complete answer. = 314 cm 2 total 11b =175cm 2 Mark for working, mark for answer.
18 Angles Level 3 1a 1b 1c 2a 2b Accept degrees 90 degrees i obtuse ii acute iii reflex iv right 130 degrees 90 degrees Level 4 Accept right angle Accept right angle 2c 2d 3a 3b 3c 3d 10 degrees 114 degrees 85 degrees 108 degrees 50 degrees 60 degrees Do not need to write degrees (and above)
19 Level 5 4a 4b 5a 5b A = 128 degrees (vertically opposite angles are equal) B = 52 degrees (cointerior angles on parallel lines add to 180 degrees) A = 65 degrees (cointerior angles on parallel lines add to 180 degrees) B = 25 degrees (Angle sum of triangle is 180 degrees) Yes e.g. 180 degrees for co-interior angles (60 plus 2 x 60). e.g. equal alternate angles. No e.g. cointerior angles don t add to 180 ( ) e.g. angle corresponding to 50 degree angle marked does not complete the triangle above AB to 180 degrees. Accept clear references to a rule, even if some words missing. Some questions may have alternative methods for calculating a correct angle. Up to 2 marks for clarity of reasoning. Up to 2 marks for clarity of reasoning
20 Number Level 3 1ai 1aii 1b 1c 1d 2a 2b 2c About , 2.07, 2.072, 2.7, 2.72, 2.77, 7.02, , 12, $ e.g. because 3 10 = = 30% accept values above 45, but below 48) 1 mark for getting any 3 in correct sequence 1 mark each. (Use consistency marking) 1 mark for the reason. Level 4 3a 3b 4a 4b 4c 4d 5a 5bi 5bii 5biii 5biv 9, 12, 5 13, 0.26, = 1, 20%, 1 18, 1.18, , 15.5% % $ (-2) 2 x (-11) = mark for each 1 mark for every 2 correct. Accept any equivalent fraction. May give 1 mark for working out 56% of 180 With or without $ sign. 2 out of the three marks towards working e.g. for working out the brackets completely.
21 Level 5 6a 6bi 6bii 7a Rate is $4.20/kg 7 kg will cost $29.40 Rate is 6m/second 1km will take 167 seconds (nearest second). 6m/second = 21600m per hour = 21.6 km/hr Bean price x 0.08 = $0.40 $0.40 / 0.08 = Bean price. Beans cost $5 7b Saves $3.60 per week. Only has to save 1/3 i.e. $200 This will take 55.6 weeks (1 d.p.), i.e. about 56 weeks.
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