Answers for Unit A. 1 Integers. 2 Algebra 1. Answers to NTTEQ. Answers to NTTEQ. Answers to NTTEQ. Hodder Education 2011 Unit A

Transcription

1 Answers for Unit A Integers a a An of,,,, or. c d An of,,, 9 e a, 9,,,,,,,,,,,, a C C Trial Working out Result Too small Too large. = =. = =. =.. =.. =.. =.... = = 9 The numer is.. Amount on words = = Numer of words = p = = Numer of seats = = Spare seats = 9 = 9 spare seats Algera a p x a m k c d a + x + x + a a² x + Perimeter = x + + x + = x + Area = x = x Hodder Education Unit A

2 Answers: Unit A Data collection For example a a leading question question is asking two things at once Frequenc Less than Numer of passengers 9 9 a Dog Cat Other Total os 9 Girls Total c a Numer of messages received Frequenc Numer of people Numer of messages Answers Hodder Education

3 a Groups overlap, so would e in groups etc. Frequencies,,, 9,, c Frequenc Decimals. +. =.9 So the alance is =.9.9 =. a. a i ii iii. iv. joins to.; joins to.; joins to.; joins to. Formulae C = 9n a F = 9 F = a P = P = 9. a P = P = a G = G = a K = K = 9 a H = H = a Q = Q = Hodder Education Unit A

4 Answers: Unit A Equations a i ii iii i ii a x = x = c x = C n = Coordinates Statistical calculations Numer of letters in a word Numer of words Class Interval Tall Frequenc a (, ) C c Trapezium a (., ) (, ) a i (, ) ii C(, ) Point D is at (, ). a A is (, ) is (, ) C is (, ) D is (, ) i = ii x = a x = = c vertical line at x = d the x axis A x D a kg 9 kg a 9. ( ) c to Modal class is minutes. a Pat s mean = and range =. Kim s mean = and range =. Kim should e chosen ecause the mean scores are the same ut she has a smaller range and is therefore more consistent. ook : mean =., median is at top of n class, range is possil. ook : mean =., median is at ottom of n class, range is possil. 9 Sequences a i ii Add i ii Add c i 9 ii Add Answers Hodder Education

5 a, Yes. You alternatel add two odd and one even numer (giving an even numer) and add two even numers and one odd numer (giving an odd numer).,,,, n,, 9,, n +,, 9,, n +,,, 9, n,,,, n a i 9 9 ii 9 i First term Add ii First term Sutract c First term Add a i, ii Add i, ii Sutract c i, ii Multipl Measures a to kg. m a C C c C. l 9 ml ml.9 l. l a. = km. = ls a.. metres. metres Constructions a C 9. cm. cm A [Marks each for A, AC ± mm, angle CA ±, arc at C.] C =. cm ± mm; angle AC = ± a Solutions with correct angles ± i ii 9 iii i ii 9 iii all ± a Hodder Education Unit A

6 Answers: Unit A a O N P N Q Statistical diagrams Answer to NTTEQ Sales PQ measures. cm on the diagram, so is. =. km c AX =. cm Using a calculator MPV Hatchack Saloon a.. c.9 a = g. = a.. a. =.. 9 =. c One tin costs. =. tins cost. =. a.. c. Flour = = g. utter = = 9 g. a 9. =.. 9 =. a =. a. c. a..9 c. a. or. c 9 or. a g 9 c. a.. c. a Others ( ) is aout half of the size of Lieral Democrats ( ), so aout councillors., accept an answer from inclusive. c Approximatel 9 (9 to ) Conservative councillors so 9 = Laour councillors (accept an answer from inclusive). Integers, powers and roots a c a = = = = = HCF = LCM = = = a cm c. or Answers Hodder Education

7 Algera a x i P = ii P = a a x + c a( + ) (a + ) = a + a x + p(p ) a(a + ) a S = S = Statistical diagrams a Numer of shoppers Time (t minutes) a Range =. cm and median =. cm 9 9 Ke 9 means.9 cm Range =. cm and median =.9 cm c The peles in o s set have a greater range and are therefore more varied in size. a Numer of journes (frequenc) Ahmed Talor Ke: means ( 9) c Equations Mrs Talor has made longer journes on average, or has travelled further. Mr Ahmed has made more short journes or smaller range of distances. a Ordered Ke: means Middle value is th, Median = Mileage (m miles) a x =. p = c m = p = x =. a x + = x = c cm a x = 9 x = ± (oth solutions required) x = x or x + = x = x = Ratio and proportion a Gold = = g Total parts = Multiplier = = Gold = = g Hodder Education Unit A

8 Answers: Unit A Mixed fruit = = g Flour = = g Multiplier = = a Vans = Cars = = Multiplier = = not exact Adrian receives = 9. Penelope receives =. Glads receives =. Check total: = (Notice p out due to rounding errors.) Pack Size Price Price per gram Standard g..p Famil g.9.p Special. kg.9.p a weeks c Weeks (x) Frequenc (f) fx Special is the est value for mone. 9 Statistical calculations Weight (w grams) Mean = =. g Numer of apples (f) Midinterval value w w w w 9 9 w 9 Total Minutes (m) Frequenc (f) Midvalue (x) m 9.. m 9.. m m 9.. m 9.. m fx fx Mean is 9 =.9 weeks Midpoints.,.,.,.,. so = Mean weight of package = =. g ( mark for midpoints, mark for products) Mean = =. messages Pthagoras theorem Numer of messages received Frequenc Midpoint fx to. to. 9. to. to.. to 9. Draw a vertical line through to meet AC. Mean is 9 =. minutes A F C AF = 9 cm Using Pthagoras Answers Hodder Education

9 F = A AF = 9 = = F = cm, to nearest cm Height of shed = F + AE = cm + m =. m a 9. cm. cm a = + c 9. = +. = 9.. =.9 =. 9 x =. cm (to d.p.) a = + c a =. +. a =. =. a =. m (to d.p.) a = or + =, since it is not a right-angled triangle. Since, angle X is igger than a right angle. Planning and collecting a This excludes all those not listed in the director. This includes onl those who go swimming. Those who onl use other facilities or none at all are excluded. c Not everone in the district has a chance of eing included. a A is a leading question, so replace with Do ou think it is a good idea to exercise regularl? or It has een said that it is a good idea to exercise regularl. Do ou agree with this statement? has responses missed out so the oxes need to e replaced with the following. none up to more than and less than or more (It could also e argued that a pilot surve might reveal that these hours are excessive and should e replaced with,,, or over, for example.) Where do ou do our exercise? gm running local sports clu video exercise Other (please state)... a The answers availale do not cover a complete range of values. Example: How much do ou expect to pa for a meal out? A: Less than : etween and C: etween and D: More than. Possile questions include: Do ou own a cat? Do ou u tinned cat food? Do ou u dr cat food? What rand(s) do ou u? Tick the following oxes. Sequences a i + ii i, 9,,, ii,,,, a 9 n a is the tenth term of the sequence. This can e found adding to, then to the answer and to the next answer and so on until ou add to to get. a,,,, 9 i 99 ii 99 a sutract c n Constructions A Diagram shown half-size. A Fence Hedge Fence Diagram not shown to given scale C D House Hodder Education Unit A 9

10 Answers: Unit A Free deliver deliver Rearranging formulae deliver Store Store Store Diagram shown half-size a d = e d = e + PV = knt PV = k or k = PV NT NT a n = ( T ) a = c i r = ii h = A ( ) + V ( ) πh V πr ( ) or d = e + Answers Hodder Education

11 Answers for Unit Working with numers a = p = weeks = = c. (. +.) =. =. a.. = seats a.,.,.,. i Anston ii.. =.m = cm ella has done the sutraction efore the multiplication. She should do the multiplication first. a ) a 9 kg. kg a c..9 =.. =.9 a + = miles = 9 miles a Amount spent =. +. =. +. = 9. Change = 9. =.9 =. =. One pizza costs. =. Three cost. =. Amount per hour = = Amount in hours = = Angles, triangles and quadrilaterals a rhomus isosceles triangle c rectangle a and a A and DC c A and AD or AD and DC a Sketch of rhomus Rhomus a Angles are, and 9. Right-angled triangle. Fractions a or more squares shaded a c more squares shaded = g = = cm =, =, =, = So order is, Lines of smmetr 9,,, Hodder Education Unit

12 Answers: Unit Solving prolems 9. p.m. a hour minutes : p (to nearest penn). das a : minutes. :. (to nearest penn) Angles a = Allied angles add to. = Corresponding angles or angles on a straight line add to. c = Angles of a triangle add to. a = Angles on a straight line add up to. = Corresponding angles are equal. c = Angles on a straight line add up to or alternate to a. d = Opposite angles are equal. e = Corresponding to or alternate to d. a Angles on a straight line add to. Alternate angles are equal. c Angles in a triangle add to and/or isosceles triangle. p = x = Verticall opposite angles are equal. = Angles round a point add up to. z = Angles on a straight line add up to. a = = + = = = = = + = + + = inch left a + = + + = + + = = 9 = a = + = + = + + = = = 9 = =,, =, = So order is,,, a 9 = 9 = = Circles and polgons a There are in a complete turn so for kg it moves =. c kg kg kg Fractions and mixed numers a + = + = = = = =, =, =, = Order is,,, that is,,, kg kg a Pentagon a) ) cm c) Diagram shown half-size Answers Hodder Education

13 a Equilateral c x = Isosceles triangle and angles in a triangle add up to. = Exterior angle of triangle is equal to sum of interior opposites or Isosceles triangle and angles on a straight line add up to. a x = Isosceles c = c is then in its simplest form 999 is then in lowest terms a is then 9 in lowest terms c is then in lowest terms a.... e.g.. Real-life graphs a c) ii) Not actual size Exterior angle of polgon = = Sum of exterior angle of polgon is, so numer of sides = = Distance (km) c) i) Powers and indices iii is true, the other options are false a x x a, so ut nearer to than so is just over 9 and 9 so 9 lies etween 9 and ut closer to, aout 9. a i 9 ii i ii a r 9 9 Decimals and fractions. a = =. 9). a + = + =. and... or. =. c =. a 9 99 so 9 =. i km ii km c i h min to h min ii h min to h min a i AU$ ii AU$. i ii a p.m.. a.m. c C a. km a stop of minutes c 9 D C A Time (hours) Distance from start (km) d. kph Time (h) ) i) ) ii) Hodder Education Unit

14 Answers: Unit a Fuel left (litres). litres c km d km a i HK$ ii HK$ i to (.) ii to (.) a a Litres Distance(km) 9 Pints i to litres ( litres) ii to 9 litres (. litres) c i to pints (9 pints) ii to pints (. pints) Temperature ( C) Time Answers Hodder Education

15 i 9 C ii C c i C ii C iii hours a F C a kilometres to miles (.) a. miles a to litres (.) to gallons (.) 9 a pounds kilograms Reflection a Triangle is at (, ), (, ) and (, ). Triangle C is at (, ), (, ), and (, ). a Image Mirror line A Percentages a squares shaded i. ii %,,.,.9, % =.,.,.,.9,. Order.,.9,.,.,. = %,.9,,., % Numer who stud French =. = Pension fund =. = Numer over = = + = a % % Deposit =. = Sale price =. = Fraction occupied = =. Percentage occupied =.9% Length left = 9 = Percentage left = = % Deductions =. = 9. Percentage deduction = 9. = % Credit card cost =. =. Rotation Rotation smmetr Answers to TTEQ a Lines of smmetr:,, Order of smmetr:,, Recognising and descriing rotations D and F Rotation through 9 clockwise aout (, ) Hodder Education Unit

16 Answers: Unit a Reflection in the line = x C D A x L A C x Estimation a. =. or. so answer is less than. Dividing a numer larger than leads to an answer lower than., and the answer is not so is not correct c = which is roughl so the answer is too + large. a Multipling a numer less than will make the answer smaller. Dividing a numer less than will make the answer larger. c The three numers are all negative so the answer will e negative also =. =. = (to s.f.) a 9 kg. kg Estimate = + = + = will e plent. Enlargement centre (, ), scale factor. Centre (, ) scale factor a (, ) c d 9 Scatter diagrams and time series a and Iron produced (million tons) Coal used (million tons) c i. million tons ii Methods of production could have changed. 9 Enlargement A x a i ii (, ) Weekl admissions (thousands) 9 Numer of screens Answers Hodder Education

17 a points plotted correctl Positive correlation c Suitale line of est fit d Value read off their line at n = a Asence (no. of people) Alwas more on Frida and Saturda, least on Monda. Slight upward trend in Weeks and followed downward trend in Week. a and c a M Tu W Th F S Numer of apples M Tu W Th F S M Tu W Th F S Week Week Week Height (m) Positive correlation. d m is too far outside the range of the data to make a reliale prediction. Sales ( thousands) 9 9 Year Straight lines and inequalities Straight-line graphs a (., ) (, ) Gradient = a i gradient = ii = x k, where k can e an value except. Gradient =. a Gradient = = x + k, where k can e an value, k. Graphical solution of simultaneous equations Answer to NTTEQ x =., =. Inequalities a i x ii x x i ii x = x + a x. x. or. x x,,,, x x + = x T x Congruence and transformations x Hodder Education Unit

18 Answers: Unit A Congruence and transformations A and F and H C and E A and C As the have the same angles, and have a. cm length etween and angles. A x C x C a and See diagram. c Reflection in the x-axis. Answers Hodder Education

19 Answers for Unit C Two-dimensional representation of solids Here is a possile net. Check the measurements on our net. cm Here is a possile net. Check the measurements on our net. cm cm cm. cm. cm. cm. cm cm cm cm. cm. cm. cm. cm a c Proailit Calculating proailities a There are no numers less than on the spinner. P S c Six of the eight numers are even. cm a Five more flags with correct colours: AC, AC, CA, CA, CA cm cm a Certain Evens c Unlikel or Ver unlikel d Impossile a or or d c Hodder Education Unit C 9

20 Answers: Unit C a Not all sandwiches are equall popular. c Peter might, or might not, e correct. There are nine different possiilities and one of them is rown read and cheese ut the choices are not equall likel. If Peter is correct, the proailit of not uing a rown read and cheese sandwich would e. Experimental proailities a 9 = 9 = a = = a 9 = or read Perimeter, area and volume Perimeter and area of a rectangle W W W G G G a. cm. cm² Two of: or cm, Perimeter cm or cm, perimeter cm or cm, perimeter cm Filling a Perimeter = cm, Area = cm Perimeter = cm, Area = cm etween 9 km and km cm 9. () m Perimeter = m, area m C E H C E H C E H The volume of a cuoid. m cm Measures a i cm ii. m (. m to d.p.). cm to. cm and. cm to. cm a 9. cm 99. g a cm (to the nearest cm) or. m (to d.p.) 9.9 km/h (to d.p.) or people per km Upper ound = cm; lower ound = cm a. hours mph The area of triangles and parallelograms a Area of triangle = ase height =.. =. cm a = + c =. +. =. a =. a =. cm (to d.p.) Area of shape = area of rectangle + area of triangle =. +. =. cm C. =.9 C. =. C =.. =. cm a 9. =. cm² ( ) AD = +. =. Perimeter = =. cm a = cm² Area of rectangles = = = cm² Total area = + + = cm² Area of triangle =.. =.. h =. h =.. =.9 cm Answers Hodder Education

21 Proailit a.. c Colour Orange White Yellow a i 9 ii iii 9 No. Traffic patterns var according to the time of da. c or a (. +.) =.. = (to nearest game). +. =., which is greater than so oth cannot e right. No. Mosna has not thrown the dice enough times for the results to settle down. She needs to roll the dice at least times. Perimeter, area and volume Area of lawn = area of rectangle area of semicircle with radius m = π =. m (to d.p.) C = πr = π r r = Numer of sweets π. cm (to d.p.) a C = π. =. m A = π π. =. m a cm + + = cm² Colour Green Red Numer of sweets a = = cm² Hpotenuse = ( + ) =. cm Perimeter = =. cm = =. m Area of the end =.. =. cm Volume =.. =. = cm³ (to s.f.) cm 9 a cm 9 cm. cm (to d.p.) Using a calculator a c. d. e.9 a. a. =.. = 9 m c. a.. c. a.9. c.9 a.. c. d =.9 =. a.. =... =. So the garden centre is cheaper.. = 9p. 9 One costs. =.. Five cost. =.. He did not use rackets so worked out + a 9 c 9 a. c. a.. c. a.. a.. c. a c 9 Trial and improvement a x x (x + ) = cm x + x = x + x = x =. x =. x =. x =. a When x =, x x + = When x =, x x + = As the outcomes have different signs, there must a root etween x = and x = x =. Hodder Education Unit C

22 Answers: Unit C a x V x =. Dimensions are. cm. cm. cm Enlargement a. cm cm a. cm. cm a cm 9 a. cm. cm a. cm i Graphs ii Distance time and other real-life graphs a to metres. seconds c. seconds d. to. seconds and. to seconds a m i to. ii to. c Straight line through (, ) and (, ) a OK kg c cm d kg to kg and kg a. km. a.m. c. minutes d km/h Distance in km 9 For example: A car accelerates and then travels at a stead speed and then stops suddenl (e.g. crashes). Quadratic graphs a x x =. and x =. a.... x i x = ii etween x =. and x =. x x Time Answers Hodder Education

23 a x x x = and x = a x x x 9 x =. and x =. x x a x x x x =. and x =. approximatel c x =. and x =. approximatel a (,, ) (,, ) c (,., ) Percentages Percentage increase and decrease Selling price including VAT =.9. =. =. Sale price =. = Value after months = (.) = 9. 9 = 9 New price =.9 = Sale price =. = Low sugar content =. =. g Reduced rent =.9 = Total cost =. =. Credit card cost =. =. Amount after ears =. =. a Value after ear = 99. = 9. Value after ears = 99. =.9 Solving prolems.9% a.% 9. (approx 9) Hodder Education Unit C