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AUTHOR GCSE LINEAR GRADE C STARTER QUESTIONS (FOUNDATION) www.mistrymaths.co.uk

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) 4) (a) Work out the nth term for the pattern of matches (b) How many matches will the 100 th pattern have? Write 32 as a product of prime factors Calculate the area of the semi-circleCalculate the perimeter of the semi-circle 4 7 10 13 3n + 1 3 x 100 + 1 = 301 32 8 4 4 2 22 22 ANSWER = 2 X 2 X 2 X 2 X 2 = Perimeter of semi-circle = 15.7 + 10 Perimeter of semi-circle = 25.7cm

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 3cm 4cm 120° a b Work out angles a and b and give reasons for your answers 4cm 10cm 1) 2) 3) 4) a = 120° (Alternate angles) b = 60° (Angles on a straight line) 120° Volume of cylinder = area of cross section x length Volume of cylinder = area of circle x length Volume of cylinder = 3.14 x 16 x 10 Work out the volume

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) 4) The price of fuel goes up from £1.36 per litre to £1.45 per litre. What is the percentage increase? The price of a car depreciates from £3500 to £2100. What is the percentage decrease? Both triangles are similar. Work out the missing length marked 4cm 20cm 30cm 5cm 13cm 136p 145p Increase = 9p Percentage Increase = 6.6% (1d.p.) £3500 £2100 Decrease = £1400 Percentage Decrease = 40% (1d.p.)

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) 4) A bag contains 20 balls. 9 balls are blue and the rest are red. A ball is drawn at random from the bag, it’s colour is noted and then it is put back in the bag. This is repeated 80 times. How many time would you expect a red ball to be drawn? The frequency table shows the speeds of 160 vehicles that pass a radar speed check on a dual carriageway. What is the experimental probability that a car is travelling faster than 70 mph? Write the vector that would translate the shape back. (b) 11 red Red ball = 44 times Total frequency = 160 =

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) 4) A fruit drink is made by mixing lemon squash with water in the ratio 4:5. How much water needs to be added to 28cl of lemon squash to make the drink? x 7 5 4 SQUASH : WATER 28cl x 7 : : ? 35cl Therefore, 35cl of water needs to be added to make the drink. Divide 77kg in the ratio 2:4:5 Construct an perpendicular bisector to the line below: Construct an angle bisector to the angle below:

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Too low LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1)2) 3) 4) x High or Low 3 3 - 5 x 3 = 12 3 Too low 4 4 - 5 x 4 = 44 3 Too high 3.5 3.5 - 5 x 3.5 = 25.38 3 Too low 3.8 3.8 - 5 x 3.8 = 35.87 3 3.9 3.9 - 5 x 3.9 = 39.82 3 Too low Replace x with 3 3.95 3.95 - 5 x 3.95 = 41.88 3 Too high ANSWER = 3.9 (closest to 40) + 7 2 < 16 ÷ 2 < 8 5678910 (a) Round 8.43 to 1d.p. (b) Round 7.845 to 2d.p. (c) Round 11.8327 to 3d.p. (d) Round 8.98 to 1d.p. 8.4 7.85 11.833 9.0 (a) Round 8.43 to 1s.f. 8 (b) Round 570 to 1s.f. 600 (c) Round 0.723 to 1s.f. 0.7

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) 4) Solve the equation: 4 + 5 = 3( + 4) 4 + 5 = 3 + 12 - 3 + 5 = 12 - 5 = 7 Rotate the original shaded flag by a quarter turn clockwise about (0,2) Fully describe the single transformation that will map triangle P to Q. A reflection in the line y = x Circle the recurring fractions from the list below: 0.5 0.6 0.333.. 0.6250.777..

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1)2) 3) 4) Draw on the line of best fit and estimate the number of typos for 6 chapters. 9 typos Name the type of correlation below: Positive Correlation Negative Correlation No Correlation Find the reciprocal of: (a) 7 (b) Volume = area of cross section x length Volume = area of triangle x length Cross section Find the volume of the prism

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3)4) Describe fully the single transformation that maps triangle A onto triangle B Enlarge the shape by scale factor 2 with (0,0) as the centre of enlargement. ScoreFrequencyMidpointfx 1-59 6-1010 11-1513 16-207 21-251 Total ScoreFrequencyfx 15 24 39 48 58 66 Total Estimated Mean = 425/40 = 10.6 Modal Group = 11-15 Mode = 3 Range = 6 – 1 = 5 Calculate the mean, mode and range from the table. Calculate the estimated mean and modal group from the table above. 5 8 27 32 40 36 148 40 Mean =148/40 = 3.7 3 8 13 18 23 27 80 169 126 23 425 40

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) 4) l w h Surface Area = 2lw + 2hw + 2lh Surface Area = 2x8x3+2x5x3 + 2x8x5 48 + 30 + 80 Surface Area = ScoreFrequency 15 24 39 48 58 66 cf 5 9 18 26 34 40 = 20.5 th value = 4 Find the median score from the table. 2 1 GRADIENT = 1 2 Find the gradient of the line. 2 6 The line slopes down from left to right, so it’s a negative gradient. GRADIENT = -6 2 GRADIENT = -3 Find the gradient of the line.

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) GRADIENT = 8 4 2 4 8 y - intercept = 3 Find the equation of the line below: 10 8 The line slopes down from left to right, so it’s a negative gradient. 5 GRADIENT = -8 10 GRADIENT = -4 y - intercept = 3

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) 4) Find the HCF of 12 and 30 Find the LCM of 6 and 8 12 1, 2, 3, 4, 6, 12 30 1, 2, 3, 5, 6, 10, 15, 30 Highest Common Factor = 6 6 6, 12, 18, 24, 30 8 8, 16, 24, 32, 40 Lowest Common Multiple = 24 Name the single transformation that moves triangle P to R Rotation of 180° from centre (0,0) Find the co-ordinates of the midpoint of the line segment = (2.5,2)

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Expand and simplify: LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) 4) -8 < 2n ÷ 2 n < -4 n > ÷ 2 n 3 Integer solutions= -3, -2, -1, 0, 1, 2, 3 = - 21 - 2 = - 23 Draw a line of best fit on your scatter graph. Use your line of best fit to estimate the number of pages in a book of weight 280g. (a) (b) Construct a frequency polygon x x x x x 138 pages

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) 5 1 -1.25 1 5 X X X X X X X y -0.61.6 0.5 -1.25 Draw all the points which are 5cm equidistant from the point below: Estimate the answer to: (a) (b) = 2000 = 7500

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) Construct an equilateral triangle below:Construct a rhombus below:

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) (c) Work out the average speed for each of the five stages of the journey. The distance–time graph below represents a car journey from Barnsley to Nottingham, a distance of 50 km, and back again. 16km 20mins A-B 20mins = 16km 60mins = x3 48km 48km/h 10mins 19km B-C 10mins = 19km 60mins = x6 114km 114km/h 20mins 15km C-D 20mins = 15km 60mins = x3 45km 45km/h D-E Represents a stop for 20 minutes 20mins 50km 60mins E-F 60mins = 50km 50km/h

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) The graph shows Amy’s progress on a sponsored walk. (a) How many times does Amy stop during her walk? Answer.......................................................................... (1 mark) (b) Between which times does Amy walk the fastest? Explain your answer. Answer............................................................... Explanation.......................................................................................................................................................................................................................................... (2 marks) (c) Bill sponsors Amy for 20 pence per kilometre. Kate sponsors Amy for 30 pence per kilometre. How much should Amy collect altogether from Bill and Kate after her walk?.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... Answer £...................... (3 marks) Stop 2 times 11:30 – 12:30 This is where the line is steepest 19km 20p x 19 = £3.80 30p x 19 = £5.70 9.50

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) 4) = = = = = = 15 x + = x + Common denominator of 15 = x3 x5 = = x + x + = Common denominator of 21 = x7 x3 = =

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 1) 95° 155° 80° Pentagon (5 sides) Sum of interior angles = (number of sides – 2)x 180° Sum of interior angles = ( 5 – 2 )x 180° Sum of interior angles = 3 x 180° Sum of interior angles = 540° - 90° - 155° - 95° - 80° 540° 120° Sum of interior = (n – 2) × 180 = (5 – 2) × 180 = 3 × 180 = 540° 2 x + 3 x + 5 + 3 x + 75 + 140 = 540° 8 x + 220 = 540° 8 x = 320° x = 40°

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LINEAR GRADE C STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 1)Calculate the size of the exterior and interior angle for a regular dodecagon Dodecagon 12 sides 18º The diagram shows the exterior angle of a regular polygon. (a) What is the value of the interior angle? (b) How many sides does it have? (c) What is the sum of interior angles? Number of sides = 20 162º 3) Exterior angle Interior angle 45º 135º 67.5º Angles in a triangle add to 180º Isosceles Triangle Base angles the same

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