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GCSE LINEAR GRADE C STARTER QUESTIONS (FOUNDATION). AUTHOR. www.mistrymaths.co.uk. Which ones are you using?. Team Worker. Creative Thinker. Effective Participator. Independent Enquirer. Reflective Learner. Self Manager. LINEAR GRADE C STARTERS. PLT Skills. 1). 2).

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

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

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

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

  5. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE C STARTERS PLT Skills 1) 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? 2) 11 red 4) Red ball = 44 times 3) 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? Total frequency = 160 = (b) Write the vector that would translate the shape back.

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

  7. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE C STARTERS PLT Skills 1) 2) x + 7 High or Low + 7 2𝑥 16 < 3 Too low ÷ 2 ÷ 2 4 Too high 𝑥 8 < 3 3 3 3 3 3 4- 5 x 4 = 44 3- 5 x 3 = 12 3.8- 5 x 3.8 = 35.87 3.95- 5 x 3.95 = 41.88 3.9- 5 x 3.9 = 39.82 3.5- 5 x 3.5 = 25.38 3.5 Too low 3.8 Too low 5 6 7 8 9 10 Replace x with 3 3.9 Too low 3.95 Too high ANSWER = 3.9(closest to 40) 4) (a) 8 Round 8.43 to 1s.f. 3) (a) 8.4 Round 8.43 to 1d.p. 600 (b) Round 570 to 1s.f. (b) 7.85 Round 7.845 to 2d.p. (c) 0.7 Round 0.723 to 1s.f. (c) 11.833 Round 11.8327 to 3d.p. (d) 9.0 Round 8.98 to 1d.p.

  8. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE C STARTERS PLT Skills 1) Solve the equation: 2) Rotate the original shaded flag by a quarter turn clockwise about (0,2) 4𝑥 + 5 = 3(𝑥 + 4) 4𝑥 + 5 = 3𝑥 + 12 - 3𝑥 - 3𝑥 5 12 𝑥 = + - 5 - 5 𝑥 7 = 3) Fully describe the single transformation that will map triangle P to Q. A reflection in the line y = x 4) Circle the recurring fractions from the list below: 0.5 0.6 0.333.. 0.625 0.777..

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

  10. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE C STARTERS PLT Skills 1) 2) 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. 3) 4) 5 27 3 8 8 80 27 13 169 32 18 126 40 23 23 36 40 425 40 148 Calculate the estimated mean and modal group from the table above. Calculate the mean, mode and range from the table. Mean =148/40 = 3.7 Range = 6 – 1 = 5 Mode = 3 Estimated Mean = 425/40 = 10.6 Modal Group = 11-15

  11. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE C STARTERS PLT Skills 1) 2) cf 5 9 18 26 h 34 40 Find the median score from the table. l w = 20.5th value Surface Area = 2lw + 2hw + 2lh = 4 Surface Area = 2 x 8 x 3 + 2 x 5 x 3 2 x 8 x 5 + 4) Surface Area = 30 80 48 + + Surface Area = Surface Area = 6 3) The line slopes down from left to right, so it’s a negative gradient. Find the gradient of the line. 1 Find the gradient of the line. 2 2 -6 GRADIENT = 1 GRADIENT = 2 2 -3 GRADIENT =

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

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

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

  15. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE C STARTERS PLT Skills 2) Draw all the points which are 5cm equidistant from the point below: 1) 5 1 5 -1 -1 -1.25 1 y X X X X X X X 3) Estimate the answer to: (a) (b) -0.6 1.6 = 2000 = 7500 0.5 -1.25

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

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

  18. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE C STARTERS PLT Skills 1) The graph shows Amy’s progress on a sponsored walk. Stop 19km Stop (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) 2 times 11:30 – 12:30 This is where the line is steepest 20p x 19 = £3.80 30p x 19 = £5.70 9.50

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

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

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

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