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

Which ones are you using? Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker LINEAR GRADE C STARTERS PLT Skills Which ones are you using? 1) 2) Write 32 as a product of prime factors 32 8 4 4 7 10 13 (a) Work out the nth term for the pattern of matches 3n + 1 4 2 2 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 2

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

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

Which ones are you using? Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker LINEAR GRADE C STARTERS PLT Skills Which ones are you using?   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.   5

Which ones are you using? Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker LINEAR GRADE C STARTERS PLT Skills Which ones are you using? 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? 2) Divide 77kg in the ratio 2:4:5 SQUASH : WATER 4 : 5 x 7 x 7 28cl : 35cl ? 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: 6

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

Which ones are you using? Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker LINEAR GRADE C STARTERS PLT Skills Which ones are you using? 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 𝑥 + 5 = 12 - 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.. 8

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

Which ones are you using? Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker LINEAR GRADE C STARTERS PLT Skills Which ones are you using? 1) Describe fully the single transformation that maps triangle A onto triangle B 2) Enlarge the shape by scale factor 2 with (0,0) as the centre of enlargement.   3) 4) Score Frequency Midpoint fx 1-5 9 6-10 10 11-15 13 16-20 7 21-25 1 Total Score Frequency fx 1 5 2 4 3 9 8 6 Total 5 3 27 8 8 80 27 13 169 32 18 126 40 23 23 36 40 148 40 425 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 Mode = 3 Range = 6 – 1 = 5 Estimated Mean = 425/40 = 10.6 Modal Group = 11-15 10

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

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

Which ones are you using? Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker LINEAR GRADE C STARTERS PLT Skills Which ones are you using? 1) Find the HCF of 12 and 30 2) Find the LCM of 6 and 8 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 3) 4) 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) 13

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

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

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

Which ones are you using? Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker LINEAR GRADE C STARTERS PLT Skills Which ones are you using? 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 10mins 20mins (c) Work out the average speed for each of the five stages of the journey. A-B B-C C-D E-F 20mins = 16km 10mins = 19km 20mins = 15km 60mins = 50km x3 x3 x6 x6 x3 x3 60mins = 48km 60mins = 114km 60mins = 45km 50km/h 48km/h 114km/h 45km/h 17

Which ones are you using? Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker LINEAR GRADE C STARTERS PLT Skills Which ones are you using? 1) The graph shows Amy’s progress on a sponsored walk. 19km Stop 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 18

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

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

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