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GCSE LINEAR GRADE D 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 D STARTERS. PLT Skills. 1). 2).

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  1. GCSE LINEAR GRADE D 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 D STARTERS PLT Skills 1) 2) Jack and Thomas find a bag of marbles that they share between them in the ratio of their ages. Jack is 10 years old and Thomas is 15 years old. What fraction of the marbles did Jack get? 3 x 1 – 1 = 2 Jack : Thomas 3 x 2 – 1 = 5 10 : 15 3 x 3 – 1 = 8 Total parts = 10 + 15 = 25 3 x 4 – 1 = 11 3 x 5 – 1 = 14 48m 60miles Speed = Time = 4m/s 0.5hour Distance = 48 m Speed = 4m/s Time = ? seconds Distance = 60 miles Speed = ? mph Time = 30 minutes 3) Distance = ? kilometres Speed = 13 km/h Time = 3 hours 4) 5) Distance = 13km/h x 3hours = 39km = 120mph = 12seconds

  3. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE D STARTERS PLT Skills 4) 1) Construct triangle EFG where EG=12cm, EF=8cm and FG=7cm. 7cm (a) Probability of a left handed female from the class? F 8cm (b) Probability of a right handed student from the class? G E (c) Probability of a right handed male from all the males? 12cm 2) A cloth bag contains a mix of black, white and red balls. Selecting one ball at random, the probability of getting a black ball is 0.2, while the probability of getting a white ball is 0.5. What is the probability of getting a red ball? Probability adds up to one whole 1 – 0.2 – 0.5 P(Red) = 8cm 7cm = 0.3 3) A paper bag contains 5 red, 7 green and 8 blue sweets. If a sweet is selected at random from the bag, find the probability that the sweet is: (a) Red or blue (b) Not blue G E 12cm =

  4. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE D STARTERS PLT Skills 1) 2) Find the bearing of B from A A is due North of B. The bearing of C from A is 115°.The bearing of C from B is 075°. MUST BE WRITTEN AS 3 FIRGURES Mark the position of C on the diagram. 054° B A C N 12 – 2p 3) Find the value of when: 2 p (b) (a) p = 8 = 3 Replace p with 8 Replace p with 3 12 – 2 x 8 12 – 2 x 3 = = 2 2 12 – 16 -4 12 – 6 6 = = -2 = = = 3 = 2 2 2 2

  5. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE D STARTERS PLT Skills 1) 2) Design a data collection sheet to see where the class want to go for their school trip this year. The headteacher wants to find out many hours his students spend on homework in a week. Design a two way table to help him collect results. Tally Frequency Place Alton Towers Year 7 Lightwater Valley Year 8 Year 9 Bradley Woods Click to reveal Xscape Year 10 Year 11 3) Translate the red triangle 2 units left and 5 units down 4) A jar of instant coffee contains 200g and cost £2. There are two special offers. 2 left 2 left Which offer is the best value? 2 left OFFER A OFFER B 5 down 5 down 5 down 200g + 50g = 250g for £2 = 200g for £1.50 133.3g for £1 125g for £1 Therefore, offer B is better value

  6. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE D STARTERS PLT Skills 2) 1) There are 7.5million people living in London. One-eight of these are over 65. Of the over-65s, three-fifths are women. How many women over 65 live in London? 7500000 7.5million Therefore, no one got the most. They all had the same share. 4) 3) Write 4 days as a fraction of 2 weeks Write £5 as a fraction of £20 2 weeks 14 days = =

  7. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE D STARTERS PLT Skills Fill in the table below and draw the graph of y = 2x + 3 Write the coordinates of where the graph crosses y = 4 1) 2) Solve the following equation: 3(𝑥 + 5) = 42 Coordinates 3𝑥 = 42 15 + 2 x -3 + 3 -3 (-3,-3) y=4 - 15 -15 2 x -2 + 3 -1 (-2,-1) 3𝑥 (0.5,4) 27 = 2 x -1 + 3 1 (-1,1) ÷ 3 ÷ 3 (0,3) 2 x 0 + 3 3 𝑥 9 = (1,5) 2 x 1 + 3 5 (2,7) 2 x 2 + 3 7 0 1 2 3 4 5 (3,9) 2 x 3 + 3 9 3) Write down the inequality represented by the lines below: (c) (a) (b)

  8. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE D STARTERS PLT Skills 1) 2) Solve the following equation: Rotate the shape 90º clockwise about the origin: 7𝑥 + 9 = 2𝑥 + 19 - 2𝑥 - 2𝑥 9 5𝑥 19 = + - 9 - 9 5𝑥 = 10 ÷ 5 ÷ 5 𝑥 2 = 3) Reflect the shape in the line y = 3: 4) y = 3 Cuts the y-axis at 3

  9. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE D STARTERS PLT Skills 1) Work out the value of angles a, b and c. Give reasons for your answers 50º a 70º 120º 120º 130º c b 70º Alternate angles Corresponding angles Interior angles 2) 3) Work out the values of: Work out the values of: (b) (d) (a) (c) (b) (d) (c) (a) = 8 x 8 = 5 = 3 x 3 = 5 x 5 x 5 = 3 = 2 x 2 x 2 = 4 & -4 = 9 & -9 = 125 = 8 = 64 = 9 5) 4) The line graph shows temperature over a week : Multiply: (a) (b) 2.4 x 0.7 8.2 x 3.9 4 2 x x 8 2 0 0 0 3 2 0 3 1 0 0 4 6 1 2 7 1 9 7 1 1 4 8 2 8 8 6 8 9 ANSWER = 1.68 ANSWER = 31.98 What was difference between the highest and lowest temperatures? 38 - 30 = 8ºC

  10. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE D STARTERS PLT Skills 1) Interpret the scatter graph below: 2) 3) Increase £60 by 30% Decrease £80 by 40% 10% = £6 10% = £8 x3 x4 x3 x3 x4 x3 £18 £32 30% = 40% = Area of a triangle = x base x vertical height Area of triangle = x 10 x 6 £60 + £18 = £78 £80 - £32 = £48 4) 5) Increase £40 by 35% Decrease £120 by 17.5% 10% = £4 10% = £12 £12 £6 30% = 5% = £2 £3 5% = 2.5% = £14 35% = £21 17.5% = As height increases, handspan increases (ignoring anomalies). Positive correlation. £99 £40 + £14 = £120 - £21 = £54 6) 7) 8) Find the area of the triangle. Find the area of the parallelogram. Area of a parallelogram = base x vertical height 2 2 Find the modal class from the table. Area of triangle = 30cm Area of parallelogram = 36cm Area of parallelogram = 9 x 4 One with highest frequency 4 < P ≤ 5

  11. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager 1m LINEAR GRADE D STARTERS PLT Skills 7cm 1) 2) A 7 x 2 A 2cm 7m 6m 4 x 4 B 4cm B 4cm 3(m - 5) (c) (b) y(y – 4x) (a) 4t(t + 2) Find the area of the compound shape. 10m TOTAL AREA = Find the area of the compound shape. 2 = 4t + 8t B = 10 x 6 3) 4cm TOTAL AREA = 5cm 3cm 4) 2 Expand the following: = y - 4xy 3 10cm = 3m - 15 Work out the area shaded black. Area of large rectangle = 10 x 5 Area of small rectangle = 4 x 3 AREA SHADED =

  12. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE D STARTERS PLT Skills 1) 2) Divide £15 in the ratio 3:2 Factorise the following: ( ) of £6 £15 = ( ) 3m + 2p = 2y of £9 £15 = = 3 2t + 3m (a) 6t + 9m (b)6my + 4py 4) 3) x x 2 3 ÷ ÷ 5 5 Enlarge triangle T by scale factor 2, with (0,0) as the centre of enlargement.

  13. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE D STARTERS PLT Skills 1) 2) Draw the plan, side elevation and front elevation for the object shown. Draw the plan, side elevation and front elevation for the object shown. 4) 3) Label the expression, equation, formula and identity below: Equation Identity Formula P = 2l + 2w Expression

  14. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE D STARTERS PLT Skills 1) 2) 0 2 8 18 1 0.25 0.25 4 2 0.5 0.5 9 18 0 1 4 9 8 y y X X X X X X X X X X X X X X X X X X -1.8 1.8 -2.3 2.3 0 0 0 0

  15. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE D STARTERS PLT Skills 1) 2) This is from a questionnaire on healthy eating. Fast food is bad for you. Don’t you agree? □ Strongly agree □ Agree □ Don’t know Give two criticisms of the question. 1) It is a leading question. 2) No response section for disagree boxes. 3) A Describe fully the transformation that maps triangle A onto triangle B A reflection in the line x = -1 4) B Change the following decimals to fractions: (a) (b) (c) 0.42 0.004 0.6 Describe fully the transformation that maps flag A onto flag B 0 0 0 4 0 6 0 4 2 Rotationof 90° anticlockwise from centre (0,0) = = =

  16. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE D STARTERS PLT Skills 1) Change the following fractions to decimals: 2) (a) (d) (b) (c) 0 5 0 3 0 0 9 4 0 0 + x + 8 = 360 3x + 10 + 2x – 4 + 28 = 0.05 = 0.3 = 0.09 = 0.4 = 360 6x + 42 3) Draw an ordered stem and leaf diagram for the following data: 6x = 318 x =53º 21, 47, 35, 32, 11, 19, 28, 22, 25, 39, 38, 41, 42, 33, 17, 35 Shape A Shape B 4) Biggest = 47 Smallest = 11 5cm 8cm 1 7 1 9 KEY: 4cm 10cm How many times bigger is the area of shape B in comparison to shape A means 3 2 32 2 1 2 8 5 3 9 2 3 5 5 8 Area of parallelogram = base x vertical height 2 7 4 1

  17. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE D STARTERS PLT Skills 1) Draw a histogram with equal class intervals for the data in the table: 2) Write down the properties of a rectangle. A histogram to show the test scores - Two pairs of equal sides No. of students - Four right angles - Opposite sides are parallel - Two lines of symmetry - Rotational symmetry of order 2 - Diagonals bisect each other 3) 4) Calculate the mean from the table: Test Scores 20mins fx x 5 x 8 x 27 x 32 x 40 x 36 148 40 = 50km/h 20mins (a) How long was the stop? (b) Average speed from E to F?

  18. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager LINEAR GRADE D STARTERS PLT Skills 1) 2) Find the area of the circle: Find the area of the circle: 4cm 14m x x Area of circle = 7 3.14 7 x x Area of circle = 4 3.14 4 (1d.p.) Area of circle = 153.9 Area of circle = 50.2 (1d.p.) radius diameter Find the circumference of the circle: Find the circumference of the circle: 3) 4) 8cm 11m 2 2 m cm x x 3.14 3.14 8 22 Circumference of a circle = Circumference of a circle = Circumference of a circle = 25.1 (1d.p.) Circumference of a circle = 69.1 (1d.p.) cm m

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