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

2. LINEAR GRADE E STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) 4) Write the term to term rule of the following sequences: (a) -3, -5, -7, -9, ….., …. Subtract 2 from the previous term each time Write down the next two terms of the following sequences: -2 (a) 1, 3, 6, 10, 15, ….., …. (b) 2, 3, 5, 9, 17, ….., …. +2 +3+4+5+6 21 +7 28 +1 +2+4 +8+16 33 +32 65 Work out the area and perimeter of: Replace with 2 and y with 3 = 2 x 2 – 3 x 3 = 4 – 9 = -5 Replace with -3 and y with -4 = 2 x -3 – 3 x -4 = -6 + 12 = 6 8.3cm 2.6cm Area of a rectangle = length x width Area of rectangle = 8.3 x 2.6 Perimeter of a rectangle = length + width + length + width Perimeter of rectangle = 8.3 + 2.6 + 8.3 + 2.6 Perimeter of rectangle = 21.8cm

3. LINEAR GRADE E STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) 4) Work out the following: = 1 x 1 x 1 = 1 = 2 x 2 x 2 = 8 = 5 x 5 x 5 = 125 What number multiplies by itself 3 times to make 27? = 3 What number multiplies by itself 3 times to make 64? = 4 Work out the following: (a) 10% of £40 = £4 10% means ÷10 (b) 10% of £57 10% means ÷10 = £5.70 Work out the following: (a) 30% of 90mm x3 10% = 9mm 30% = x3 27mm (b) 90% of 40years x9 10% = 4years 90% = x9 36years (c) 35% of 80cl x3 10% = 8cl 30% = x3 24cl 5% =4cl 35% = 28cl Add 30% and 5% answers (d) 17.5% of 60litres ÷2 10% = 6litres 5% = ÷2 3litres ÷2 2.5% = 1.5litres 17.5% = 10.5litres Add 10%, 5% and 2.5% answers On the map, how many km would 5cm be? x5 1cm = 160km 5cm = x5 800km

4. LINEAR GRADE E STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1)2) 3) (b) His speed for the first hour? (c) How long did he stop for? (d) How long did it take him to run 40km? 15mins30mins45mins 8km 10km/h 15mins 2hours 45mins P = 2L + 2W Use the formula to find W when L= 2 and P = 20 Replace L with 2 and P with 20 20 = 2 x 2 + 2 x W 20 = 4 + 2W - 4 16 = 2W ÷ 2 8 = W W = 8 Work out the value of each of the angles below: Angles in a triangle add to 180º 40º 60º 75º Isosceles triangle so base angles are the same

5. LINEAR GRADE E STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 5) 4) NOT THE SAME F = 1.8C + 32 Use the formula to find F when C= 4 Replace C with 4 F = 1.8 x 4 + 32 F = 7.2 + 32 F = 39.2 2 + 3 = 11 6 + 2= 9 + 2 6 = 9 6 - 5 = 34 - 3 2 = 8 ÷ 2 = 4 + 5 6 = 39 ÷ 6 = 6.5 - 2 6 = 7 x 6 = 42 x 6 + 2 = 54 - 2 = 52 3) 6)

6. LINEAR GRADE E STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) 5) (a)2y + 3y – 7y (b) 7x + 9 + 3x - 6 (c)5m – 6n + 4m – 3n = -2y = 10x Simplify by collecting like terms: + 3 = 9m – 9n 40º 70º (Exterior angle is equal to the sum of the opposite interior angles) = 110º Round the following to 1d.p.: (a) 4. 8 3 (b) 7. 2 8 = 4. 8= 7. 3 4) Round the following to 2d.p.: (a) 6. 8 3 2 (b) 3. 6 6 8 = 6. 8 3 = 3. 6 7 Round the following to 1s.f.: (a) 7. 1 (b) 6 7 (c) 3 8 2 = 7 = 70 = 400 (d) 0. 0 3 4 = 0.03

7. LINEAR GRADE E STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) 4) Reflect the shape in the y-axisReflect the shape in the x-axis y-axis Write down all the prime numbers below 30 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29 Which is the only even prime number? 2 xy = 3x - 5 0 1 2 Fill in the table above for y. 3 x -1 - 5 -8 3 x 0 - 5 -5 3 x 1 - 5 -2 3 x 2 - 5 1

8. 1 4 LINEAR GRADE E STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) (a) - 8 X +4 = +7 X - 6 = +3 X +5 = - 11 X - 2 = -32 -42 15 22 -15 +3 = +12 - 4 = +80 +10 = - 28 - 2 = -5 -3 8 14 (a) (b) (c) (d) (a) (b) (c) (d) 1 2 3 17 9 12 5 8 23558 9 27 KEY: 3 2 means 32 Stem-and-leaf to show the ages of people at a table tennis club How many people were asked their age? (b) What is the range of ages? (c) What is the median age? Count the amount of leaves 16 47 - 11 = 36 Find the middle age 32.5 4) Find the volume of the cuboid below: Volume = length x width x height Volume = 12cmx 6cm x 9cm Volume = 648cm 3 5) 5cm 100cm 60cm ÷20

9. LINEAR GRADE E 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 missing numbers below: (a) -7, -5. -3, …., …. (b) -6, -9. -12, …., …. (c) 1 -15 -18 a) UT th H b) 60 100 7 = 007. UT th H 06. 7% 6 10 = 60% = Change the decimals to fractions and percentages: Estimate the answers below: (a) 3.9 x 2.2 (b) -4.11 x 6.82 (c) -19.75 ÷ -4.91 4 x 2 = 8 -4 x 7 = -28 -20 ÷ 5 = -4 Enlarge the triangle by scale factor 2:

10. LINEAR GRADE E STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) 4) 1m = 1cm Draw an accurate scale drawing of the triangle above: 3m 2m 3m 2m Draw the lines with equations y=2 and y =-5: Draw the lines with equations x=3 and x =-7: Draw the lines with equations y=x and y =-x: x=3 x=-7 y=2 y=-5 y=x y=-x

11. (b) 48 ounces to pounds LINEAR GRADE E STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) Draw a 4 by 6 by 3 cuboid below: (c) 4 feet to inches (a) 36 feet to yards smaller to bigger (÷) 36 ÷ 3 = 12 yards smaller to bigger (÷) 48 ÷ 16 = 3 pounds bigger to smaller (x) 4 x 12 = 48 inches Convert the following units: (a) 732cm to m (b) 450cl to litres (c) 1.2m to cm (d) 3m to mm smaller to bigger (÷) 732 ÷ 100 = 7.32m smaller to bigger (÷) 450 ÷ 100 = 4.5 litres bigger to smaller (x) 1.2 x 100 = 120cm bigger to smaller (x) 3 x 1000 = 3000mm

12. y = 180º - 95º LINEAR GRADE E STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 3) Construct a pie chart for the table below: Musical Instruments Guitar35 Violin10 Recorder15 Drum5 Keyboard25 TOTAL = 90 Guitar Violin Recorder Drum Keyboard Find the averages and range for the data below: 2, 5, 6, 3, 1, 1, 15, 7 Ordered: 1, 1, 2, 3, 5, 6, 7, 15 Mode = 1 (most common) Median = 4 (middle when in order) Mean = = = 5 Range =Biggest - Smallest = 15 -1 = 14 y Work out the value of x and y above. x = 360º - 100º - 60º - 95º = 105º (Angles in a quadrilateral add to 360º) = 85º (Angles on a straight line add to 180º)

13. 4 LINEAR GRADE E STARTERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 1) 2) 6)7) 7.9 + 4.7 28.6 + 3.12 3) 7.52 - 4.45 4) 10.2 - 6.19 5) 5.8 x 9.8 7. 9 4. 7 + 6 1. 12 2 8. 6 3. 1 2 + 0 0 2 7. 1 1 3 7. 5 2 4. 4 5 - 1 7 0. 3 1 0. 2 0 0 6. 1 9 - 1 1 1 0. 1 4 0 58 x 9 8 4 5 7 2 4 0 6 4 48 6 1 5... 56.84 2 5 x 4 6 2 x 4 5 x 6 = 8 30 = 4 15 = 1 12 + 1 6 X 2 12 + 12 = 3 = 1 4 = 1 3 - 1 6 X 2 6 - 6 21 = 1 6 = 8)