Corbettmaths

Workout

Question 1:

(a)   LB: 3.5g,  UB: 4.5g

(b)   LB: 11.5cm, UB: 12.5cm

(c)   LB:  74.5miles, UB: 75.5miles

(d)  LB:  45kg,  UB:  55kg

(e)  LB:  125 seconds,  UB:  135 seconds

(f)  LB:  222.5km,  UB:  227.5km

(g)  LB:  350ml,  UB:  450ml

(h)  LB: 1895 hours,  UB:  1905 hours

(i)   LB:  2650mm,  UB:  2750mm

(j)   LB:  4950km,   UB:  5050km

(k)  LB:  27995kg,   UB:  28005kg

(l)  LB:  25000km/h,   UB:  35000km/h

Question 2:

(a)   LB:  75,   UB:  84

(b)   LB:  £9.50,   UB:  £10.49

(c)   LB:  450 chairs,  UB:  549

(d)   LB:  13500,  UB:  14499

(e)   LB:  £28950,   UB:  £29050

Question 3:

(a)   LB:  3.75cm,   UB:  3.85cm

(b)   LB:  15.15,   UB:  15.25

(c)   LB:  6.35g,   UB:  6.45g

(d)   LB:  515.85kg,   UB:  515.95kg

(e)   LB:   0.065 seconds,   UB:  0.075 seconds

(f)   LB:  5.255mm,   UB:  5.265mm

(g)   LB:  24.0905kg,    UB:  24.0915kg

(h)  LB:  7.95cm,    UB:  8.05cm

Question 4:

(a)  LB:  3.5 miles,   UB:  4.5 miles

(b)   LB:  25cm,   UB:  35cm

(c)  LB:  850ml,   UB:  950ml

(d)  LB:  0.15m,  UB:  0.25m

(e)   LB:  13.5 hours,  UB:  14.5 hours

(f)   LB:  275g,   UB:  285g

(g)   LB:  41500km,  UB:  42500km

(h)  LB: 747.5 gallons,  UB:  748.5 gallons

(i)   LB:  395m,   UB: 405m

(j)   LB:  7950kg,  UB:  8050kg

(k)  LB:  289950km/h,   UB:  290050km/h

(l)   LB:  0.0235,   UB:  0.0245

(m)  LB:  15.05,  UB:  15.15km

(n)   LB:  95g,  UB: 150g

Apply:

Question 1:   No yet! As the space may be as little as 205cm, he really needs to go back and measure again… a bit more accurately!

Question 2:  349

Question 3:  No, to the nearest 10, the LB would be 395m and UB 405m

Question 4:  (a)  £2.94    (b)  £3.68

Question 5:  I agree with the 12%… 9.5 and 15.

Option 1 – 5 is already to 1 significant figure

Option 2 – 10.5 isn’t the upper bound, 11 rounds to 10 to 1st, so do 14 etc.

Option 3 – I agree!

Option 4 – 7.5 rounds to 8 to 1 sf.

 

Workout Answers

Question 1(a)

Question 1(b)

Question 1(c)

Question 1(d)

Question 1(e)

Question 1(f)

Question 1(g)

Question 1(h)

Question 1(i)

Question 2(a)

Question 2(b)

Question 2(c)

Question 2(d)

Question 2(e)

Question 2(f)

Question 2(g)

Question 2(h)

Question 2(i)

Question 2(j)

Question 3

(a)  y < x + 1

(b)  y ≥ x − 1

(c)   y > 2x

(d)   y ≤ 2x + 4

(e)  y < −3x + 6

(f)   y > 4x + 1

Question 4:

(a)

(b)

(c)

(d)

(e)

(f)

Question 5:

(a)   x > 2,   y ≤ 4,   y ≥ x − 1

(b)   y ≥ −1,   y ≤ −2x + 6,   y < 4x

(c)   y < 6,  x ≤ 2,  y ≥ −6x + 6

(d)   y < 8,  y > 4x − 2,   y < 10x + 10

(e)   y ≤ 4,  x ≤ 1,  y > − x + 2,  y ≤ 2x + 5

(f)   y ≥ x + 2,   y < 4.5x + 2.5,   y ≤ −0.5x + 5

Apply

Question 1:    Taylor has selected the wrong region

Question 2:    The line should be dashed

Question 3:     Region A

Question 4:

Question 5:   (a)   yes    (b)   no

(c)   £9800 with 20 economy and 40 first class

Question 6:

Workout

Question 1:

(a)   5           (b)   6           (c)  4           (d)  6

(e)   3           (f)   16          (g)  10        (h)  7

(i)   4.5         (j)  13           (k)  6          (l)  12

Question 2:

(a)   10         (b)  14          (c)  12         (d)  24

(e)   27         (f)   8            (g)  33         (h)  36

(i)  35           (j)   39          (k)  26         (l)  32

Question 3:

(a)  £7         (b)  75kg       (c)  18cm      (d)  28 seconds

(e)  36 miles    (f)  £125     (g)  100ml    (h)  279 students

(i)  3 hours    (j)  800m     (k)  6 days     (l)   2mm

Question 4:

(a)  9.6miles    (b)  3.6kg    (c)  2.666… litres    (d)   £4.20

(e)  6.25cm      (f)  986.2km    (g)  £42.75     (h)  46.888…km

Question 5:

(a)  1/3 of 21       (b)  2/3 of 9         (c)  2/5 of 65

(d)  3/4 of 60cm    (e)   3/8 of a day

(f)   2/3 of 453        (g)  2/7 of 420

Apply

Question 1:   15

Question 2:    3

Question 3:   16 good apples

Question 4:    (a)  9 hours      (b)   15 hours     (c)   5/8

Question 5:    £2400

Question 6:    £600

Question 7:   11893

Question 8:    194 is not divisible by 4 and there cannot be 48.5 students

Question 9:   4/15

Question 10:   Smaller than the original (100g –> 120g –> 96g)

Question 11:   £1,816,448

Workout

Question 1

(a)   16cm      (b)  24cm     (c)  28cm

(d)  24cm       (e)  34cm     (f)   46cm

Question 2

(a)  52cm      (b)  48cm      (c)  110mm

(d)  6.6m      (e)  360m       (f)  192mm

Question 3

(a)  60cm      (b)  136cm      (c)  3.6m

Question 4

(a)  24cm      (b)   13.5cm      (c)  213m      (d)  0.78cm

Question 5

(a)  58cm     (b)  24cm     (c)   26.5cm

Question 6

(a)  42cm     (b)  85cm     (c)  24.8cm

Question 7

(a)  42cm     (b)  14cm      (c)  54m

(d)   44cm    (e)  74cm

Question 8

(a)  5cm      (b)  26cm      (c)  5cm

(d)  7cm      (e)  12cm      (f)  22cm

(g)  13.5cm    (h)  40cm     (i)  37cm

Apply

Question 1:   The answer depends on the size of printing.

Question 2:   length 8cm, width 1cm. Other answers available.

Question 3:   12cm

Question 4:   17.8m

Question 5:   1120m (1.12km)

Question 6:    £261

Question 7:    width = 75cm  and length = 115cm

Question 8:    48cm

Question 9:    24cm

Question 10:   3cm by 8cm (A = 24 and P = 22)    2cm by 12cm (A = 24 and P = 28)

Question 11:   (a)  The area of A is less than B    (b)  The perimeters are the same

Question 12:    90cm

Question 13:    74cm

Question 14:     4.5cm

Workout

Question 1:

(a)    £8  £12           (b)   5cm    10cm            (c)    £6    £18           (d)   20 sweets  15 sweets

(e)   33g   22g         (f)   9kg   45kg                (g)   £60   £150         (h)   50 hours   70 hours

(i)    105m   245m    (j)  72°  288°

Question 2:

(a)  £39   £65        (b)  138 miles  23 miles    (c)  70ml   245ml     (d)   $200  $450

(e)  £352  £448     (f)  90kg  1110kg        (g)  €442  €68          (h)  124mm  992mm

Question 3:

(a)  £5  £15  £20     (b)  14ml  21ml  28ml     (c)   16p  32p  40p

(d)  40°  40°  100°    (e)  $11  $22  $132      (f)  120cm  160cm  80cm  360cm

Question 4:

(a)  400m 600m  (or 0.4km 0.6km)          (b)  180cm  20cm  (or 1.8m 0.2m)

(c)  8 hours 16 hours (or 1/3 day 2/3day)   (d)  96 seconds 144 seconds (or 1.6 min 2.4 min)

(e)  £1.20  £4.80                                            (f)  €3.50  €8.50

Question 5:

(a)  2.5ml  7.5ml          (b)  6.8g    10.2g         (c)  129.375ml   215.625ml

(d)  £81.25  £178.75     (e)  12.888…°  45.111…°   (f)  97.777… s  244.444…s  537.777… s

Apply

Question 1:  12 red sweets

Question 2:  Liam £15 and Nathan £45

Question 3:  45 children

Question 4:  (a) 50kg   (b) 100kg  (c) 150kg

Question 5: (a) 30° 30°  120°    (b) Isosceles

Question 6:  (a)  64 blue beads   (b) 1/5       (c)  80%

Question 7:  (a) 28 is not divisible by 5        (b)  any multiple of 5 (perhaps 35 or less)

Question 8:  £19800

Question 9:   18 boys study Spanish

Question 10:  262 votes

Question 11:  £2.64

Question 12:  96 chocolate, 24 strawberry, 32 vanilla

Question 13:  147 black cars

Question 14:  250 stayed in caravans