Round each of these numbers to the accuracy shown.
(a)Round 47 382 to the nearest 1000.(1)
(b)Round 9.647 to 2 decimal places.(1)
(c)Round 0.03812 to 3 significant figures.(1)
(Total for Question 1 is 3 marks)
2
A recipe requires 1.5 kg of flour, correct to the nearest 0.1 kg.
(a)Write down the minimum possible mass of flour (the lower bound).(1)
(b)Write down the maximum possible mass of flour (the upper bound).(1)
(Total for Question 2 is 2 marks)
3
The number of spectators at a rugby match is given as 8600, correct to the nearest 100. Write down the error interval for the number of spectators, s.
(Total for Question 3 is 2 marks)
4
The number of pupils in a school year group is 175, correct to the nearest 5. Write down the error interval for the number of pupils, p.
(Total for Question 4 is 2 marks)
5
The volume of petrol in a tank is V = 42.6 litres, correct to 1 decimal place. Write down the error interval for V.
(Total for Question 5 is 2 marks)
6
The attendance at a concert was 7200, correct to 2 significant figures. Write down the error interval for the attendance, a.
(Total for Question 6 is 2 marks)
7
A garden hose has length 15 m, correct to the nearest metre. Circle the correct error interval for the length, L.
A) 14.5 ≤ L < 15.5
B) 14 ≤ L < 15
C) 14.5 < L ≤ 15.5
D) 15 ≤ L < 15.5
(Total for Question 7 is 1 mark)
8
A length is recorded as r = 0.128 m, correct to 3 significant figures. Write down the error interval for r.
(Total for Question 8 is 2 marks)
9
The error interval for a number k is 3.65 ≤ k < 3.75. State the value that k was rounded to, and the degree of accuracy used.
(Total for Question 9 is 2 marks)
10
A parcel has mass 3.6 kg, correct to the nearest 100 g. Write down the error interval for the mass, m kilograms.
(Total for Question 10 is 2 marks)
11
Two numbers are each given correct to the nearest whole number: p = 14 and q = 9. Work out the lower bound of p + q.
(Total for Question 11 is 2 marks)
12
The number n = 40, correct to the nearest 10. For each statement below, write True or False.
(i)The error interval for n is 35 ≤ n < 45.(1)
(ii)n could equal 44.9.(1)
(iii)n could equal 45.(1)
(iv)n could equal 34.(1)
(Total for Question 12 is 4 marks)
13
a = 6.2, correct to 1 decimal place. b = 3.5, correct to 1 decimal place. Work out the upper bound for a x b. Give your answer correct to 3 significant figures.
(Total for Question 13 is 2 marks)
14
A rectangular ice rink has length 60 m and width 30 m, each measured correct to the nearest metre. Work out the lower bound for the perimeter of the rink.
(Total for Question 14 is 3 marks)
15
A triangular flower bed has base 10 m and height 6 m, each measured correct to the nearest metre. Work out the lower bound for the area of the flower bed.
Figure (to be drawn): Triangle with its base labelled 10 m and its height labelled 6 m.
(Total for Question 15 is 3 marks)
16
A cyclist travels 45 km, correct to the nearest km, in a time of 2 hours, correct to the nearest 0.5 hours. Work out the lower bound for the average speed of the cyclist. Give your answer correct to 3 significant figures.
(Total for Question 16 is 3 marks)
17
The force exerted on a surface is F = 850 N, correct to 2 significant figures. The area of the surface is A = 4.5 m2, correct to 2 significant figures. Pressure = Force / Area. Work out the maximum possible pressure. Give your answer correct to 3 significant figures.
(Total for Question 17 is 3 marks)
18
a = 5.4, correct to 1 decimal place. b = 12, correct to the nearest whole number. Work out the error interval for 2a + b.
(Total for Question 18 is 3 marks)
19
The length of a rope is given as 6 m, correct to the nearest whole number.
(a)Priya calculates the lower bound for the total length of two of these ropes joined together by working out 6 - 0.5 = 5.5 m. Explain why Priya's method is incorrect.(1)
(b)Work out the correct lower bound for the total length of two of these ropes joined together.(2)
(Total for Question 19 is 3 marks)
20
A classroom floor is rectangular with length 5 m and width 4 m, each measured correct to the nearest metre. New carpet costs 15.20 pounds per square metre. Mrs Ahmed has a budget of 330 pounds. By considering the upper bound of the area of the classroom floor, determine whether Mrs Ahmed definitely has enough money to pay for the carpet. You must show your working.
Figure (to be drawn): Rectangle representing the classroom floor, labelled length 5 m and width 4 m.
(Total for Question 20 is 4 marks)
Mark scheme · 3.1B Error Intervals (Part 2)
Question 1
(a) B1 47000 cao
(a) Answer: 47000
(b) B1 9.65 cao
(b) Answer: 9.65
(c) B1 0.0381 cao
(c) Answer: 0.0381
Question 2
(a) B1 1.45 (kg) cao
(a) Answer: 1.45 kg
(b) B1 1.55 (kg) cao
(b) Answer: 1.55 kg
Question 3
M1 one correct bound identified, 8550 or 8650 oe
A1 8550 ≤ s < 8650 cao
Answer: 8550 ≤ s < 8650
Question 4
M1 one correct bound identified, 172.5 or 177.5 oe
A1 172.5 ≤ p < 177.5 cao
Answer: 172.5 ≤ p < 177.5
Question 5
M1 one correct bound identified, 42.55 or 42.65 oe
A1 42.55 ≤ V < 42.65 cao
Answer: 42.55 ≤ V < 42.65
Question 6
M1 one correct bound identified, 7150 or 7250 oe
A1 7150 ≤ a < 7250 cao
Answer: 7150 ≤ a < 7250
Question 7
B1 A (14.5 ≤ L < 15.5) cao
Answer: A) 14.5 ≤ L < 15.5
Question 8
M1 one correct bound identified, 0.1275 or 0.1285 oe
A1 0.1275 ≤ r < 0.1285 cao
Answer: 0.1275 ≤ r < 0.1285
Question 9
M1 recognises the interval has width 0.1, so k was rounded to 1 decimal place (nearest 0.1) oe
A1 3.7 cao
Answer: 3.7, correct to 1 decimal place (nearest 0.1)
Question 10
M1 converts 100 g to 0.1 kg and identifies one correct bound, 3.55 or 3.65 oe
A1 3.55 ≤ m < 3.65 cao
Answer: 3.55 ≤ m < 3.65
Question 11
M1 lower bound of p = 13.5 and lower bound of q = 8.5 oe
A1 22 cao
Answer: 22
Question 12
(i) B1 True cao
(i) Answer: True
(ii) B1 True cao
(ii) Answer: True
(iii) B1 False cao
(iii) Answer: False
(iv) B1 False cao
(iv) Answer: False
Question 13
M1 upper bound of a = 6.25 and upper bound of b = 3.55 oe
A1 22.2 awrt cao
Answer: 22.2 (awrt)
Question 14
M1 lower bound of length = 59.5 and lower bound of width = 29.5 oe
M1 dep uses perimeter = 2(length + width) oe
A1 178 (m) cao
Answer: 178 m
Question 15
M1 lower bound of base = 9.5 and lower bound of height = 5.5 oe
M1 dep uses area = 0.5 x base x height with the lower bounds oe
A1 26.125 cao
Answer: 26.125 m2
Question 16
M1 lower bound of distance = 44.5 and upper bound of time = 2.25 oe
M1 dep 44.5 / 2.25 oe
A1 19.8 (km/h) awrt, ft from correct bounds
Answer: 19.8 km/h (awrt)
Question 17
M1 upper bound of F = 855 and lower bound of A = 4.45 oe
M1 dep 855 / 4.45 oe
A1 192 (N/m2) awrt, ft from correct bounds
Answer: 192 N/m2 (awrt)
Question 18
M1 bounds for a: 5.35 and 5.45; bounds for b: 11.5 and 12.5 oe
M1 dep finds bounds for 2a (10.7 and 10.9) and adds them to the bounds for b oe
A1 22.2 ≤ 2a + b < 23.4 cao
Answer: 22.2 ≤ 2a + b < 23.4
Question 19
(a) B1 states that the lower bound of ONE rope (5.5 m) must be used for BOTH ropes, not just found once for a single rope, oe
(a) Answer: Priya has only found the lower bound for one rope; the lower bound of each of the two ropes (5.5 m each) should be added together.
(b) M1 5.5 x 2 oe (or 5.5 + 5.5)
(b) A1 11 cao
(b) Answer: 11 m
Question 20
M1 upper bound of length = 5.5 and upper bound of width = 4.5 oe
M1 dep uses area = length x width to find upper bound of area = 24.75 (m2) oe
M1 dep multiplies upper bound of area by 15.20 to find upper bound of cost = GBP376.20 oe, ft
A1 correct conclusion with correct supporting figures, e.g. No, because the cost could be as much as GBP376.20, which is more than her GBP330 budget cao
Answer: No - the upper bound cost is GBP376.20, which exceeds Mrs Ahmed's GBP330 budget, so she does not definitely have enough money.