Round each of these numbers to the accuracy shown.
(a)Round 3872 to the nearest 100.(1)
(b)Round 6.482 to 1 decimal place.(1)
(c)Round 0.00567 to 2 significant figures.(1)
(Total for Question 1 is 3 marks)
2
A plank of wood is measured as 8 cm, correct to the nearest centimetre.
(a)Write down the minimum possible length of the plank (the lower bound).(1)
(b)Write down the maximum possible length of the plank (the upper bound).(1)
(Total for Question 2 is 2 marks)
3
A number, n, is rounded to the nearest whole number. The result is 15. Write down the error interval for n.
(Total for Question 3 is 2 marks)
4
The mass of a bag of sugar is 750 g, correct to the nearest 10 g. Write down the error interval for the mass, m grams.
(Total for Question 4 is 2 marks)
5
A number x is given as 6.4, correct to 1 decimal place. Write down the error interval for x.
(Total for Question 5 is 2 marks)
6
The population of a town is 24 000, correct to 2 significant figures. Write down the error interval for the population, P.
(Total for Question 6 is 2 marks)
7
A steel rod has length L = 12 cm, correct to the nearest centimetre. Circle the correct error interval for L.
A) 11 ≤ L < 12
B) 11.5 ≤ L < 12.5
C) 11.5 < L ≤ 12.5
D) 11 < L ≤ 12
(Total for Question 7 is 1 mark)
8
A value v = 3.80, correct to 3 significant figures. Write down the error interval for v.
(Total for Question 8 is 2 marks)
9
The error interval for a number w is 15.5 ≤ w < 16.5. Write down the value that w was rounded to.
(Total for Question 9 is 2 marks)
10
A plank of wood has length 2.4 m, measured to the nearest 10 cm. Write down the error interval for the length, l metres.
(Total for Question 10 is 2 marks)
11
Two numbers are each given correct to the nearest 10: a = 60 and b = 30. Work out the upper bound for a + b.
(Total for Question 11 is 2 marks)
12
The number n = 25, correct to the nearest 5. For each statement below, write True or False.
(i)The error interval for n is 22.5 ≤ n < 27.5.(1)
(ii)n could equal 27.4.(1)
(iii)n could equal 27.5.(1)
(iv)n could equal 22.(1)
(Total for Question 12 is 4 marks)
13
a = 8.2, correct to 1 decimal place. b = 3.7, correct to 1 decimal place. Work out the lower bound for a - b.
(Total for Question 13 is 2 marks)
14
A rectangular field has length 40 m and width 25 m, each measured correct to the nearest metre. Work out the upper bound for the perimeter of the field.
Diagram NOT accurately drawn
(Total for Question 14 is 3 marks)
15
A rectangle has length 12 cm and width 5 cm, each correct to the nearest centimetre. Work out the lower bound for the area of the rectangle.
Diagram NOT accurately drawn
(Total for Question 15 is 3 marks)
16
A car travels 150 miles, correct to the nearest 10 miles, in a time of 3 hours, correct to the nearest 0.5 hours. Work out the upper bound for the average speed of the car. Give your answer correct to 3 significant figures.
(Total for Question 16 is 3 marks)
17
The mass of a metal cube is 540 g, correct to the nearest 10 g. The volume of the cube is 65 cm3, correct to the nearest 5 cm3. Density = mass / volume. Work out the minimum possible density of the metal. Give your answer correct to 3 significant figures.
(Total for Question 17 is 3 marks)
18
x = 7.2, correct to 1 decimal place. y = 3, correct to the nearest whole number. Work out the error interval for x + y.
(Total for Question 18 is 3 marks)
19
The length of a side of a square is given as 9 cm, correct to the nearest whole number.
Diagram NOT accurately drawn
(a)Sam calculates the upper bound for the area of the square by working out 9 x 9.5 = 85.5 cm2. Explain why Sam's method is incorrect.(1)
(b)Work out the correct upper bound for the area of the square.(2)
(Total for Question 19 is 3 marks)
20
A rectangular garden has length 15 m and width 8 m, each measured correct to the nearest metre. A fence is to be built around the perimeter of the garden. Fencing costs 12.50 pounds per metre. James has a budget of 575 pounds. By considering the upper bound of the perimeter, determine whether James definitely has enough money to pay for the fencing. You must show your working.
Diagram NOT accurately drawn
(Total for Question 20 is 4 marks)
Mark scheme · 3.1 Error Intervals
Question 1
(a) B1 3900 cao
(a) Answer: 3900
(b) B1 6.5 cao
(b) Answer: 6.5
(c) B1 0.0057 cao
(c) Answer: 0.0057
Question 2
(a) B1 7.5 (cm) cao
(a) Answer: 7.5 cm
(b) B1 8.5 (cm) cao
(b) Answer: 8.5 cm
Question 3
M1 one correct bound identified, 14.5 or 15.5 oe
A1 14.5 ≤ n < 15.5 cao
Answer: 14.5 ≤ n < 15.5
Question 4
M1 one correct bound identified, 745 or 755 oe
A1 745 ≤ m < 755 cao
Answer: 745 ≤ m < 755
Question 5
M1 one correct bound identified, 6.35 or 6.45 oe
A1 6.35 ≤ x < 6.45 cao
Answer: 6.35 ≤ x < 6.45
Question 6
M1 one correct bound identified, 23500 or 24500 oe
A1 23500 ≤ P < 24500 cao
Answer: 23500 ≤ P < 24500
Question 7
B1 B (11.5 ≤ L < 12.5) cao
Answer: B) 11.5 ≤ L < 12.5
Question 8
M1 one correct bound identified, 3.795 or 3.805 oe
A1 3.795 ≤ v < 3.805 cao
Answer: 3.795 ≤ v < 3.805
Question 9
M1 recognises the interval has width 1, so w was rounded to the nearest whole number oe
A1 16 cao
Answer: 16
Question 10
M1 converts 10 cm to 0.1 m and identifies one correct bound, 2.35 or 2.45 oe
A1 2.35 ≤ l < 2.45 cao
Answer: 2.35 ≤ l < 2.45
Question 11
M1 upper bound of a = 65 and upper bound of b = 35 oe
A1 100 cao
Answer: 100
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 lower bound of a = 8.15 and upper bound of b = 3.75 oe
A1 4.4 cao
Answer: 4.4
Question 14
M1 upper bound of length = 40.5 and upper bound of width = 25.5 oe
M1 dep uses perimeter = 2(length + width) oe
A1 132 (m) cao
Answer: 132 m
Question 15
M1 lower bound of length = 11.5 and lower bound of width = 4.5 oe
M1 dep multiplies the two lower bounds oe
A1 51.75 cao
Answer: 51.75 cm2
Question 16
M1 upper bound of distance = 155 and lower bound of time = 2.75 oe
M1 dep 155 / 2.75 oe
A1 56.4 (mph) awrt, ft from correct bounds
Answer: 56.4 mph (awrt)
Question 17
M1 lower bound of mass = 535 and upper bound of volume = 67.5 oe
M1 dep 535 / 67.5 oe
A1 7.93 (g/cm3) awrt, ft from correct bounds
Answer: 7.93 g/cm3 (awrt)
Question 18
M1 bounds for x: 7.15 and 7.25; bounds for y: 2.5 and 3.5 oe
M1 dep adds the two lower bounds and adds the two upper bounds oe
A1 9.65 ≤ x + y < 10.75 cao
Answer: 9.65 ≤ x + y < 10.75
Question 19
(a) B1 states that both sides of the square should use the upper bound (9.5 cm), not just one side, oe
(a) Answer: Sam has only used the upper bound for one side; both sides of the square should use the upper bound of 9.5 cm.
(b) M1 9.5 x 9.5 oe
(b) A1 90.25 cao
(b) Answer: 90.25 cm2
Question 20
M1 upper bound of length = 15.5 and upper bound of width = 8.5 oe
M1 dep uses perimeter = 2(length + width) to find upper bound of perimeter = 48 (m) oe
M1 dep multiplies upper bound of perimeter by 12.50 to find upper bound of cost = GBP600 oe, ft
A1 correct conclusion with correct supporting figures, e.g. No, because the cost could be as much as GBP600, which is more than his GBP575 budget cao
Answer: No - the upper bound cost is GBP600, which exceeds James's GBP575 budget, so he does not definitely have enough money.