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GCSE · Number

3.1D Error Intervals: Fluency and Exam Drill

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 40 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write down the lower bound and upper bound for a number which is 12, correct to the nearest integer, using inequality notation.

(Total for Question 1 is 1 mark)

A measurement is 3.7, correct to 1 decimal place. Give the lower and upper bounds using inequalities.

(Total for Question 2 is 1 mark)

A length is 250 cm, correct to the nearest 10 cm. State its bounds using inequality notation.

(Total for Question 3 is 1 mark)

A mass is recorded as 0.03, correct to 2 decimal places. Give the lower and upper bounds in inequality form.

(Total for Question 4 is 1 mark)

A number is 4.6, correct to 2 significant figures. Write down the lower and upper bounds using inequalities.

(Total for Question 5 is 2 marks)

A rectangle has length 12 cm, correct to the nearest centimetre, and width 3.5 cm, correct to 1 decimal place. Work out the greatest possible area of the rectangle. Give your answer as an inequality.

(Total for Question 6 is 3 marks)

A metal sheet has length 8.02 m correct to 3 significant figures and width 0.450 m correct to 3 significant figures. Find the lower bound for the area of the sheet. Give your answer as an inequality.

(Total for Question 7 is 3 marks)

Write down the bounds for 4.00, correct to 3 significant figures, using inequality notation.

(Total for Question 8 is 1 mark)

x is 2.3, correct to 1 decimal place. Work out the greatest possible value of 3x. Give your answer as an inequality.

(Total for Question 9 is 3 marks)

A cylindrical rod has radius 2.5 cm (to 2 significant figures) and height 40 cm (to the nearest centimetre). Find an inequality giving the range of possible volumes. Give numeric bounds.

(Total for Question 10 is 4 marks)

x is 12, correct to the nearest integer. Let y = x/3. Find the range of possible values of y, giving your answer in exact fractional form with inequalities.

(Total for Question 11 is 3 marks)

Give the lower and upper bounds for 0.7, correct to 1 significant figure, using inequalities.

(Total for Question 12 is 1 mark)

A cuboid has dimensions 2.0 cm, 3.0 cm and 4.0 cm, each given to 2 significant figures. Work out the greatest possible volume. Give your answer as an inequality.

(Total for Question 13 is 3 marks)

A baker uses 250 g of flour (to the nearest 10 g) and 120 g of sugar (to the nearest 10 g). Find the possible range for the total mass of flour and sugar. Give your answer using inequalities.

(Total for Question 14 is 2 marks)

A rectangle has length 7.8 cm, correct to 2 significant figures, and width 2.45 cm, correct to 3 significant figures. Work out the least possible perimeter of the rectangle. Give your answer to 2 decimal places.

(Total for Question 15 is 4 marks)

Write down the bounds for a number given as 5, correct to 1 significant figure, using inequality notation.

(Total for Question 16 is 1 mark)

Mark scheme · 3.1D Error Intervals: Fluency and Exam Drill

Question 1

B1 11.5 ≤ x < 12.5 cao
Answer: 11.5 ≤ x < 12.5

Question 2

B1 3.65 ≤ x < 3.75 cao
Answer: 3.65 ≤ x < 3.75

Question 3

B1 245 ≤ x < 255 cao
Answer: 245 ≤ x < 255

Question 4

B1 0.025 ≤ x < 0.035 cao
Answer: 0.025 ≤ x < 0.035

Question 5

M1 identify bounds 4.55 ≤ x < 4.65 or equivalent oe
A1 4.55 ≤ x < 4.65 cao
Answer: 4.55 ≤ x < 4.65

Question 6

M1 use upper bounds: length < 12.5 and width < 3.55
M1 multiply upper bounds oe
A1 area < 44.375 cm² cao
Answer: area < 44.375 cm², since 12.5 * 3.55 = 44.375. WorkingCheck: upper bounds 12.5 and 3.55, 12.5*3.55 = 44.375 so area is less than 44.375.

Question 7

M1 identify lower bounds: 8.015 ≤ L and 0.4495 ≤ W
M1 multiply lower bounds oe
A1 area ≥ 3.6027425 m² cao
Answer: area ≥ 3.6027425 m². WorkingCheck: L_low = 8.015, W_low = 0.4495, product = 8.015*0.4495 = 3.6027425.

Question 8

B1 3.995 ≤ x < 4.005 cao
Answer: 3.995 ≤ x < 4.005

Question 9

M1 use upper bound x < 2.35
M1 multiply by 3: 3x < 3*2.35
A1 3x < 7.05 cao
Answer: 3x < 7.05. WorkingCheck: x < 2.35 so 3x < 3*2.35 = 7.05.

Question 10

M1 state bounds r: 2.45 ≤ r < 2.55 and h: 39.5 ≤ h < 40.5
M1 form inequality for volume: π*(2.45)²*39.5 ≤ V < π*(2.55)²*40.5
A1 evaluate lower bound to 3 significant figures or better
A1 evaluate upper bound to 3 significant figures or better
Answer: π*(2.45)²*39.5 ≤ V < π*(2.55)²*40.5. Numerically: 744.868... cm³ ≤ V < 827.342... cm³. WorkingCheck: (2.45)²*39.5 = 237.09875, *π = 237.09875*π = approx 744.868; (2.55)²*40.5 = 263.35125, *π = approx 827.342.

Question 11

M1 divide bounds 11.5 ≤ x < 12.5 by 3
M1 write bounds as fractions 23/6 ≤ y < 25/6
A1 23/6 ≤ y < 25/6 cao
Answer: 23/6 ≤ y < 25/6. WorkingCheck: x bounds 11.5 and 12.5; 11.5/3 = 23/6, 12.5/3 = 25/6.

Question 12

B1 0.65 ≤ x < 0.75 cao
Answer: 0.65 ≤ x < 0.75

Question 13

M1 use upper bounds 2.05, 3.05 and 4.05
M1 calculate product 2.05*3.05*4.05
A1 V < 25.322625 cm³ cao
Answer: V < 25.322625 cm³. WorkingCheck: 2.05*3.05 = 6.2525; *4.05 = 25.322625, so volume is less than 25.322625.

Question 14

M1 identify bounds: flour 245 ≤ f < 255, sugar 115 ≤ s < 125
A1 360 ≤ total < 380 cao
Answer: 360 ≤ total < 380 g. WorkingCheck: min total 245+115=360, max total <255+125=380.

Question 15

M1 identify lower bounds: length 7.75 ≤ l and width 2.445 ≤ w
M1 add bounds l_low + w_low
M1 double to get perimeter
A1 perimeter = 20.39 cm cao (to 2 dp)
Answer: Least possible perimeter = 20.39 cm. WorkingCheck: l_low = 7.75, w_low = 2.445, sum = 10.195, perimeter = 2*10.195 = 20.39.

Question 16

B1 4.5 ≤ x < 5.5 cao
Answer: 4.5 ≤ x < 5.5

Error Intervals: Fluency and Exam Drill - Worksheets, Questions and Revision