The table shows four calculations that all use the numbers 8, 3 and 2, arranged with different brackets and operations. Work out the value of each calculation.
(a)8 + 3 x 2(1)
(b)(8 + 3) x 2(1)
(c)8 x (3 - 2)(1)
(d)(8 - 3) x 22(1)
(Total for Question 7 is 4 marks)
8
A stationery shop sells notebooks at 3 pounds each and pens at 1 pound each. Aaliyah buys 4 notebooks and 5 pens, and pays with a 20 pound note. Work out how much change Aaliyah receives.
(Total for Question 8 is 3 marks)
9
Work out 50 - (12 + 4)2 / 8.
(Total for Question 9 is 3 marks)
10
Work out 3 x (7 - 2)2 - (20 / 4).
(Total for Question 10 is 3 marks)
11
Work out 23 x (10 - 7) / 4.
(Total for Question 11 is 3 marks)
12
Work out 40 - (12 - 4) x 3 + 23.
(Total for Question 12 is 4 marks)
13
Show that (18 - 23) / (4 - 2) x 3 = 15.
(Total for Question 13 is 4 marks)
14
Tomasz was asked to work out 20 - 3 x (7 - 4)2. He wrote: 20 - 3 = 17, then (7 - 4)2 = 9, then 17 x 9 = 153. Explain the mistake Tomasz made and work out the correct answer.
(Total for Question 14 is 3 marks)
15
Work out -12 + 5 x (3 - 7).
(Total for Question 15 is 2 marks)
16
Insert one pair of brackets into 4 + 6 x 3 - 2 so that the calculation is equal to 28. Write out the calculation with the brackets in place and show that it equals 28.
(Total for Question 16 is 2 marks)
17
Work out (9 + 32) / 3 - 1.
(Total for Question 17 is 3 marks)
18
Work out (4 x (32 + 1)) - (18 - 23) / 2.
(Total for Question 18 is 4 marks)
Mark scheme · 1.10DB BIDMAS: Fluency and Exam Drill (Part 2)
Question 1
B1 27 cao
Answer: 27
Question 2
B1 24 cao
Answer: 24
Question 3
B1 3 cao
Answer: 3
Question 4
B1 17 cao
Answer: 17
Question 5
M1 evaluate (9 - 4)2 or show (9 - 4) = 5 and 52 = 25
A1 15 cao
Answer: 15
Question 6
M1 evaluate bracket 9 - 5 = 4 and multiply 4 x 4 = 16
A1 8 cao
Answer: 8
Question 7
(a) B1 14 cao
(a) Answer: 14
(b) B1 22 cao
(b) Answer: 22
(c) B1 8 cao
(c) Answer: 8
(d) B1 20 cao
(d) Answer: 20
Question 8
M1 4 x 3 = 12 (cost of notebooks) or 5 x 1 = 5 (cost of pens) seen
M1 total cost 12 + 5 = 17 (or 20 - 17 attempted)
A1 3 cao
Answer: 3 pounds
Question 9
M1 evaluate bracket 12 + 4 = 16
M1 evaluate index 162 = 256 and divide 256 / 8 = 32
A1 18 cao
Answer: 18
Question 10
M1 evaluate (7 - 2)2 = 52 = 25
M1 multiply 3 x 25 = 75 and evaluate 20 / 4 = 5
A1 70 cao
Answer: 70
Question 11
M1 evaluate index 23 = 8
M1 evaluate bracket 10 - 7 = 3 and multiply 8 x 3 = 24
M1 identify that Tomasz subtracted 20 - 3 before completing the bracket, index and multiplication (BIDMAS order not followed) oe
M1 correct method: (7 - 4)2 = 9 then 3 x 9 = 27
A1 -7 cao
Answer: Tomasz's mistake: he subtracted 20 - 3 first instead of completing the bracket, index and multiplication before the subtraction. Correct answer: -7
Question 15
M1 evaluate bracket 3 - 7 = -4 and multiply 5 x (-4) = -20
A1 -32 cao
Answer: -32
Question 16
M1 brackets placed around 4 + 6, giving (4 + 6) x 3 - 2