A calculator display shows 3.2 x 104. Write this value as an ordinary number.
(2)
9
Simplify 10 - 2 x 3 + (6 - 1).
(2)
10
A student writes 12 - 4 x 2 = (12 - 4) x 2. Explain the mistake and give the correct answer.
(2)
11
Work out and show your working: (18 - 3) / 3 + 22.
(2)
12
Work out 30 / (2 x 3).
(1)
13
Work out 52 + 1.
(1)
14
A key sequence is entered into a scientific calculator: 6 + 4 x 3 =. The calculator applies the standard order of operations (BIDMAS). What number appears on the display, and why?
(2)
15
Work out and show all steps: (4 + 2)2 - 3 x (7 - 4).
(3)
16
A recipe requires 23 grams of salt and 3 x (5 + 2) grams of sugar. What is the total mass of salt and sugar, in grams? Show your working.
(3)
17
A student uses a calculator and types 80 - 25% = to try to find 25% of 80. Explain the mistake and give the correct method and answer for 25% of 80.
(3)
18
A calculator shows 5/7 = 0.714285714286. Give this value correct to 2 decimal places, and correct to 4 decimal places. Explain why using the full calculator display gives a more accurate rounded answer than rounding in two separate steps.
(3)
19
Give a correct key-press order for a scientific calculator to compute (16 - 4) x (3 + 5), and state the final result.
(3)
20
Stretch: Work out and show all steps: (2 x 5)2 / (9 - 4) + 3.
(3)
Mark scheme · KS3.M-N8D Order of Operations and Calculator Methods: Fluency and Exam Drill
Question 1
B1 19 cao
Answer: 19
Question 2
B1 17 cao
Answer: 17
Question 3
B1 13 cao
Answer: 13
Question 4
B1 3 cao
Answer: 3
Question 5
M1 correctly evaluates the bracket and multiplication, 3 x (8-5) = 9
A1 15 cao
Answer: 15
Question 6
M1 correctly evaluates the bracket and the power, (5+3)2 = 64
A1 16 cao
Answer: 16
Question 7
M1 correctly evaluates the power and the bracket, 23 = 8 and 7-4 = 3
A1 23 cao
Answer: 23
Question 8
M1 correct method, moving the decimal point 4 places
A1 32000 cao
Answer: 32,000
Question 9
M1 correctly evaluates the multiplication and bracket, 2 x 3 = 6 and 6-1 = 5
A1 9 cao
Answer: 9
Question 10
B1 identifies that multiplication must be done before subtraction (BIDMAS), not left to right
B1 4 cao
Answer: 4
Question 11
M1 correctly evaluates the bracket and the power, 18-3 = 15 and 22 = 4
A1 9 cao
Answer: 9
Question 12
B1 5 cao
Answer: 5
Question 13
B1 26 cao
Answer: 26
Question 14
M1 recognises that the calculator performs 4 x 3 before the addition
A1 18, with a correct reason given
Answer: 18, because BIDMAS means multiplication is carried out before addition
Question 15
M1 correctly evaluates both brackets, 4+2 = 6 and 7-4 = 3
M1 correctly evaluates the power and the multiplication, 62 = 36 and 3 x 3 = 9
A1 27 cao
Answer: 27
Question 16
M1 correctly evaluates the power, 23 = 8
M1 correctly evaluates the bracket and multiplication, 3 x (5+2) = 21
A1 29 grams cao
Answer: 29 grams
Question 17
B1 identifies that this key sequence subtracts 25% of 80 from 80, rather than finding 25% of 80 itself
M1 correct method, 0.25 x 80
A1 20 cao
Answer: 20
Question 18
M1 0.71 cao (correct to 2 decimal places)
M1 0.7143 cao (correct to 4 decimal places)
A1 valid reason, e.g. rounding only once from the full display avoids compounding rounding errors
Answer: 0.71 (2dp), 0.7143 (4dp)
Question 19
M1 recognises each bracket must be entered as a group, e.g. ( 1 6 - 4 ) x ( 3 + 5 ) =
M1 correctly evaluates each bracket, 16-4 = 12 and 3+5 = 8
A1 96 cao
Answer: 96
Question 20
M1 correctly evaluates both brackets, 2 x 5 = 10 and 9-4 = 5
M1 correctly evaluates the power and the division, 102 = 100 and 100/5 = 20