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KS3 · Number

KS3.M-N8 Order of Operations and Calculator Methods

AQA KS3.M-N8 · Calculators not allowed · about 60 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Work out each of these. Write down the answers.

(a)7 + 3 x 2(1)

(b)12 - 4 ÷ 2(1)

Calculate 5² + (8 - 3) x 2.

(1)

Work out 18 ÷ (3 + 3).

(1)

Evaluate each expression. Remember BIDMAS.

(a)4 x (2 + 5)(1)

(b)(9 - 4) x 3(1)

Simplify 3 + 6 x 2 - (4 + 1).

(2)

A calculator display shows 2.5 x 10³. Write this value as an ordinary number.

(2)

Calc method check. State whether the calculator step shown is correct, and if not give the correct result.
Ben types (6 + 4) x 2 into his calculator. The display shows 20. Is Ben correct? Explain briefly and give the correct answer if needed.

(3)

Use order of operations to simplify: 2³ + 4 x (3 + 1).

(2)

A student writes 8 - 3 x 2 = (8 - 3) x 2. Explain the mistake and give the correct answer.

(2)

Calculate the value of 5 + 2 x (9 - 6¹) - 3.

(3)

A scientific calculator applies the standard order of operations (BIDMAS). Show what it will display for the key sequence: 7 + 5 x 2 = . What number appears and why?

(2)

Calculate and show working: (14 - 6) ÷ 2 + 3².

(2)

Two calculator displays are given. Which is more reliable for 1/3 and why? A: 0.3333 B: 0.3333333333. Give a brief reason and state which display you would record for an exam answer.

(3)

A sequence of calculator steps is used to compute (25 - 5) x (2 + 3). Suggest an efficient sequence of key presses for a scientific calculator and give the final result.

(3)

Multi-step problem. A recipe needs 3² grams of sugar and 2 x (4 + 1) grams of flour. What is the total mass of sugar and flour? Give your answer in grams.

(4)

A student uses a calculator and types 50 - 12% = to find 12% of 50. Explain the mistake and give the correct method and answer for 12% of 50.

(3)

Stretch: Work out and show all steps: (3 x 4)² ÷ (6 - 2) + 5.

(4)

Stretch: Sophie evaluates 2⁴ x (5 - 3) - 10 ÷ 2. Find the correct answer and show a one-line explanation of the order used.

(4)

Mark scheme · KS3.M-N8 Order of Operations and Calculator Methods

Question 1

(a) B1 13 cao
(a) Answer: 13
(b) B1 10 cao
(b) Answer: 10

Question 2

B1 35 cao
Answer: 35

Question 3

B1 3 cao
Answer: 3

Question 4

(a) B1 28 cao
(a) Answer: 28
(b) B1 15 cao
(b) Answer: 15

Question 5

M1 correct method: 6 x 2 = 12 and (4+1)=5 or equivalent
A1 10 cao
Answer: 10

Question 6

M1 recognition that 10³ = 1000 or shifting decimal 3 places
A1 2500 cao
Answer: 2500

Question 7

M1 identifies that (6+4)=10 then times 2 should give 20 OR recognises order applied correctly
A1 20 cao
B1 clear explanation that calculator is correct because brackets were used oe
Answer: 20

Question 8

M1 method: 2³ = 8 and (3+1)=4 or 4x4=16
A1 24 cao
Answer: 24

Question 9

M1 explanation that multiplication has priority so 3 x 2 must be done before subtraction
A1 2 cao
Answer: 2

Question 10

M1 correct handling of power: 6¹ = 6 and brackets evaluated 9 - 6 = 3
M1 then multiply 2 x 3 = 6
A1 8 cao
Answer: 8

Question 11

M1 recognition that a scientific calculator applies BIDMAS, so the multiplication 5 x 2 is done before the addition; accept explanation
A1 17 cao (5 x 2 = 10, then 7 + 10 = 17)
Answer: 17

Question 12

M1 method: (14-6)=8 then 8÷2=4 and 3²=9
A1 13 cao
Answer: 13

Question 13

M1 identifies that 1/3 is recurring so both are approximations
M1 notes that B shows more digits and is closer to the true value
A1 record 0.333... or 1/3 as exact answer cao
Answer: B is closer; record 1/3 or 0.333... in an exam

Question 14

M1 method showing use of brackets or compute sub-results first e.g. (25-5)=20 then (2+3)=5
M1 shows key presses or steps: 25 - 5 = -> 20; 2 + 3 = -> 5; 20 x 5 =
A1 100 cao
Answer: 100

Question 15

M1 compute sugar: 3² = 9 g or recognise 3²
M1 compute flour: 4+1=5 then 2x5=10 g
M1 method to add masses: 9 + 10
A1 19 g cao
Answer: 19 g

Question 16

M1 states mistake: 50 - 12% subtracts a percent from 50 instead of finding 12% of 50
M1 gives correct method: 50 x 0.12 or 12/100 x 50
A1 6 cao
Answer: 6

Question 17

M1 compute inside brackets: 3 x 4 = 12 and 6 - 2 = 4
M1 square the result: 12² = 144
M1 divide: 144 ÷ 4 = 36
A1 41 cao
Answer: 41

Question 18

M1 power first: 2⁴ = 16 and bracket: (5-3)=2
M1 multiply: 16 x 2 = 32
M1 division then subtraction: 10 ÷ 2 = 5 and 32 - 5
A1 27 cao
Answer: 27

Order of Operations and Calculator Methods - Worksheets, Questions and Revision