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KS3 · Number

KS3.M-N7 Negative Numbers

AQA KS3.M-N7 · Calculators not allowed · about 60 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write these numbers in order, starting with the smallest: -2, 5, -7, 0, 3

(2)

State which is larger: -4 or -9

(1)

On a number line mark the point that is 3 units to the right of -6. Write its value.

(1)

Calculate: -3 + 7

(1)

Calculate: -8 - 5

(1)

Calculate: 6 - (-2)

(1)

Calculate: -4 x 3

(1)

Calculate: -18 ÷ 6

(1)

Work out: -5 + 4 - (-2)

(2)

Complete the missing value: x + (-7) = -2. Find x.

(2)

A hiker starts at 120 m above sea level. She walks down 250 m and then climbs 80 m. What is her final height above sea level?

(3)

A shop records a loss of 45 pounds on Monday and a profit of 30 pounds on Tuesday. What is the net change over the two days?

(2)

Calculate: (-2) x (-5) + (-3)

(2)

Work out: -20 ÷ (-4) - 2

(2)

A thermometer reads -6 degrees at 6 am. By midday the temperature rises by 9 degrees. By evening it falls by 14 degrees. What is the temperature in the evening?

(3)

Sarah owes 28 pounds to a friend. She pays back 10 pounds and then borrows another 6 pounds. What is her final balance (negative means she still owes money)?

(3)

A small research submarine is at -80 m below sea level. It descends 30 m further and then rises 50 m. What is its final depth relative to sea level?

(3)

Calculate: (-3) x 4 + 5 - (-6)

(3)

A hill walker starts at 450 m above sea level. He goes down 520 m, then climbs 95 m, then goes down another 30 m. What is his final height above sea level?

(4)

Solve the equation: x - (-3) = -1. Find x.

(2)

Mark scheme · KS3.M-N7 Negative Numbers

Question 1

M1 convert to clear numeric order or compare negatives correctly
A1 correct order: -7, -2, 0, 3, 5 cao
Answer: -7, -2, 0, 3, 5

Question 2

B1 correct answer stated: -4 oe
Answer: -4

Question 3

B1 value -3 cao
Answer: -3

Question 4

B1 4 cao
Answer: 4

Question 5

B1 -13 cao
Answer: -13

Question 6

B1 8 cao
Answer: 8

Question 7

B1 -12 cao
Answer: -12

Question 8

B1 -3 cao
Answer: -3

Question 9

M1 shows correct method: -5 + 4 = -1 and then -1 - (-2) or equivalent method
A1 1 cao
Answer: 1

Question 10

M1 sets up or shows adding 7 to both sides or equivalent method
A1 x = 5 cao
Answer: 5

Question 11

M1 uses subtraction for going down: 120 - 250 = -130 or equivalent
M1 adds the climb: -130 + 80 or shows correct sequence of operations
A1 -50 m cao
Answer: -50 m

Question 12

M1 correct method: -45 + 30 or equivalent
A1 -15 pounds (loss) cao
Answer: -15 pounds

Question 13

M1 multiply negatives correctly to get 10 then show addition of -3 or equivalent
A1 7 cao
Answer: 7

Question 14

M1 divides: -20 ÷ -4 = 5 or equivalent
A1 3 cao
Answer: 3

Question 15

M1 shows rise: -6 + 9 = 3 or equivalent
M1 shows fall: 3 - 14 = -11 or equivalent sequence
A1 -11 degrees cao
Answer: -11 degrees

Question 16

M1 shows paying back: -28 + 10 = -18 or equivalent
M1 shows borrowing again: -18 - 6 or equivalent
A1 -24 pounds cao
Answer: -24 pounds

Question 17

M1 shows descent: -80 - 30 = -110 or equivalent
M1 shows rise: -110 + 50 or equivalent
A1 -60 m cao
Answer: -60 m

Question 18

M1 correct multiplication: (-3) x 4 = -12
M1 adds 5 correctly: -12 + 5 = -7
A1 -1 cao (after adding 6 from -(-6))
Answer: -1

Question 19

M1 first move: 450 - 520 = -70 or equivalent
M1 second move: -70 + 95 = 25 or equivalent
M1 third move: 25 - 30 = -5 or equivalent
A1 -5 m cao
Answer: -5 m

Question 20

M1 adds 3 to both sides or shows equivalent method
A1 x = -4 cao
Answer: -4

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