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Student Book - Series H-2

Directed Numbers

Mathletics Instant

Workbooks

+5 x -3 = _____

Directed numbers

Student Book - Series H 2

Contents

Topics

Topic 1 - Plotting on number lines __/__/__ Date completed

Topic 2 - Opposite directions — negative numbers __/__/__ Topic 3 - Extending the number line __/__/__ Topic 4 - Addition of directed numbers __/__/__ Topic 5 - Subtraction of directed numbers __/__/__ Topic 6 - Multiplication of directed numbers __/__/__ Topic 7 - Division of directed numbers __/__/__ Topic 8 - The four operations with directed numbers __/__/__ Topic 9 - The number plane __/__/__ Topic 10 - Problem solving with directed numbers __/__/__

Directed numbersMathletics Instant Workbooks – Series H 2 Copyright © 3P Learning

Author of The Topics and Topic Tests: AS Kalra

Practice Tests

Topic 1 - Topic test A __/__/__ Topic 2 - Topic test B __/__/__ Topic 3 - Topic test C __/__/__

1

Directed numbers


Topic 1: Plotting on number lines

97EXCEL ESSENTIAL SKILLS: YEAR 7 MATHEMATICS REVISION AND EXAM WORKBOOK 2 – EXTENSION

Directed numbers

P l o t t i n g o n n u m b e r l i n e sEXCEL YEAR 7 MATHEMATICS

Ch. 11.1, p. 168

QUESTION 2 Plot the following sets of points on the number line.

a {1, 3, 4, 6}0 1 2 3 4 5 6 7 8 9 10 11 12

b {0, 2, 5, 7}0 1 2 3 4 5 6 7 8 9 10 11 12

c {0, 2, 4, 6}0 1 2 3 4 5 6 7 8 9 10 11 12

d {1, 3, 5, 7}0 1 2 3 4 5 6 7 8 9 10 11 12

e {0, 1, 2, 3, 4}0 1 2 3 4 5 6 7 8 9 10 11 12

f {1, 5, 6, 7, 9}0 1 2 3 4 5 6 7 8 9 10 11 12

QUESTION 1 Giving distance and direction, write where you would be from your starting point if youtravelled on the east-west line.

a 4 km west and then 7 km east ____________________________________________________________

b 6 km west and then 11 km east ____________________________________________________________

c 2 km west and then 8 km east ____________________________________________________________

d 6 km east and then 7 km west ____________________________________________________________

e 2 km east and then 5 km east ____________________________________________________________

f 3 km west and then 6 km west ____________________________________________________________

QUESTION 3 Graph each set of points on a separate number line.

a the numbers from 3 to 70 1 2 3 4 5 6 7 8 9 10 11

b the numbers 1, 2, 5, 6, 8, 90 1 2 3 4 5 6 7 8 9 10 11

c odd numbers less than 100 1 2 3 4 5 6 7 8 9 10 11

d even numbers less than 100 1 2 3 4 5 6 7 8 9 10 11

e prime numbers less than 100 1 2 3 4 5 6 7 8 9 10 11

f the numbers 2, 3, 4, 8, 9, 100 1 2 3 4 5 6 7 8 9 10 11

W E10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10

CHAPTER 8

2

Directed numbers


Topic 2: Opposite directions — negative numbers

98 EXCEL ESSENTIAL SKILLS: YEAR 7 MATHEMATICS REVISION AND EXAM WORKBOOK 2 – EXTENSION

Directed numbers

QUESTION 2 For each of the following statements, write a directed number to show the size and directionof the number.

a Michelle Russett deposited $120 ___________________________________________________________

b Tim Eastman walked 40 km east ___________________________________________________________

c The price came down by $20 ______________________________________________________________

d Maddy took 65 steps forwards _____________________________________________________________

e The water level dropped by 3 m ___________________________________________________________

f I lost 8 points _________________________________________________________________________

QUESTION 1 What is the opposite of each of these statements?

a going up _______________________________ b going north _______________________________

c going east ______________________________ d depositing money __________________________

e winning $50 ____________________________ f five floors up ______________________________

g 9° below zero ___________________________ h increase of 40 _____________________________

i 20 steps to the right _____________________ j 90 m above sea level _______________________

O p p o s i t e d i r e c t i o n s ( n e g a t i v e n u m b e r s )EXCEL YEAR 7 MATHEMATICS

Ch. 11.1, p. 168

QUESTION 4 Write a number sentence for each of the following.

a A deposit of $30 and a deposit of $25 ______________________________________________________

b A deposit of $100 and a withdrawal of $18 ___________________________________________________

c A withdrawal of $20 and a deposit of $65 ___________________________________________________

d A deposit of $15 and a deposit of $20 ______________________________________________________

e A withdrawal of $9 and a withdrawal of $12 __________________________________________________

f A deposit of $30 and a deposit of $70 ______________________________________________________

g A withdrawal of $18 and a deposit of $30 ___________________________________________________

h A deposit of $55 and a deposit of $17 _______________________________________________________

i A deposit of $83 and a withdrawal of $28 ___________________________________________________

j A withdrawal of $50 and a withdrawal of $60 ________________________________________________

QUESTION 3 Showing distance and direction, state where you would be from your starting point if youtravelled:

a 9 km east then 5 km west ________________________________________________________________

b 12 km west then 5 km east _______________________________________________________________

c 7 km north then 6 km south ______________________________________________________________

d 25 km east then 15 km west ______________________________________________________________

e 8 km east, 12 km west and then 7 km east __________________________________________________

3

Directed numbers


Topic 3: Extending the number line


Directed numbers

QUESTION 4 Arrange in descending order.

a +2, +4, –2, –7, –9, –1 __________________________________________________________________

b –2, –8, –6, –9, 3, 5 ____________________________________________________________________

c 8, 9, 3, 1, 2, –4 _______________________________________________________________________

d –3, –5, 2, 6, 3, –1 _____________________________________________________________________

e 2, 5, 8 –4, –2, –6 ______________________________________________________________________

E x t e n d i n g t h e n u m b e r l i n eEXCEL YEAR 7 MATHEMATICS

Ch. 11.1, p. 168

QUESTION 1 Represent each of the following trips on the number line using a directed number (a positiveor negative number).

a 0 to +7 _________________________________ b +1 to +8 _________________________________

c –8 to +3 ________________________________ d +3 to +9 _________________________________

e –2 to +5 _______________________________ f –1 to +10 ________________________________

g +6 to +10 _______________________________ h –8 to –1 _________________________________

i –7 to –3 ________________________________ j –9 to +5 _________________________________

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

Use the number line to answer the following questions.

QUESTION 3 Use the number line to complete the following.

a 5 – 8 = _________________ b 4 + 7 = ________________ c 6 + 3 = ___________________

d 3 + 4 = ________________ e 9 – 2 = ________________ f 8 – 2 = ___________________

g –2 + 7 = ________________ h 7 – 3 = ________________ i 5 – 9 = ___________________

j 4 – 8 = _________________ k 8 – 10 = _______________ l –3 – 4 = __________________

QUESTION 5 Write > or < to make the following statements true.

a 8 ________ –5 b 4 ________ –8 c 3 ________ –5

d 6 ________ 9 e –5 ________ 5 f 4 ________ –9

g –6 ________ 2 h –2 ________ 2 i 8 ________ 10

j 9 ________ –4 k –7 ________ +3 l –2 ________ –7

m –8 ________ –6 n –3 ________ +2 o –1 ________ 6

QUESTION 2 Which is the smaller number?

a +10 or +6 ________ b +8 or –1 ________ c –8 or –2 _________ d –2 or +2 ________

e +6 or +1 _________ f –7 or –5 _________ g –3 or +7 _________ h +10 or +8 ________

i –6 or –1 _________ j –4 or –2 ________ k –6 or +7 _________ l +8 or +9 _________

m –8 or –1 ________ n –7 or +2 ________ o +2 or +8 _________

4

Directed numbers



Directed numbers

QUESTION 1 Find the sum of the following. Use the number line if necessary.

a +4 + +9 = ________________ b +1 + +2 = ______________ c +1 + +7 = _________________

d +6 + +2 = ________________ e +3 + +6 = ______________ f +2 + +9 = _________________

g +8 + +3 = _______________ h +2 + +4 = ______________ i +4 + +7 = _________________

A d d i t i o n o f d i r e c t e d n u m b e r sEXCEL YEAR 7 MATHEMATICS

Ch. 11.2, p. 169

QUESTION 2 Find each sum.

a +1 + –1 = ________________ b +3 + –8 = ______________ c +5 + –9 = _________________

d +2 + –3 = ________________ e +9 + –5 = ______________ f +8 + –6 = _________________

g +4 + –2 = ________________ h +10 + –4 = _____________ i +7 + –7 = _________________

QUESTION 3 Add the following.

a –9 + +1 = ________________ b –18 + +6 = _____________ c –15 + +11 = _______________

d –10 + +3 = _______________ e –24 + +7 = _____________ f –17 + +4 = ________________

g –12 + +5 = _______________ h –28 + +10 = ____________ i –7 + +15 = ________________

QUESTION 4 Find the answers to these additions.

a –2 + –3 = ________________ b –7 + –1 = ______________ c –1 + –7 = _________________

d –5 + –9 = ________________ e –3 + –2 = ______________ f –10 + –5 = ________________

g –9 + –4 = ________________ h –8 + –10 = _____________ i –4 + –8 = _________________

j –12 + –17 = ______________ k –6 + –14 =______________ l –11 + –6 = ________________

QUESTION 5 Find the values of the following.

a +6 + +2 + +5 = ____________ b +17 + –3 + –2 = _________ c +10 + +2 + –3 = ____________

d –18 + +8 = _______________ e –8 + –6 = ______________ f –20 + –5 = ________________

g +7 + –4 + –1 = ____________ h –14 + +3 + +8 = _________ i –9 + –6 = _________________

j +10 + –5 + –3 =___________ k +15 + –8 + –3 = _________ l –8 + +4 = _________________

QUESTION 6 Find the missing number.

a +4 + _____________ = +2 b ____________ + –5 = 0 c +10 + –3 = _____________

d +8 + _____________ = +6 e +5 + –9 + –2= __________ f –7 + –8 = _____________

g +9 + –6 = _____________ h +8 + +4 = _____________ i –4 + _____________ = –13

j –10 + _____________ = –21 k –3 + –4 + –2 = _________ l +15 + +6 = _____________

m +15 + –3 + –4 = _________ n –5 + ____________ = –14 o –4 + _____________ = –18

Topic 4: Addition of directed numbers

5

Directed numbers


Topic 5: Subtraction of directed numbers


Directed numbers

QUESTION 1 Find the answers to the following questions.

a 8 – 5 = _________________ b 10 – 7 = _______________ c 25 – 18 = _________________

d +6 – +4 = ________________ e +14 – +2 = _____________ f +35 – +8 = ________________

g +5 – +2 = ________________ h +18 – +3 = _____________ i +12 – +1 = ________________

j +9 – +3 = ________________ k +31 – +6 = _____________ l +18 – +8 = ________________

S u b t r a c t i o n o f d i r e c t e d n u m b e r sEXCEL YEAR 7 MATHEMATICS

Ch. 11.3, p. 170

QUESTION 2 Complete these subtractions. Use the number line if necessary.

a +6 – –2 = ________________ b +18 – –6 = _____________ c +27 – –10 = _______________

d +10 – –3 = _______________ e +25 – –12 = ____________ f +14 – –7 = ________________

g +11 – –4 = _______________ h +9 – –11 = _____________ i +19 – –9 = ________________

j +15 – –5 = _______________ k +8 – –8 = ______________ l +32 – –13 = _______________

QUESTION 3 Find each difference.

a –20 – +2 = _______________ b –8 – +6 = ______________ c –7 – +12 = ________________

d –10 – +8 = _______________ e –16 – +9 = _____________ f –17 – +4 = ________________

g –15 – +10 = ______________ h –12 – +3 = _____________ i –27 – +7 = ________________

j –5 – +5 = ________________ k –24 – +13 =_____________ l –38 – +11 = _______________

QUESTION 4 Find the answers to the following subtractions.

a –3 – –1 = ________________ b –2 – –5 = ______________ c –13 – –8 = ________________

d –5 – –6 = ________________ e –8 – –2 = ______________ f –6 – –3 = _________________

g –7 – –10 = _______________ h –12 – –7 = _____________ i –15 – –9 = ________________

j –9 – –12 = _______________ k –11 – –4 = _____________ l –4 – –11 = ________________

QUESTION 5 Find the values of the following.

a –1 – –3 = ________________ b –34 – +23 = ____________ c –88 – +35 = _______________

d –12 – –7 = _______________ e +45 – –19 = ____________ f –91 – –31 = _______________

g –23 – +11 = ______________ h –56 – –27 = ____________ i +14 – –39 = _______________

j –36 – –15 = ______________ k +67 – +43 = ____________ l –19 – –47 = _______________

QUESTION 6 Simplify the following.

a 9 – 4 = _________________ b –23 – 10 = _____________ c 17 – 9 = __________________

d –7 – (–6) = ______________ e 11 – (–14) = ____________ f 5 – (–12) = _______________

g –11 – 8 = ________________ h 36 – (–6) = _____________ i 28 – 11 = _________________

j –15 – (–9) =______________ k 3 – 8 = ________________ l 2 – 17 = __________________

6

Directed numbers


Topic 6: Multiplication of directed numbers


Directed numbers

QUESTION 1 Multiply the following.

a +5 × +1 = ________________ b +15 × +8 = _____________ c +14 × +9 = ________________

d +12 × +6 = _______________ e +7 × +2 = ______________ f +18 × +3 = ________________

g +11 × +11 = ______________ h +13 × +5 = _____________ i +9 × +10 = ________________

j +16 × +21 = ______________ k +17 × +7 = _____________ l +21 × +4 = ________________

M u l t i p l i c a t i o n o f d i r e c t e d n u m b e r sEXCEL YEAR 7 MATHEMATICS

Ch. 11.4, p. 171

QUESTION 2 Work out the following.

a +4 × –2 = ________________ b +1 × –3 = ______________ c +3 × –15 = ________________

d +2 × –9 = ________________ e +5 × –12 = _____________ f +18 × –5 = ________________

g +7 × –6 = ________________ h +8 × –4 = ______________ i +6 × –8 = _________________

j +15 × –7 = _______________ k +10 × –11 = ____________ l +21 × –5 = ________________

QUESTION 3 Find the answers to the following.

a –3 × +10 = _______________ b –6 × +8 = ______________ c –7 × +9 = _________________

d –10 × +15 = ______________ e –2 × +11 = _____________ f –1 × +12 = ________________

g –5 × +13 = _______________ h –11 × +14 = ____________ i –8 × +15 = ________________

j –9 × +6 = ________________ k –4 × +5 = ______________ l –12 × +7 = ________________

QUESTION 4 Simplify.

a –7 × –10 = _______________ b –1 × –4 = ______________ c –8 × –14 = ________________

d –2 × –11 = _______________ e –9 × –12 = _____________ f –3 × –13 = ________________

g –10 × –2 = _______________ h –4 × –3 = ______________ i –11 × –5 = ________________

j –5 × –6 = ________________ k –12 × –1 = _____________ l –6 × –7 = _________________

QUESTION 5 Find each product.

a +4 × –3 = _______________ b –10 × –10 = ____________ c –9 × +6 = _________________

d –3 × +5 = _______________ e +12 × +12 = ____________ f –15 × +5 = ________________

g +8 × –6 = _______________ h –11 × –14 = ____________ i +18 × –4 = ________________

j –6 × +8 = _______________ k +8 × –9 = ______________ l –25 × –7 = ________________

QUESTION 6 Complete the following tables.

a × + − ++−+

8 6 10

6

8

3

b × − + −+−+

8 9 5

4

2

5

c × + − +−+−

4 6 8

7

12

15

7

Directed numbers


Topic 7: Division of directed numbers


Directed numbers

QUESTION 1 Divide the following.

a +10 ÷ +2 = _______________ b +25 ÷ +5 = _____________ c +14 ÷ +7 = ________________

d +12 ÷ + 4 = ______________ e +27 ÷ +3 = _____________ f +8 ÷ +4 = _________________

g +36 ÷ +6 = _______________ h +38 ÷ +2 = _____________ i +9 ÷ +3 = _________________

j +18 ÷ +9 = _______________ k +64 ÷ +8 = _____________ l +26 ÷ +2 = _______________

D i v i s i o n o f d i r e c t e d n u m b e r sEXCEL YEAR 7 MATHEMATICS

Ch. 11.5, p. 172


a +38 ÷ –2 = _______________ b +48 ÷ +8 = _____________ c +81 ÷ –9 = ________________

d –46 ÷ +2 = _______________ e –25 ÷ –5 = _____________ f –74 ÷ +2 = ________________

g –68 ÷ –4 = _______________ h +35 ÷ +7 = _____________ i +68 ÷ –2 = ________________

j +72 ÷ –9 = _______________ k –66 ÷ –11 = ____________ l +56 ÷ +7 = _______________

QUESTION 2 Work out the following divisions.

a +6 ÷ –2 = ________________ b +18 ÷ –9 = _____________ c +27 ÷ –9 = ________________

d +9 ÷ –3 = ________________ e +39 ÷ –3 = _____________ f +21 ÷ –7 = ________________

g +12 ÷ –4 = _______________ h +24 ÷ –8 = _____________ i +33 ÷ –11 = _______________

j +15 ÷ –5 = _______________ k +30 ÷ –15 = ____________ l +36 ÷ –4 = ________________


a –15 ÷ +3 = _______________ b –36 ÷ +9 = _____________ c –42 ÷ +6 = ________________

d –21 ÷ +7 = _______________ e –48 ÷ +8 = _____________ f –35 ÷ +5 = ________________

g –24 ÷ +8 = _______________ h –64 ÷ +4 = _____________ i –26 ÷ +2 = ________________

j –30 ÷ +10 = ______________ k –56 ÷ +7 = _____________ l –18 ÷ +9 = ________________

QUESTION 4 If a = 5, b = 3, c = 6 and d = 10, find the value of each of the following.

a a ÷ b = __________________ b c2 ÷ d = ________________ c ac ÷ d = __________________

d c ÷ d = __________________ e a2 + b2 = _______________ f c2 ÷ b2 = __________________

g a2 ÷ b = _________________ h d ÷ ab = _______________ i d ÷ c = ___________________

j d2 ÷ a = _________________ k bd ÷ ac = ______________ l cd ÷ ab = _________________

QUESTION 5 Fill in the missing number.

a –60 ÷ __________ = –6 b –144 ÷ +12 = __________ c –12 ÷ +4 = __________

d __________ ÷ –4 = +9 e +48 ÷ __________ = –6 f __________ ÷ –7 = +7

g –64 ÷ –16 = __________ h –64 ÷ –4 = __________ i –33 ÷ __________ = –3

j __________ ÷ –7 = –6 k –63 ÷ __________ = 7 l +28 ÷ __________ = –7

8

Directed numbers


Topic 8: The four operations with directed numbers


Directed numbers

QUESTION 1 Find the answers to the following.

a 7 + –8 = ________________ b 36 + +3 = ______________ c 18 – –4 = ________________

d –9 – +5 = _______________ e 45 + –1 = ______________ f –24 – –6 = _______________

g 10 + –7 = _______________ h –54 – +2 = _____________ i 36 + +7 = ________________

j –21 – +6 = ______________ k –9 – –3 = ______________ l –48 + +8 = _______________

T h e f o u r o p e r a t i o n s w i t h d i r e c t e d n u m b e r sEXCEL YEAR 7 MATHEMATICS

Ch. 11.1–11.5,p. 168–173

QUESTION 6 Complete the tables.

a × + − + − − +−

−

6 8 10 12 3 5

3

5

9

b × − − + + − ++−+

5 3 2 6 8 9

4

8

7

QUESTION 2 Find the value of the following.

a –28 ÷ –4 = _______________ b +36 ÷ –4 = _____________ c –72 ÷ –4 = ________________

d –15 + –3 = _______________ e +25 – +6 = _____________ f –42 – –12 = _______________

g +19 – –8 = _______________ h +28 + –10 = ____________ i –45 + +14 = _______________

j –29 + +7 = _______________ k –32 – +9 = _____________ l –64 – –15 = _______________

QUESTION 3 Work out the following.

a +63 ÷ –9 = _______________ b –32 × +2 = _____________ c –42 ÷ –7 = ________________

d –56 ÷ –7 = _______________ e –48 ÷ –8 = _____________ f +20 × +5 = ________________

g +28 ÷ +4 = _______________ h +81 ÷ –9 = _____________ i –10 × –6 = ________________

j –24 × –3 = _______________ k +96 ÷ –6 = _____________ l –8 × +9 = _________________


a (+5 × +4) × –2 = __________ b +10 – +4 × –5 = _________ c –6 + –5 + –8 = _____________

d (–3 × –2) × –5 = __________ e –64 ÷ –8 × +3 = _________ f 16 ÷ (–6 + 2) = ____________

g 24 ÷ (–3 × –2) = __________ h (–6 – 6) × –5 = _________ i 30 × (15 ÷ 5) = ____________

j (+8 × –3) ÷ –4 = __________ k –300 ÷ –50 × 2 = ________ l (–8 – 4) ÷ 6 = _____________

QUESTION 5 Fill in the missing number.

a +72 ÷ –9 = __________ b __________÷ 2 = –12 c +24 – __________= +18

d +9 × –6 = __________ e __________÷ +9 = –6 f –10 – __________= –7

g +8 + –7 = __________ h +15 + –6 = __________ i +8 × __________= –80

j –6 – –3 = __________ k –18 – –5 = __________ l –9 + __________= –15

9

Directed numbers


Topic 9: The number plane


Directed numbers

QUESTION 2 Write down the coordinates of the following points shown in the number plane.

a A ______________

b B ______________

c C ______________

d D ______________

e E ______________

f F ______________

g G ______________

h H ______________

i I ______________

j J ______________

k K ______________

l L ______________

m M ______________

n N ______________

o O ______________

p P ______________

q Q ______________ r R ______________ s S _______________ t T ______________

u U ______________ v V ______________ w W _______________ x X ______________

y Y ______________ z Z ______________

T h e n u m b e r p l a n eEXCEL YEAR 7 MATHEMATICS

Ch. 11.11, p. 178

QUESTION 1 Write the letter used to name the following points.

a (0, 0) ___________ b (1, 1) ___________

c (2, 2) ___________ d (3, 3) ___________

e (4, 4) ___________ f (0, 1) ___________

g (0, 2) ___________ h (0, 3) ___________

i (0, 4) ___________ j (1, 0) ___________

k (2, 0) ___________ l (3, 0) ___________

m (4, 0) ___________ n (2, 1) ___________

o (2, 3) ___________ p (2, 4) ___________

q (1, 2) ___________ r (1, 3) ___________

s (1, 4) ___________ t (3, 1) ___________

u (3, 2) ___________ v (3, 4) ___________ w (4, 1) ___________ x (4, 2) ___________

4

3

2

1

0 1 2 3 4

U V W X Y

P Q R S T

J K L M N

E F G H I

O A B C D

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7

Z

A

N G

Q

C

XB

O

LE

R F

M

W

P

V K D

U

Y

J

T

SI

H

y

x

–y

–x

10

Directed numbers


Topic 10: Problem solving with directed numbers


Directed numbers

1 Where would I be after a trip of 5 km south, followed by a trip of 9 km north?

______________________________________________________________________________________

2 What would be the net result of a deposit of $700 in my account followed by a withdrawal of $900?

______________________________________________________________________________________

3 Two numbers have a product of 56 and their sum of –15. What are the numbers?

______________________________________________________________________________________

4 If the sum of two numbers is –2 and their product is –24, find the numbers?

______________________________________________________________________________________

5 I am a negative number divisible by 7 and greater than –9. What number am I?

______________________________________________________________________________________

6 Find the sum of a profit of $9000 and a loss of $21 000.

______________________________________________________________________________________

7 The temperature fell 5° during the day and fell another 5° during the night. What was the total change intemperature?

______________________________________________________________________________________

8 What is the combined effect of a gain of 8 kg and a loss of 7 kg?

______________________________________________________________________________________

9 Find the two integers whose sum is –11 and product is 30.

______________________________________________________________________________________

10 Start with the integer 5, add 7 and multiply the result by –3. What is the answer?

______________________________________________________________________________________

11 If 6 more than –4 is added to the product of 5 and 9, what is the result?

______________________________________________________________________________________

12 Divide –72 by –9 and multiply the result by –5. What is the answer?

______________________________________________________________________________________

13 Which of the integers –9, –5, –2, –1, 3, 7 is closest to zero?

______________________________________________________________________________________

14 From the integers –7, –5, –3, 4, 9, find the three integers whose sum is –1.

______________________________________________________________________________________

15 Multiply 8 by –12 and add 6 to the result. What is the answer?

______________________________________________________________________________________

P r o b l e m s o l v i n g w i t h d i r e c t e d n u m b e r sEXCEL YEAR 7 MATHEMATICS

Ch. 11.13, p. 180


Directed numbers

TOPIC TEST PART A

1 –16 + +4 equals

A –12 B –20 C 12 D 20

2 –9 + –2 + –1 equals

A –12 B 12 C –11 D –10

3 +8 – –5 equals

A 3 B 13 C –3 D –13

4 (–3)2 equals

A –9 B 9 C –6 D 6

5 –12 – – 12 equals

A 24 B –24 C 0 D 144

6 (–7 × 5) + 9 equals

A –26 B 26 C –18 D 18

7 –7 – (8 – –2) equals

A 3 B –3 C –17 D 17

8 –10 + –4 × –5 equals

A –10 B 10 C –30 D 30

9 If a = 5 and b = 4 then (a – b)2 equals

A 81 B 25 C 16 D 1

10 If x = 3 and y = –8 then xy + 7 equals

A 17 B –17 C 31 D –31

Marks

1

1

1

1

1

1

1

1

1

1

Directed numbers

Instructions • This part consists of 15 multiple choice questions

• Fill in only ONE CIRCLE for each question• Each question is worth 1 mark• Calculators are NOT allowed

Time allowed: 15 minutes Total marks = 15


Directed numbers

TOPIC TEST PART A

1 –16 + +4 equals

A –12 B –20 C 12 D 20

2 –9 + –2 + –1 equals

A –12 B 12 C –11 D –10

3 +8 – –5 equals

A 3 B 13 C –3 D –13

4 (–3)2 equals

A –9 B 9 C –6 D 6

5 –12 – – 12 equals

A 24 B –24 C 0 D 144

6 (–7 × 5) + 9 equals

A –26 B 26 C –18 D 18

7 –7 – (8 – –2) equals

A 3 B –3 C –17 D 17

8 –10 + –4 × –5 equals

A –10 B 10 C –30 D 30

9 If a = 5 and b = 4 then (a – b)2 equals

A 81 B 25 C 16 D 1

10 If x = 3 and y = –8 then xy + 7 equals

A 17 B –17 C 31 D –31

Marks

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1

1

1

1

1

1

1

1

1

Directed numbers

Instructions • This part consists of 15 multiple choice questions

• Fill in only ONE CIRCLE for each question• Each question is worth 1 mark• Calculators are NOT allowed


11Directed numbersMathletics Instant Workbooks – Series H 2 Copyright © 3P Learning

Directed numbersTopic Test PART AInstructions This part consists of 12 multiple-choice questions Each question is worth 1 mark Fill in only ONE CIRCLE for each question Calculators are NOT allowed


Marks


Directed numbers

Total marks achieved for PART A

Marks

1

1

1

1

15

1

11 –9 × –6 ÷ –2 equals

A –27 B 27 C –54 D 54

12 +48 + +10 – –2 equals

A 58 B 60 C 56 D 62

13 –64 ÷ +16 – –3 equals

A –7 B +1 C –1 D 7

14 (–8 × –4) ÷ –16 equals

A 2 B –2 C 16 D –16

15 –15 – (9 – –1) equals

A –25 B 25 C –6 D 6


Directed numbers

Total marks achieved for PART A

Marks

1

1

1

1

15

1

11 –9 × –6 ÷ –2 equals

A –27 B 27 C –54 D 54

12 +48 + +10 – –2 equals

A 58 B 60 C 56 D 62

13 –64 ÷ +16 – –3 equals

A –7 B +1 C –1 D 7

14 (–8 × –4) ÷ –16 equals

A 2 B –2 C 16 D –16

15 –15 – (9 – –1) equals

A –25 B 25 C –6 D 6


Directed numbersTopic Test PART A continued

15Total marks achieved for PART A

Marks

Instructions This part consists of 15 questions Each question is worth 1 mark Write answers in the answers-only columnTime allowed: 20 minutes Total marks = 15

Questions Answers only

Total marks achieved for PART B 15

Marks

Directed numbersTopic Test PART B



Directed numbers

Total marks achieved for PART B

TOPIC TEST PART B

Marks

Instructions • This part consists of 15 questions

• Each question is worth 1 mark• Write answers in the ‘Answers only’ column


15


1 18 ÷ –6 = ___________________

2 5 – –12 = ___________________

3 (–7)2 = ___________________

4 –8 – 10 = ___________________

5 15 – 8 × 4 = ___________________

6 –36 ÷ –9 = ___________________

7 –8 × (5 – 9) = ___________________

8 5 – 812

= ___________________

9 (–6 – –15) × (8 – 12 ) = ___________________

10 –36 ÷ 9 ÷ –4 = ___________________

11 (–3)2 × (5 – 12) = ___________________

12− − −

−6 185 7

= ___________________

13 8 × –2 – (6 – 11) = ___________________

14 1 + –15 = ___________________

15 5 – –12 + 8 × –3 = ___________________

1

1

1

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Directed numbers


Directed numbers


TOPIC TEST PART B

Marks




15


1 18 ÷ –6 = ___________________

2 5 – –12 = ___________________

3 (–7)2 = ___________________

4 –8 – 10 = ___________________

5 15 – 8 × 4 = ___________________

6 –36 ÷ –9 = ___________________

7 –8 × (5 – 9) = ___________________

8 5 – 812

= ___________________

9 (–6 – –15) × (8 – 12 ) = ___________________

10 –36 ÷ 9 ÷ –4 = ___________________

11 (–3)2 × (5 – 12) = ___________________

12− − −

−6 185 7

= ___________________

13 8 × –2 – (6 – 11) = ___________________

14 1 + –15 = ___________________

15 5 – –12 + 8 × –3 = ___________________

1

1

1

1

1

1

1

1

1

1

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1

1

1

1

Directed numbers


Directed numbers


TOPIC TEST PART B

Marks




15


1 18 ÷ –6 = ___________________

2 5 – –12 = ___________________

3 (–7)2 = ___________________

4 –8 – 10 = ___________________

5 15 – 8 × 4 = ___________________

6 –36 ÷ –9 = ___________________

7 –8 × (5 – 9) = ___________________

8 5 – 812

= ___________________

9 (–6 – –15) × (8 – 12 ) = ___________________

10 –36 ÷ 9 ÷ –4 = ___________________

11 (–3)2 × (5 – 12) = ___________________

12− − −

−6 185 7

= ___________________

13 8 × –2 – (6 – 11) = ___________________

14 1 + –15 = ___________________

15 5 – –12 + 8 × –3 = ___________________

1

1

1

1

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1

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Directed numbers

Instructions This part consists of 4 questions Each question is worth 5 marks Show all necessary


Questions

Total marks achieved for PART C 20

Marks

Directed numbersTopic Test PART C



Directed numbers

Total marks achieved for PART C

TOPIC TEST PART C

Marks


• Each question is worth 5 marks• Show all necessary working


20

1 Evaluate the following.

a –8 × –5 × –2 = ___________________ b +8 + –7 + –3 × –4 = _________________

c –36 ÷ –9 + –8 = __________________ d (–9)2 + (–12 ÷ 6) = __________________

e 8 × –6 – (7 – 8) = ________________

2 Complete the number pattern.

a –3, –2, –1, 0, __________ , __________ , __________

b –5, –3, –1, 1, __________ , __________ , __________

c –2, –4, –6, –8, __________ , __________ , __________

d 3, –6, 12, –24, __________ , __________ , __________

e 32, –16, 8, __________ , __________ , __________

3 Simplify the following.

a− + −

−8 10

6 = _____________________ b

− −−

27 94

= _________________________

c8 3 5

7+ × −( )

= ___________________ d− × −− +12 615 7

=________________________

e5 5325 9

−−

= ________________________

4 Find the value of the following.

a [26 – (–4)] × –3 = __________________________________________________________

b [–8 – (–19)] ÷ 11 = _________________________________________________________

c 96 – (–5 × 12) = ____________________________________________________________

d [(9 × –6) – 3] ÷ –3 = ________________________________________________________

e –9 + –12 × –6 ÷ –3 = ________________________________________________________

5

5

5

5

Directed numbers


Directed numbers

Total marks achieved for PART C

TOPIC TEST PART C

Marks


• Each question is worth 5 marks• Show all necessary working


20

1 Evaluate the following.

a –8 × –5 × –2 = ___________________ b +8 + –7 + –3 × –4 = _________________

c –36 ÷ –9 + –8 = __________________ d (–9)2 + (–12 ÷ 6) = __________________

e 8 × –6 – (7 – 8) = ________________

2 Complete the number pattern.

a –3, –2, –1, 0, __________ , __________ , __________

b –5, –3, –1, 1, __________ , __________ , __________

c –2, –4, –6, –8, __________ , __________ , __________

d 3, –6, 12, –24, __________ , __________ , __________

e 32, –16, 8, __________ , __________ , __________

3 Simplify the following.

a− + −

−8 10

6 = _____________________ b

− −−

27 94

= _________________________

c8 3 5

7+ × −( )

= ___________________ d− × −− +12 615 7

=________________________

e5 5325 9

−−

= ________________________

4 Find the value of the following.

a [26 – (–4)] × –3 = __________________________________________________________

b [–8 – (–19)] ÷ 11 = _________________________________________________________

c 96 – (–5 × 12) = ____________________________________________________________

d [(9 × –6) – 3] ÷ –3 = ________________________________________________________

e –9 + –12 × –6 ÷ –3 = ________________________________________________________

5

5

5

5

Directed numbers

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