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Name SOLUTION (TEACHER’S COPY)

Class

Centre

Course Outline Year 7 Term 1

© XJS Coaching School 2016 version 1

Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8

Sat 30-Jan 6-Feb 13-Feb 20-Feb 27-Feb 5-Mar 12-Mar 19-Mar

Sun 31-Jan 7-Feb 14-Feb 21-Feb 28-Feb 6-Mar 13-Mar 20-Mar

Textbook: Warwick, M., (2013) Understanding Year 8 Maths, Five Senses Education

Week Content Exercises

1 Base 10 and base 2 numbers (p. 5)

Conversion of base 10 numerals to

base 2

Conversion of base 10 to base 2 –

Choose easy and challenging numbers

Conversion of base 2 numerals to base

10

Do 10, 11, 100, 101, 110, 100011 (to

base2)

p. 27 L1, Q. 9

p. 31 L5, Q. 8

Worksheet 1 – Binary

numbers

2 Directed Numbers (p. 17 – 26)

Directed Numbers: Integers,

Graphing an integer line using

number notation, x >, <, and =. Use

of open and closed dots on a number

line.

p. 27 L1, Q. 10

p. 28 L2, Qs. 7, 8, 9

Worksheet 2 - Directed

Numbers 1

3 Continue with Directed Numbers.

Do harder problems: -3 - -2 + -17 – 8

Rules on „+‟, „-„, „x‟ and „ ' of

directed numbers.

Know the words „Ascending‟ and

„Descending‟ order.

p. 29, L3, Q. 9

p. 30, L4, Q. 8

p. 31, L5, Qs. 2, 3, 4,

p. 32, L6, Q. 3

Worksheet 3 – Directed

Numbers 2

Practice Exam 1

4 Geometry (p. 172 – 178)

Types of angles: Acute, Right Angle,

Obtuse, Straight, Reflex, Perigon.

Complementary / Supplementary

Sum of angle of a triangle.

Sum of angle of quadrilateral

Congruent triangles

p. 189 L1, Qs.1 – 4, 6

p. 190 L2, Q. 1

p. 191 L3, Qs. 1, 2

Worksheet 4 –

Geometry 1

5 Continue with Geometry (p. 179 –

180)

Parallel Lines

Corresponding / Alternate angles /

vertically opp. angles

Co-interior angles

p. 191 L3, Q5

p.192 L4, Qs. 3, 4

p. 193, L5, Q.4

Worksheet 5 –

Geometry 2

Course Outline Year 7 Term 1


6 Geometry (p. 184 – 187)

Similar triangles / Congruent

triangles

Congruent triangles have the same

size triangles, identical corresponding

sides and angles

Similar triangles have different size

triangles but of the same shapes, same

corresponding side ratios and same

corresponding angle ratios.

p. 190 L 2, Qs. 1, 2

p. 191 L3, Qs. 1, 2

Work Sheet 6 –

Geometry 3

7 Practice Exam .

8 Exam Do holiday homework

Worksheet 1 – Binary Numbers Year 7 Term 1


Name: SOLUTION____________ Date:_________

1. Complete the following base 10 numbers by converting each individual

digit into powers of 10: The first one has been done for you. The powers

of 10 has been designated with a *.

(a) 123 = (1 × 10*) + (2 × 10*) + (3 × 10*)

= (1 × 102) + (2 × 10

1)) + (3 × 10

0 )

= (1 × 100) + (2 × 10) + (3 × 1)

= 100 + 20 + 3 = 123

(b) 100 = (1 × 10*) + (0 × 10*) + (0 × 10*)

= (1× 102) + (0 × 10

1) + (0 × 10

0)

= (1× 100) + (0 × 10) + (0 × 1)

= 100 + 0 + 0

(c) 216 = (2 × 10*) + (1 × 10*) + (6 × 10*)

= (2 × 102) + (1 × 10

1) + (6 × 10

0)

= (2 × 100) + (1 × 10) + (6 × 1)

= 200 + 10 + 6

(d) 752 = (7 × 102) + (5 × 10

1) + (2 ×10

0)

= 700 + 50 + 2

= 752

(e) 1010 = (1 × 10*) + (0 × 10*) + (1 × 10*) + (0 × 10*)

= (1 × 103) + (0 × 10

2) + (1 × 10

1) + (0 × 10

0)

= (1 × 1000) + (0 × 100) + (1 × 10) + (0 × 1)

= 1000 + 0 + 10 + 0

(f) 1262 = (1 × 103 ) + (2 × 10

2) + (6 × 10

1) + (2 × 10

0)

= (1 × 1000 ) + (2 × 100) + (6 × 10) + (2 × 1)

= 1000 + 200 + 60 + 2

= 1262

(g) 25678 = (2 × 104 ) + (5 × 10

3 ) + (6 × 10

2) + (7 × 10

1) + (8 × 10

0)

= (2 × 10000 ) + (5 × 1000 ) + (6 × 100) + (7 × 10) + (8 × 1)

= 20 000 + 5 000 + 600 + 70 + 8

= 25 678

Key words: Binary Numbers / Base Numbers / Power / Conversion

123

100

216

752

1010

1262

25678



2. Complete the following binary numbers by converting each individual digit into

powers of 2, then changing them to base 10 numbers. The first one has been done

for you. Find *

(a) 110two = (1 × 2* ) + (1 × 2*) + (0 × 2*)

= (1 × 22 ) + (1 × 2

1 ) + (0 × 2

0 )

= (1 × 4) + (1× 2) + (0 × 1)

= 4 + 2 + 0

= 6ten

(b) 10two = (1 × 2*) + (0 × 2*)

= (1 × 21) + (0 × 2

0)

= (1 × 2) + (0 × 1)

= 2 + 0

= 2

(c) 11two = (1 × 2*) + (1 × 2*)

== (1 × 21) + (1 × 2

0)

= (1 × 2) + (1 × 1)

= 2 + 1

= 3

(d) 101 two = (1 × 2*) + (0 × 2*) + (1 × 2*)

= = (1 × 22) + (0 × 2

1) + (1 × 2

0)

= (1 × 4) + (0 × 2) + (1 × 1)

= 4 + 0 + 1 = 7

(e) 111 two = (1 × 22) + (1 × 2

1) + (1 × 2

0) (fill the empty space)

= (1 × 22) + (1 × 2

1) + (1 × 2

0)

= (1 × 4) + (1 × 2) + (1 × 1)

= 4 + 2 + 1 = 7

(f) 1101 two = ( × 2*) + ( × 2* ) + ( × 2*) + ( × 2* )

(fill in the empty space and *)

= (1 × 23) + ((1 × 2

2) + (0 × 2

1) + (1 × 2

0)

= (1 × 8) + (1 × 4) + (1 × 2) + (1 × 1)

= 8 + 4 + 0 + 1 = 13

(g) 1001 two = ( × ) + ( × ) + ( × ) + ( × )

(fill in the empty space)

= (1 × 23) + ((0 × 2

2) + (0 × 2

1) + (1 × 2

0)

= (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1)

= 8 + 0 + 0 + 1 = 9

(h) 10101 two = (1 × 24) + (0 × 2

3) + ((1 × 2

2) + (0 × 2

1) + (1 × 2

0)

= (1 × 16) + (0 × 8) + (1 × 4) + (0 × 2) + (1 × 1)

= 16 + 0 + 4 + 0 + 1

= 21

(i) 11111 two = = (1 × 24) + (1 × 2

3) + ((1 × 2

2) + 10 × 2

1) + (1 × 2

0)

= (1 × 16) + (1 × 8) + (1 × 4) + (1 × 2) + (1 × 1)

= 16 + 8 + 4 + 2 + 1

= 31

6

2

3

7

5

13

9

21

31



3. Convert the following base 10 numbers to binary numbers

(a) 2

(b) 11

(c) 24

(d) 30

(e) 50

(f) 63

(g) 65

(h) 75

4. Convert the following binary numbers to the base 10 equivalent:

(a) 100two

(b) 1010 two

(c) 1110 two

(d) 1100 two

(e) 10110 two

(f) 11101 two

(g) 101001 two

(h) 111110 two

10TWO

110010TWO

1011TWO

111111TWO

11000TWO

1000001TWO

11110TWO

1001011TWO

4

22

10

29

14

41

12

62

Worksheet 2 Numbers and Fractions Year 7 Term 1


5. Complete the following base-2 table, using the powers of 2 to convert the binary

numbers to base 10 numbers. The first one has been done for you.

Base 2

numbers

28

256

27

128

26

64

25

32

24

16

23

8

22

4

21

2

20

1

Base 10

Numbers

101111 1 0 1 1 1 1

32 8 4 2 1 47

100000 1 0 0 0 0 0

32 32

1000001 1 0 0 0 0 0 1

64 1 65

1000011 1 0 0 0 0 1 1

64 2 1 67

1000111 1 0 0 0 1 1 1

64 4 2 1 71

1001111 1 0 0 1 1 1 1

64 8 4 2 1 79

1011111 1 0 1 1 1 1 1

64 16 8 4 2 1 95

1111111 1 1 1 1 1 1 1

64 32 16 8 4 2 1 127

10101010 1 0 1 0 1 0 1 0

128 32 8 2 170

6. The early Chinese invented an abacus (suan pan) which is capable of doing base 5

calculations. It can calculate faster than a person doing base 10 calculations.

Complete the base 5 calculation below and convert it to base 10 answers. The first

one has been done for you.

Base 5

Numbers 5

5

3125

5 4

625

5 3

125

5 2

25

5 1

5

5 0

1

Base 10 Numbers

413 4×25=100

1×5=5

3×1=3

108 444 4×25=100

4×5=20

4×1=4

124

1234 1×125=125 2×25=50

3×5=15

4×1=4

194

21301 2×625=1250 1×125=125

3×25=75

0×5=0

1×1=1

1451 30000 3×625=1875

0×125=0 0×25=0

0×5=0

0×1=0

1875

102432 1×3125=3125

0×625=0 2×125=250

4×25=100

3×5=15

2×1=2

3492 210411 2×3125=6250

1×625=625

0×125=0 4×25=100

1×5=5

1×1=1

6981

Worksheet 2 - Directed Numbers 1 Year 7 Term 1



1. Which number from the list is an integer? [Circle your answer(s), if any]

−2, −3.2, 0.5, 2 ½ , −101.5

2. Is it True (T) or False (F) that 3 > −6?

For questions 3 to 5, answer “Yes” (Y) or “No” (N).

3. Can x be equal to - 3 if x < 2?

4. In the following number notation, x ≥ 5, can x be 5 and also 1000?

5. If the number notation is x ≤ - 5, can x be -10?

6. What is the meaning of the following number notation, -6 ≤ x ≤ 7?

7. What is the difference between x = 3, x ≤ 3 and x ≥ 3?

8. Arrange the numbers in descending order.

0, −5, 3, 12, 2, −11, −8

Key words: Integer / Descending / Ascending / Number Line / Directed Numbers / Inequation / Algebraic Equation / Substitution

Y

Y

Y

x is a number greater or equal to -6 but less or equal to 7

x = 3 means x can take one and only one value, that is 3;

x ≤ 3 means x can take any value less than 3 or exactly 3;

x ≥ 3 means x can be 3 or larger.

12, 3, 2, 0, -5, -8, -11

T



9. Arrange the following in ascending order

-10, -3, 0, -5, -7, -1, -13

10. List the integers between −6 and 2.

11. Graph each set of integers on a number line.

(a) x > −3

(b) x ≤ 2

(c) −10 ≤ x ≤ −5

(d) -3 ≤ x < 5

12. Describe the integers graphed on each number line in number notation.

(a)

(b)

13. Do the following:

(a) 3 + 2 =

(b) 3 + - 2 =

(c) 3 - + 2 =

(d) - 3 + 2 =

(e) -3 + -2 =

(f) -3 – 2 =

(g) -3 - -2 =

14. Fill in the following rule:

(a) + + =

(b) + - =

(c) - + =

(d) - - =

-13, -10, -7, -5, -3, -1, 0

-5, -4, -3, -2, -1, 0, 1 {Should not include -6 and 2}

x ≤ 2

-4 < x < 1

5 - 5

1

1

- 1

-5

-1

+

-

-

+



15. Evaluate:

(a) 3 + 4 + 5 =

(b) 3 + 4 – 5 =

(c) 3 + - 4 + 5 =

(d) -3 + 4 + 5 =

(e) -3 + - 4 + 5 =

(f) -3 + 4 + - 5 =

(g) -3 – 4 – 5 =

(h) 3 – 4 - - 5 =

(i) 3 - -4 - - 5 =

16. Evaluate the following algebraic expression if a = −4, b = −3 and c = 2.

(a) c − a − b

(b) c + a – b

(c) – c – b + a

(d) – c – b – c

17. Evaluate the following.

(a) −2 × – 2 =

(b) -2 × -2 × -2 =

(c) -2 × -2 × -2 × -2 =

18. From the above, the rule for multiplying negative numbers is:-(fill in the space

given):

(a) – × – = positive (enter positive or negative) Multiplying two or even

number of negative numbers will give a positive value.

(b) – × – × – = negative (enter positive or negative) Multiplying three or odd

number of negative numbers will give a negative value.

12

2

4

6

- 4

- 12

4

12

- 2

9

1

- 3

- 1

4

- 8

16



19. Evaluate the following:

(a) 3 – 10 × – 2 + 3 =

(b) 2 × – 4 + 6 =

(c) – 5 + - 6 + - 2 × – 4 =

26

- 2

- 3




1. Evaluate the following.

(a) (−2)3

× −3 = (b) −4 × 2 × 9 =

2. Evaluate the following algebraic expression if c = −5 and d = −3.

(a) 2 × c2 × d

(b) d 3

(c) 2c × 3d

(d) c2 × d

3. Compute the following;

(a) – 6 ÷ + 2 =

(b) – 6 ÷ - 3 =

(c) – 6 ÷ - 2 ÷ -3 =

4. Fill in the rule for dividing directed numbers:

(a) – ÷ – = positive. Choose either a negative or positive sign.

Division of 2 negative or even number of negative numbers will produce a

positive value.

(b) – ÷ – ÷ – = negative. Choose either a negative or positive sign.

Division of 3 negative or odd number of negative numbers will produce a

negative value.

5. Evaluate the following:

(a) – 48 ÷ 6 =

(b) – 39 ÷ - 3 =

(c) – 40 ÷ -2 ÷ - 4 =

(d) – 50 ÷ - 2 ÷ -5 ÷ -1 =

Key words: Continue with Directed Numbers - harder problems / Rules on ‘+’, ‘-‘, ‘x’ and ‘ ‚' of directed numbers / Know the words ‘Ascending’ and ‘Descending’ order.

24 -72

- 150 90

- 27 - 75

- 3 - 1

2

- 8

13

- 5

5



6. Use BODMAS to evaluate the following.

7.

(a) - 2 × 5 – 5 =

(b) 3 + - 5 × 2 =

(c) 2 × 5 + -2 × 4 =

(d) – 10 ÷ 5 + 5 =

(e) 12 + - 20 ÷ 2 =

(f) 20 × -2 +12 – 40 ÷ 2 =

For the following questions 7 & 8, write the word sentences into number sentences before solving the problem.

8. Jack borrowed $85 from his brother. He repaid $20 but then borrowed another $12.

How much does he now owe his brother?

9. Sharon‟s body temperature was 37°C. After 1 hour it increased by 2 degrees after 2

hours it decreased by 0.5 degrees and then decreased a further 1.5 degrees after 3

hours. What is her final temperature?

10. Arrange in ascending order:

½, 0, - ¼, −5.3, 4.8, −9.2

11. Graph the following sets of directed numbers on a number line

(a) x ≥ − 6.5

(b) −11

4 ≤ x ≤ 2.3

12. Write the same missing number in all the three boxes below.

−

−

- 15 3

- 7 2

2 - 48

$77

He still owes his brother $77 (positive value), though a negative

implies owing, - $77 or $-77 are both unacceptable as it will be a

double negative.

37°C

−9.2, −5.3, -¼, 0, ½,, 4.8,

3

3

3



13. Calculate the following.

−2

5 −2

3−1

15

14. Find the answer.

1

2 −1

5− −

1

3

−12

15

19

30

81

9 15

41

19

31 50

81

153



1

4

Practice Test 1 Year 7 Term 1



Section A: Multiple Choice Questions 1. What does (7 + 7 3) ( 4)

equal?

A 8

B 4

C 0

D 4

E 7

E

2. - 3 + - 2 × 3 is:

A. - 15

B. 15

C. - 9

D. 9

E. -2

C

3. What does 6 + 12 3 (2 + 12 0)

equal?

A 8

B 4

C 0

D 4

E 8

E

4. Which signs need to be inserted to

make the following equation true?

6 – 6 8 4 = 3

A ,,

B ,,

C ,,

D ,,

E ,,

E

5. What is 0.299 513 7 correct to 3

decimal places?

A 0.300

B 0.295

C 0.3

D 0.299

E 0.30

A

6. Find - 3 - - 2 + 5 + - 10:

a) -6

b) -10

c) -5

d) -14

e) -4

A

7. A number has been rounded to

27.40, which of the following could

the unrounded number have been?

A 27.351 32

B 2.740

C 27.45

D 27.459 89

E 0.2740

A

8. The day temperature started at 13°.

By 12 p.m the temperature had risen

3°. It then increased by another

2°by the end of the day. A cold

change caused a sudden drop in

temperature of 9°. Find the new

temperature.

A 5°

B 18°

C 6°

D 9°

E 8°

D

9. Mary has in her account $40.00. On

Monday she deposited $15 into the

account but withdrew $70.00 from

it on Tuesday. On Wednesday she

deposited $20.00 into the same

account. How much money has she

in her account now?

A $15.00

B $5

C $55

D $50

E $0.00

B

10. Find - 4 × - 3 × – 2 × – 1 + -5 × - 4

A 4

B - 4

C 44

D -44

E 20

C



Section B: Short Answer Questions

1 Remembering to use the correct order of

operations, evaluate these expressions.

(a) 12 4 2 + 3

(b) 6 10 + 12

(c) 12 11

(d) 6 (4 + 2) + 3 2

(a) 12 4 2 + 3 = 12 8 + 3

= 4 + 3 = 7

(b) 6 10 + 12 = 6 +

10 12

= 4 12

= - 8

(c) 12 11 = 132

(d) 6 (4 + 2) + 3 2 = 6

2 + 3 2

= 12

+ 6 = - 6

2 Round the number 469.79518 to:

(a) 4 decimal places

(b) 3 decimal places

(c) 2 decimal places

(d) 1 decimal place

(e) 0 decimal places

(a) 469.7952

(b) 469.795

(c) 469.80

(d) 469.8

(e) 470

3 Use your calculator to evaluate the following

correct to 3 decimal places.

(a) 212

2448

(b) 336

)10(4 23

(c) 23 )30.8(.)2(

(a) 212

2448

= - 3

(b) 2

36

36

10064

336

)10(4 23

= 18

(c) 258)30.8(.)2( 23

= - 33

Could also be - 18 if

you take √(36) = ±6



4 Evaluate the following:

a) 1112930

22

b) - 4 + - 6 - -5

- 5

c) 8 – 14 + 4 – 12

- 14

d). )911(22

22 ÷ 2 = 11

e) 270480

20 + 35 = 55

f) 9915

- 3

g) )53(717

17 – 7 × - 2 = 17 + 14 = 31

5 Insert signs to make the following equation

true.

2 3 6 5 = –11

2 – 3 × 6 + 5

6 Evaluate.

(a) 10

9

4

3

5

4

(b) 6

5

10

9

(c) -21

20

7

10

(a) 20

17

20

181516

(b) 4

3

(c) -2

3

20

21

7

10

7 If a = -5, b = -3 and c = 3, evaluate the

following:

(a) 3a (3 × b)

(b) a × b × c

(c) a × 3b + 5c

(d) ab + bc – a

(a) 3 × - 5 ÷ (3 × - 3) = - 15 ÷ -

9 = 3

21

3

5

(b) - 5 × - 3 × 3 = 45

(c) - 5 × 3 × - 3 + 5 × 3 = -

15 × -3 + 15

= 45 + 15 = 60

(d) - 5 × – 3 + - 3 × 3 - - 5

= 15 – 9 + 5 = 11

- + ×



8 Graph each of the integers on a number line

(a) x < 5

(b) x > - 4

(c) 24 x

Worksheet 4 Geometry 1 Year 7 Term 1



1. Find the complementary angle of the following angles:

(a) 20°

(b) 55°

(c) 63°

(d) 89°

2. Find the supplementary angles of the following angles:

(a) 125°

(b) 95°

(c) 150°

(d) 145°

3. Solve the following:

(a) x + 10° = 90°

(b) x – 25° = 90°

(c) x + 60° = 180°

(d) 2y + 45° = 90°

(e) 3a – 30° = 90°

(f) 5h + 100° = 180°

4. Find the pronumeral of the following equations.

(a) x + x + 10 = 40

(b) x + 1 + x + 2 = 63

(c) x + 2x + 60 = 120

Key words: Pronumeral / Exterior angle / Types of angles: Acute,

Right Angle, Obtuse, Straight, Reflex, Perigon /

Complementary / Supplementary / Sum of angle of a triangle /

Sum of angle of quadrilateral

70°

35°

27°

1°

55°

85°

30°

35°

80°

115°

22.5°

40°

120° 16°

15

30

20



5. Find the value of the pronumeral in each triangle.

(a)

(b)

(c)

6. Find the pronumeral of the following triangles

(a)

(b)

(c)

7. Find the value of the interior angle x in the triangle below:-

8. Find the value of the exterior angles of the triangles below.

(a

)

(b)

x = 136°

y = 160°

x = 85°

x = 40° x = 50° x = 30°

48° 51° 10°



9. The value of the exterior angle of a triangle = sum of 2 opposite __interior__

angles

10. Find the value of the pronumeral:

(a)

(b)

(c)

(d)

11. The sum angle of a quadrilateral is ______________

12. Find the sum angle of a heptagon.(Use the rule a = 180°× (n – 2), where a is the

angle and n=no. of sides)

Sum angle of heptagon = 180(7 -2) = 180 × 5 = 900°

x = 118° x = 30°

x = 92°

360°

900°

57° 112°

x° 73°

4x °

x °

2x °

5x °

x = 138°




1. Find the value of the pronumerals.

2. Use the following rules(corresponding angles, alternate angles, vertically opposite

angles, straight angles, co- interior angles) to describe the following equations

(a) y = z Rule:

(b) z = 69° Rule:

(c) x + 69° = 180° Rule:

(d) y = 69°

Rule:

(e) x + y = 180°

Rule:

3. Are the following statements true (T) or false (F)?

(a) Angles a and d are alternate.

(b) Angles c and f are corresponding.

(c) Angles b and f are co-interior

Key words: Complementary / Supplementary / Pronumeral /

Exterior angle Parallel Lines / Corresponding / Alternate angles /

vertically opp. Angles / Co-interior angles

x =

y =

z =

111°

69°

69°

Vertically opposite

Corresponding angles

Straight angles (or Supplementary)

Alternate angles

Co-interior angles

True

False

False



4. Find the value of the pronumerals given.

5. Find the value of the pronumerals

6. Find the value of the pronumeral:

7. Find the value of the pronumerals given:

8. Find the pronumeral given:

a 60°

b c

d e

f g

115°

x°

x°

y°

120°

30°

35°

h°

a =

b =

c =

d =

e =

f =

g =

x =

y =

z =

x =

y =

x =

h =

120°

120°

60°

120°

120°

60°

60°

33°

57°

57°

65°

120°

60°

65°



9. Find the exterior angle of an equilateral triangle.

Exterior angle = 360 ÷ 3 = 120°

10. Find the exterior angle of an isosceles triangle in line with the base angle which

equals 60°

11. In a triangle, the first angle is designated x, the second angle is twice that of the first

and the third angle is three times that of the second angle. What angle is x?

x + 2x + 3(2x) = 180, 9x = 180, x = 180/9 = 20

12. Find out the sum of all three exterior angles of a triangle

13. How many times is the 3 exterior angles of a triangle bigger than its three interior

angles?

120°

120°

If the base is 60°, it is possible an equilateral

20°

360°

The sum of all exterior angles of any polygon is 360°

2 times

Any polygon has 360° as the sum of exterior angles including triangle. The sum of

interior angles is 180°

165°



Challenge Questions

1. A car travelled 281 kilometres in 4 hours 41 minutes. What was the average speed

of the car in kilometres per hour?

281 ÷ (4 × 60 + 41) × 60

2. The length of a rectangle is four times its width. If the area is 100 m2 what is the

length of the rectangle?

4w × w = 100 w2 = 25 w = 5

Length = 4 w = 20 m

3. The length of a rectangle is increased to 2 times its original size and its width is

increased to 3 times its original size. If the area of the new rectangle is equal to

1800 square meters, what is the area of the original rectangle?

Length 2 times, width 3 times, hence Area will be 6 times.

1800 ÷ 6 = 300 m2.

4. Each dimension of a cube has been increased to twice its original size. If the new

cube has a volume of 64,000 cubic centimetres, what is the area of one face of the

original cube?

Volume would be increased by 23 = 8 times, hence original volume = 64000 ÷ 8 =

8000 cm3. Each side =√ 000

20 Each face = 20

2 = 400 cm

2.

5. Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8

hours. How long does it take the two pumps working together to fill the tank?

(Round your answer to the nearest minute).

Assume capacity = x Rate of Pump A = x/5, Rate of Pump B = x/8

Combined rate = x/5 + x/8 = 13x/40. Time = x ÷ 13x/40

40/13 = 3.07692 hours = 3 hours 5 minutes.

60 km/hour

20 m

300 m2

400 cm2

3 hours 5 minutes




1 Find the value of the pronumeral a in this pair

of similar triangles.

cm7

210

1814

8

14

8

18

a

a

a

2 Find the value of the pronumeral b in this pair


cm11

921

811

30

11

30

8

b

b

b

3 Find the value of the pronumeral c in the figure

below.

3

211

1059

2401359

1615159

9

16

15

15

c

c

c

c

c

4 Find the value of the pronumeral d in the figure

below.

7

19

1614

8

14

8

16

d

d

d

5 Which of the following triangles are congruent.

Give a reason for your answer.

PNG HDJ (SAS)

Key words: Similar Triangles / Congruent Triangles / Pronumeral



6 A flagpole casts a shadow 7 m long. A metre

ruler at the same time casts a shadow 65 cm

long. How high is the pole?

m11

m13

1010

10065

7

65

7

100

x

x

x

x

The height of the flagpole is

about 11 m.

7 Prove that the diagonal of a rectangle divides

the figure into two congruent triangles.

In ABD and CDB

AB = CD (opposite sides of

rectangle)

AD = CB (opposite sides of

rectangle)

DB is common

(SSS)

ABD CDB

So the diagonal divides the

rectangle into two congruent

triangles.

8 Given that PQR PSR, find the values of

the pronumerals shown.

PQR PSR

So QR = SR that is,

a = 2 cm

Also PQR = PSR that is,

b = 55

In PSR

c + 90 + 55 = 180

c + 145 = 180

c + 145 145 = 180 45

c = 35

9 Find the value of the pronumerals in the

following pair of congruent triangles.

Congruent triangles means all

corresponding sides and all

corresponding angles equal.

Therefore:

a = 4

b = 3

10 Find the value of the pronumerals in the


Congruent triangles means all

corresponding sides and all

corresponding angles equal.

Therefore both triangles are

equilateral triangles. Therefore

a = 60°

b = c = d = e = 4:

Pactice Test 2 Year 7 Term 1



Multiple Choice Questions:

1 The value of the angle which is

complementary to 27° is

A 72°

B 63°

C 153°

D 163°

E None of the above

B

2 The value of the angle, a, in the

figure below is:

A 111°

B 69°

C 79°

D 89°

E None of the above

B


figure below is:

A 28°

B 62°

C 79°

D 69°

E 59°

E

4 The value of the angle which is

supplementary to 34° is:

A 43°

B 56°

C 146°

D 156°

E None of the above

C

5 The values of the angles a and

b, in the figure below are:

A a = 108° , b = 68°

B a = 72°, b = 68°

C a = 72° , b = 22°

D a = 72° , b = 40°

E a = 108° , b = 4°

D

6 An obtuse-angled triangle has:

A 1 angle equal to 90°

B 1 angle less than 90°

C 1 angle more than 90°

D 2 equal angles

E no equal angles

C

7 The co-interior angles of 2

parallel lines adds up to:

A. 60°

B. 90°

C 180°

D 120°

E 30°

C


figure below is:

A 18°

B 26°

C 62°

D 118°

E 128°

D

Pactice Test 2 Year 7 Term 1


9 An acute-angled triangle has:

A 1 angle less than 90°

B 2 angles less than 90°

C 3 angles less than 90°

D 1 angle more than 90°

E None of the above

C

10 The 2 triangles in the figure

below are congruent. Therefore

we would write:

A ABC = PQR

B ABC PQR

C ABC = RQP

D ABC RPQ

E All the above are correct

D

11 In the figure below the 2

triangles are similar.

Which of the following

statements is correct?

A DE = 15

B EF = 15

C EF = 35

D DE = 35

E None of the above

B

12 Which of the following

statements is true?

A All similar triangles are

congruent.

B Some similar triangles

are congruent.

C Some congruent triangles

are not similar.

D All right–angled triangles

are similar.

E All equilateral triangles

are congruent.

B

13 The value of the pronumeral b

in the figure below is:

A 9

4

B 4

111

C 5

4

D 2

12

E 4

12

E

15 The value of the pronumerals c

and d, respectively, in the pair

of congruent triangles in the

figure below is:

A 11 and 50

o

B 5.5 and 25o

C 5.5 and 80o

D 5.5 and 40o

E 11 and 40o

A



Section B: Short Answer Questions:

1. Determine the supplementary angles to:

a) 34 b) 124 c) 91 d) 179

Ans: 180 – 34 = 146 56 89 1

2. Find the value of the angle, a, in the figure below.

a = 90 – 28 = 62

3. Find the values of the angles a, b and c as shown in the figure below

a = 180 – 115 = 65

c = 38

b = 180 – 65 – 38 = 77

d = d = 77

4. Find the angles of the pronumerals listed.

a + a + 20 = 180

2a = 180 – 20 = 160

a = 160/2 a= 80

b = 80 + 20 b= 100

c = 180 – 100 c= 80

5. Find the value of „a‟ and thus the 3 angles of the triangle.

a + 2a + 3a = 180

6a = 180

a = 180/6 = 30°

2a = 60°

3a = 90°

a

3a

2a



6. Find the sum of interior angle of an octagon.

180 × (8 – 2) = 180 × 6

= 1080

7. If 3 angles of a quadrilateral equal 290°, what will the magnitude of the fourth

angle?

360 – 290 = 70

8. Find the following pronumerals.

a) x + 20 = 180° b) x +2 +x +3 = 45°

x = 180 – 20 x = 160° 2x + 5 = 45

2x = 45 – 5 = 40

x = 40/2 x = 20°

c) x – 10 +2x + 20 = 130° d) 2x + x + 5 + 2x + 10 = 115°

3x + 10 = 130 5x + 15 = 115

3x = 130 – 10 = 120 5x = 115 – 15 = 100

x = 120/3 x = 40° x = 100/5 x = 20°

9. Determine the value of the angle a in the figure

below.

90 + a + a = 180

90 + 2a = 180

2a = 90

a = 45°

10. Find the values of the angles a and b in the

figure below, using the exterior angle theorem.

b + 70 = 125

b = 55°

a + b + 70 = 180 (angle sum of a triangle)

a + 55 + 70 = 180

a + 125 = 180

a = 55°

11. Find the height, h, of the building in the figure

below.

The small triangle is similar to the large

triangle, therefore their sides are in equal ratio.

4

7 =

h

277

7h = 4(7 + 27)

7h = 136

h = 19.43 m



12. Find the value of the pronumeral a in the pair


11

113

811

18

11

18

8

a

a

a

13. The width of a river can be determined using

similar triangles. How wide is the river?

m31

m4

131

5040

25

40

25

50

w

w

w

w

The width of river is about 31 m.

14. Find the value of the pronumerals d and e in the


Congruent triangles means all corresponding

sides and all corresponding angles are equal.

Therefore:

d = 7

e = 9

Holiday Homework (Last Year) Year 7 Term 1


1. Sands of time.

The problem is to find the most efficient way of using 2 sand glasses to time the

cooking of a 15 minute hard-boiled egg. You only have an 11 minute timer and a 7

minute timer to judge cooking time. How would you use them?

Ans: Start the 11 min and the 7 minute sand glasses at the same time. Start

boiling the egg when the 7 minute sand glass has just finished flowing.

The 11 minute sand glass now has 4 minutes of time left. When the sand

stop flowing in the 11 minute sand glass, turn it around and start timing

the 11 minute sand glass again. You will have another 11 minutes. Total

time now will be 4 + 11 = 15 minutes

2 Lily Pad.

A frog sits in the middle of a lily pond which has a diameter of 30 metres. It can

hop 8 m after which it is so tired it can only hop half that length. Its next hop is half

the length he hopped before and so on. It goes on hopping half its last hop. How

many hops does it take for the frog to get to the edge of the pond?

Ans: Since it sits in the of the lily pond, it will only need to jump 15 m to reach the

edge.

Its first jump is 8m, giving it another 15 – 8 = 7 m to jump.

2nd

jump is 4m, giving it 3 more m to jump,

3rd

jump is 2m, giving it another 1m to jump

4th

jump is 1m which will help it to reach the edge of the lily pad

Its needs 4 jumps to reach the edge of the lily pad.

3. Dividing the clock.

Draw a straight line across the centre of the clock so that the sum of the numbers on

each half of the clock is the same.

Ans:

12 and 1 (being next to each other) will be on the same side – to balance up) so

directly opposite of 6 and 7(total also 13) will be on the other side. Likewise, 11

and 2 balances up 8 and 5 (total 13) and 10 and 3 as well as 9 and 4.

Draw a line between 9 and 10 passing through a point between 3 and 4.

Therfore 10 + 11 + 12 + 1 + 2 + 3 = 4 + 5 + 6 + 7 + 8 =+9 = 39

Holiday Homework (Last Year) Year 7 Term 1


4. Capacity of Football Stadium

In a football grand match, blocks of seats are red, yellow, blue or green. Each block

is labelled in rows A to Z, then rows AA, BB, to ZZ. (Note: There‟s no row marked

AB, AC….). Each row has 100 seats in it.

a) How many people can be seated at the match?

b) In an attempt to determine how many people attended a particular match, the

manager counted the empty seats. He noticed that none of the rows VV to ZZ, were

occupied in the yellow zone, and all rows XX to ZZ were vacant in the green zone.

Red zone was full except for 10 seats and blue except for 15 seats. How many

people attended the match?

Ans:

a) A to Z means 26 × 4 (colors) = 104 rows of seats.

AA to ZZ means another 26 × 4 = 104 rows of seats. Total number of rows = 2 ×

104 = 208

Each row is capable of seating 100 seats.

Capacity = 100 × 208 = 20800 seats, i.e., it can accommodate 20800 people.

b) VV to ZZ = 5 rows empty i.e., 500 empty seats

XX to ZZ means 3 rows empty or 300 empty seats.

There are a further 10 seats empty in the red zone and 15 seats in the blue zone.

Number of people who attended the match = 20800 – 500 – 300 – 10 – 15 = 19975

5. Diet

The number of Kj (kilojoules) provided by each type of food is given inside the

brackets below:

1 boiled egg (335), 1 sliced bread (335),

100ml milk (538), 1 lamp chop (1460),

100g potato (370) 100g carrots (108),

100g cheese (1833), 100g fish (400),

100g peas (368)

Grandma can only have 4500Kj. Her normal diet is an egg, a slice of bread, 100g of

fish and 50ml. of milk.

a) How many Kj is this?

Ans: Number of calories = 335 + 335 + 400 + 538/2 = 1339Kj

b) How many Kj is left from her daily allowance?

Ans: Number of calories left = 4500 – 1339 = 3161Kj

c) If she decides to forgo her normal diet and instead have 2 lamp chops for dinner,

how much cheese is she allowed making it to 4500Kj?

Ans: 2 lamp chops = 2 × 1460 = 2920kj.

She will then have 4500 – 2920 = 1580 kj left over

Since 100g of cheese = 1833kj, 1580 kj = 1580 / 1833 × 100 g of cheese = 86.20 g

So, grandma is only allowed roughly 86 g of cheese

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