week: one lesson: one topic: verbal statements and

of 84

Week: One

Lesson: One

Topic: Verbal Statements and Algebraic Expressions (Part 1)

Example

Write an algebraic expression to represent the verbal statement below.

𝑥 𝑝𝑙𝑢𝑠 3

Step 1: determine the mathematical operation to use by examining the word used.

The word used is “plus” and the operational sign for “plus” is “+”.

Step 2: write an expression using the operation sign and the symbols given.

The operational sign is “+”.

The symbols used are “𝑥” and “3”.

The algebraic expression is “𝑥 + 3”.

Write an algebraic expression to represent each of the verbal statements below.

1. 𝑥 𝑝𝑙𝑢𝑠 5 6. 𝑡𝑤𝑖𝑐𝑒 𝑐

2. 𝑦 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑏𝑦 9 7. 10 𝑑𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 𝑎

3. 7 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 𝑧 8. ℎ𝑎𝑙𝑓 𝑜𝑓 𝑞

4. 𝑏 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑏𝑦 4 9. 8 𝑝𝑙𝑢𝑠 𝑡𝑤𝑖𝑐𝑒 𝑟

5. 6 𝑡𝑖𝑚𝑒𝑠 𝑝 10. 𝑜𝑛𝑒 𝑡ℎ𝑖𝑟𝑑 𝑜𝑓 𝑛 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑏𝑦 12

of 84

Week: One

Lesson: Two

Topic: Verbal Statements and Algebraic Expressions (Part 2)

Example

Express the statement below algebraically.

Sam had $20 dollars. How many dollars had he left if he spent $x?

Step 1: determine the mathematical operation to use by examining the question asked

The question asked was “how many dollars Sam had left?” This indicates subtraction.

Step 2: write an expression using the operation sign and the symbols given.

The operational sign is “-”.

The symbols used are “𝑥” and “20”.

The algebraic expression is “20 − 𝑥”.

Express the following statements below algebraically.

1. Jane has $10 and her sister Mary has $x. How many dollars do they have altogether?

2. Ann had 3 apples. Her father gave her more 5 apples. How many apples does she have

altogether? (use the letter ‘a’ to represent 1 apple).

3. Peter has 7 sweets. He gave his friend Paul 2 sweets. How many sweets does he have

remaining? (use the letter ‘s’ to represent 1 sweet).

4. Sara is m years old today. What is her age five years ago?

5. A soda costs $100. What is the cost of y sodas?

of 84

6. A school has 20 classes. In each class there are z number of students. How many students

are there in the school?

7. A bag has 25 chocolates. The chocolates are to be shared equally among c number of

children. How many chocolates does each child receive?

8. Daniel has p number of pens. He has to share his pens equally among his 3 siblings. How

many pens does each sibling get?

9. Sachin bought n notebooks, each of which cost c dollars. Represent in dollars the change

he received from a $500 note, assuming his purchase is less than $500.

10. Joan had g genips. She gave her brother two-fifths of the genips. How many genips was

Joan left with?

of 84

Week: One

Lesson: Three

Topic: The Distributive Law (Part 1)

Example

Remove the bracket using the distributive law and then simplify the expression below.

3(𝑥 + 4) + 5 (𝑥 − 𝑦)

Step 1: divide the expression into the number of parts as the number of brackets

3(𝑥 + 4) + 5 (𝑥 − 𝑦)

Step 2: multiply the elements inside of the brackets by the number outside of the bracket. This

will remove the brackets.

3 × 𝑥 + 3 × 4 + 5 × 𝑥 − 5 × 𝑦)

= 3𝑥 + 12 + 5𝑥 − 5𝑦

Step 3: group the like terms and simplify expression

3𝑥 + 5𝑥 − 5𝑦 + 12

= 8𝑥 − 5𝑦 + 12

Remove the brackets using the distributive law and simplify the following

1. 3(𝑥 + 𝑦) 5. 3(𝑥 − 𝑦) 9. 4(𝑥 + 𝑦) + 3(𝑥 + 𝑦)

2. 5(𝑥 + 3) 6. 5(𝑥 − 3) 10. 5(𝑥 + 3𝑦) + 4(3𝑥 + 2𝑦)

3. 4(𝑥 + 2𝑦) 7. 4(𝑥 − 2𝑦) 11. 4(𝑥 + 𝑦) + 3(𝑥 − 𝑦)

4. 6(2𝑥 + 3𝑦) 8. 6(2𝑥 − 3𝑦) 12. 5(𝑥 + 3𝑦) + 4(3𝑥 − 2𝑦)

of 84

Week: One

Lesson: Four

Topic: The Distributive Law (Part 2)

Example:

Factorize the expression below using the distributive law.

5𝑥 + 5𝑦

Step 1: identify the highest common factor of the two terms.

Factors of 5x are 1, 5, x, 5x

Factors of 5y are 1, 5, y, 5y

Highest common factor (HCF) is 5

Step 2: use the common factor to divide both terms

5𝑥

𝟓 +

5𝑦

𝟓

= 5𝑥

𝟓 +

5𝑦

𝟓

= 𝑥 + 𝑦

Step 3: rewrite the expression using both HCF and the quotient.

5(𝑥 + 𝑦)

Factorize the following expressions below using the distributive law.

1. 6𝑥 + 6𝑦 4. 𝑟𝑥 + 𝑟𝑦 7. 𝑎𝑥 − 𝑎𝑦 10. 9𝑥 − 6

2. 9𝑥 + 9𝑦 5. 7𝑥 − 7𝑦 8. 𝑏𝑥 − 𝑏𝑦

3. 𝑚𝑥 + 𝑚𝑦 6. 8𝑥 − 8𝑦 9. 4𝑥 + 2

of 84

Week: Two

Lesson: One

Topic: Equations (Part 1)

Example

Solve the equation 𝑥 + 2 = 7

Step 1: identify the number that you want to transfer to the opposite side of the equal sign

The number to be transferred is 2.

𝑥 + 𝟐 = 7

Step 2: determine the operation between the number to be transferred and the unknown.

The operation is addition (+).

Step 3: transfer 2 from the left-hand side of the equation by subtracting it from both sides of the

equation.

𝑥 + 2 − 𝟐 = 7 − 𝟐

Step 4: simplify the above expression to solve the equation

𝑥 + 2 − 𝟐 = 7 − 𝟐

𝑥 + 0 = 5

𝑥 = 5

Solve the following equations.

1. 𝑥 + 5 = 7

2. 𝑥 + 6 = 8

3. 𝑥 + 7 = 12

4. 𝑦 + 8 = 15

5. 𝑦 + 4 = 18

6. 𝑦 + 3 = 20

7. 𝑧 + 12 = 21

8. 𝑧 + 15 = 37

9. 𝑧 + 42 = 18

10. 𝑧 + 30 = 20

of 84

Week: Two

Lesson: Two


Example

Solve the equation 𝑥 − 2 = 7



𝑥 − 𝟐 = 7


The operation is subtraction (-).

Step 3: transfer 2 from the left-hand side of the equation by adding it to both sides of the

equation.

𝑥 − 2 + 𝟐 = 7 + 𝟐


𝑥 − 2 + 𝟐 = 7 + 𝟐

𝑥 + 0 = 9

𝑥 = 9


1. 𝑥 − 5 = 7

2. 𝑥 − 6 = 8

3. 𝑥 − 7 = 12

4. 𝑦 − 8 = 15

5. 𝑦 − 4 = 18

6. 𝑦 − 3 = 20

7. 𝑧 − 12 = 21

8. 𝑧 − 15 = 37

9. 𝑧 − 18 = −42

10. 𝑧 − 20 = −30

of 84

Week: Two

Lesson: Three


Example

Solve the equation 2𝑥 = 6



𝟐𝑥 = 6


The operation is multiplication (×).

Step 3: transfer 2 from the left-hand side of the equation by dividing both sides of the equation.

2𝑥

= 6

𝟐 𝟐


2𝑥

= 6

𝟐 𝟐

𝑥 =

3

𝟏 𝟏

𝑥 = 3


1. 5𝑥 = 10

2. 6𝑥 = 18

3. 7𝑦 = 14

4. 8𝑦 = 16

5. 4𝑦 = 28

6. 3𝑧 = 21

7. 12𝑧 = 24

8. 15𝑧 = 30

9. 18𝑎 = 36

10. 20𝑎 = 60

of 84

Week: Two

Lesson: Four


Example

Solve the equation 2𝑥 + 1 = 7

Step 1: identify the numbers that you want to transfer to the opposite side of the equal sign

The numbers to be transferred are 2 and 1.

𝟐𝑥 + 𝟏 = 7

Step 2: determine the operations between the numbers to be transferred and the unknown.

The operations are addition (+) and multiplication (×).

Step 3: transfer the numbers, one at a time, from the left hand side of the equation and simplify

2𝑥 + 1 − 𝟏 = 7 − 𝟏

2𝑥 + 0 = 6

2𝑥 = 6

2𝑥

= 6

𝟐 𝟐

𝑥 =

3

𝟏 𝟏

𝑥 = 3


1. 5𝑥 + 1 = 11

2. 6𝑥 + 2 = 20

3. 7𝑦 + 5 = 19

4. 8𝑦 + 4 = 28

5. 4𝑦 − 3 = 27

6. 3𝑧 − 9 = 21

7. 12𝑧 − 8 = 16

8. 15𝑧 − 7 = 38

9. 18𝑎 − 54 = 36

10. 20𝑎 + 40 = 60

of 84

Week: Three

Lesson: One

Topic: Symbols of Inequality (Part 1)

Note: There are two main symbols of Inequality

“>” means “more than.”

“<” means “less than.”

Example:

Use > or < between the pair of numbers below in order to make the statement true.

4 7

Step 1: identify the smaller number.

The smaller number is 4

Step 2: choose the symbol that points to the smaller number.

The “less than” symbol points to the smaller number (<)

Step 3: place the symbol that points to the smaller number between the pair of numbers to make

the statement true.

4 < 7

Use > or < between the following pairs of numbers below in order to make the statements true.

1. 5

2. 12

8 4. -3

9 5. -9

-8 7. 3 1

4 2

-2 8. 1 1 3 2

10. 7.5 2.9

3. -3 0 6. -6 4 9. 0.2 0.5

of 84

Week: Three

Lesson: Two

Topic: Symbols of Inequality (Part 2)

Example:

State whether the statement below is true.

5 + 4 > 7

Step 1: simplify the inequality when necessary.

5 + 4 > 7

9 > 7

Step 2: examine the inequality to ensure symbol points to the smaller number.

In the inequality “9 > 7”, the symbol points to the smaller number.

Step 3: if the symbol points to the smaller number, the statement is true. If the symbol points to

the larger number the statement is false.

5 + 4 > 7 true

State whether the following statements are true or false.

1. 12 − 8 < 15

2. 6 + 5 > 8

3. 15 < 10 − 19

4. 9 + 1 > 13 − 3

5. 3 × 5 < 48 ÷ 3

6. 6 × 0 > 3 + 2

7. −7 + 2 < 8 ÷ 4

of 84

Week: Three

Lesson: Three

Topic: Inequations (Part 1)

Example:

State whether the statement below is true or false for each given value of 𝑥

5𝑥 + 4 > 7

(a) 𝑥 = 0

Step 1: substitute the value of x in the inequation.

5𝑥 + 4 > 7

5(0) + 4 > 7

Step 2: simplify the new inequality.

5(0) + 4 > 7

0 + 4 > 7

4 > 7

Step 3: examine the inequality to ensure the symbol points to the smaller number.

In the inequality “4 > 7”, the symbol points to the larger number.

Step 3: if the symbol points to the smaller number, the statement is true. If the symbol points to

the larger number then the statement is false.

5𝑥 + 4 > 7 false

State whether the following statements are true or false.

1. 12𝑥 − 8 < 15

𝑥 = 0

𝑥 = 1

of 84

2. 6𝑦 + 5 > 8

𝑦 = 2

𝑦 = 3

3. 15 < 10𝑧 − 19

𝑧 = 4

𝑧 = 5

4. 9𝑥 + 1 > 13 − 3x

𝑥 = 0

𝑥 = 1

5. 3 × 5𝑦 < 54 ÷ 3𝑦

𝑦 = 2

𝑦 = 3

6. 6𝑧 × 0 > 3𝑧 + 2

𝑧 = 4

𝑧 = 5

7. −7𝑥 + 2 < 8 ÷ 4𝑥

𝑥 = 0

𝑥 = 1

8. 8𝑦 > 7 − 2𝑦

𝑦 = 2

𝑦 = 3

of 84

Week: Three

Lesson: Four

Topic: Inequations (Part 2)

Example:

Construct a suitable inequation to represent the statement below.

The length of a rectangle is x cm and the width is 3 cm. The area of the rectangle is less than 15

cm2.

Step 1: look for key words that imply which inequality to use.

The length of a rectangle is 𝑥 cm and the width is 3 cm. The area of the rectangle is less than 15

cm2

The words “less than” tell us to use this symbol “<”.

Step 2: look for key words that imply which operation/s to use.

The length of a rectangle is 𝑥 𝑐𝑚 and the width is 3 cm. The area of the rectangle is less than

15 cm2

The words “area of rectangle” implies that we must multiply the length and the width.

Step 3: construct the inequation using information obtained

Area of rectangle is less than 15 cm2 , Area of rectangle = length × width

length × width < 15 cm2

𝑥 𝑐𝑚 × 3 𝑐𝑚 < 15 𝑐𝑚2

3𝑥 𝑐𝑚2 < 15 𝑐𝑚2

1. Anna had $10. After spending $x on snacks, she had less than $5 left.

2. When a whole number, 𝑥 is subtracted from 20, the result is less than 15.

3. The length of a rectangle is y cm and the width is 9 cm. The perimeter must not exceed

50 cm

of 84

4. If 3 is added to a whole number w, the result exceeds 20.

5. John has 3 apples more than his friend Paul. Paul has x number of apples. Together, they

have at least 13 apples

of 84

Week: Four

Lesson: One

Topic: Base and Index of an Expression

Example:

Identify the base and the index of the expression below.

5𝑥3

Step 1: identify the small number at the top right hand of the expression. That is the Index.

In 5𝑥𝟑 the index is 3.

Step 2: identify the number or symbol that is attached to the index. That is the Base.

In 5𝒙3 the base is 𝒙.

Note: If there is no visible index, then the index is 1. For example, the expression “y” can be

written as “y1”. Therefore, the index is 1.

Copy and complete the table below.

Expression Base Index

1. 𝑎2

2. 𝑝3

3. −𝑟6

4. −𝑠3

5. 7𝑎2

6. 4𝑝3

7. −5𝑞4

8. −3𝑥9

9. 6𝑢

10. −2𝑤

of 84

Week: Four

Lesson: Two

Topic: Expanding Index Notation

Example:

Expand the index notation below.

5𝑥3

Step 1: identify the base and the index.

Base = 𝑥 index = 3

Step 2: multiply the base by itself the number of times indicated by the base.

𝑥 × 𝑥 × 𝑥

Step 3: multiply the coefficient by the expression above

5 × 𝑥 × 𝑥 × 𝑥

Expand the following index notation below.

1. 53

2. 62

3. −74

4. −92

5. 𝑥4

6. 𝑦5

7. −𝑧2

8. 2𝑥3

9. 3𝑦4

10. −4𝑎4

of 84

Week: Four

Lesson: Three

Topic: Multiplication Law of Indices

Example:

Simplify the expression below

5𝑥3 × 2𝑥4

Step 1: multiply the coefficients

5 × 2 = 10

Step 2: rewrite the base and add the indices

𝑥3+4 = 𝑥7

Step 3: rewrite the product of the coefficients and indices

10𝑥7

Simplify the following below.

1. 5𝑥3 × 6𝑥2

2. 4𝑥2 × 5𝑥4

3. 3𝑥1 × 4𝑥3

4. 2𝑥2 × 3𝑥2

5. 𝑥3 × 2𝑥1

6. 3𝑦4 × 4𝑦5

7. 5𝑦4 × 2𝑦3

8. 2𝑦3 × 3𝑥𝑦2

9. 5𝑦4 × 3𝑥𝑦3

10. 3𝑥3𝑦2 × 2𝑥4𝑦5

of 84

Week: Four

Lesson: Four

Topic: Division Law of Indices

Example:

Simplify the expression below

6𝑥5 ÷ 2𝑥3

Step 1: divide the coefficients

6 ÷ 2 = 3

Step 2: rewrite the base and subtract the indices

𝑥5−3 = 𝑥2

Step 3: rewrite the quotient of the coefficients and indices

3𝑥2

Simplify the following below.

1. 12𝑥3 ÷ 6𝑥2

2. 15𝑥6 ÷ 5𝑥4

3. 8𝑥5 ÷ 4𝑥3

4. 18𝑥2 ÷ 3𝑥2

5. 2𝑥3 ÷ 2𝑥1

6. 12𝑦8 ÷ 4𝑦5

7. 10𝑦4 ÷ 2𝑦3

8. 6𝑥3𝑦5 ÷ 3𝑥𝑦2

9. 15𝑥4𝑦3 ÷ 3𝑥𝑦3

10. 16𝑥5𝑦7 ÷ 2𝑥4𝑦5

of 84

Mathematics Grade 7

Week: Five

Lesson: One

Topic: Mathematical Instruments ( Part 1)

Note:

There are four main mathematical instruments.

Name Picture Uses

Ruler

Used to draw and measure lines

Protractor

Used to draw and measure angles

Set Squares

Used to draw specific angles (30, 45, 60, 90) and

parallel lines.

Compass

Used to draw arcs and circles

State the instrument/s that were used to draw the shapes below.

1. 3.

(a)

(b)

(a)

(b)

2. 4.

(a)

(b)

(a)

(b)

of 84

Week: Five

Lesson: Two

Topic: Mathematical Instruments (Part 2)

Note:

There are four main mathematical instruments.

Name Picture Uses

Ruler

Used to draw and measure lines

Protractor

Used to draw and measure angles

Set Squares

Used to draw specific angles (30, 45, 60, 90) and

parallel lines.

Compass

Used to draw arcs and circles

1. Measure the length of the line below.

2. Measure the angle below.

3. Use the set squares to draw a square with side 3cm.

4. Use the compass to draw a circle.

of 84

Week: Five

Lesson: Three

Topic: Lines (Part 1)

Note:

There are five types of straight lines

Types of lines Description

1. Horizontal These lines run from left to right

2. Vertical lines These lines run from top to bottom

3. Oblique lines These are slanted lines

4. Parallel lines These are lines that never meet and maintain

the same distance apart.

5. Perpendicular lines These lines meet (intersect) at right angle.

Use appropriate mathematical instruments to draw the following lines.

1. Horizontal line measuring 5 cm

2. Vertical line measuring 20 mm

3. Oblique line measuring 2 inches.

4. Two lines Parallel to each other

5. Two lines perpendicular to each other.

of 84

Week: Five

Lesson: Four

Topic: Lines (Part 2)

Note: There are five types of straight lines

Types of lines Description

1. Horizontal These lines run from left to right

2. Vertical lines

These lines run from top to bottom

3. Oblique lines

These are slanted lines

4. Parallel lines

These are lines that never meet and

maintain the same distance apart.

5. Perpendicular

lines

These lines meet (intersect) at right

angle.

Identify two types of lines found on the shapes below. Each type of line must be identified at

LEAST once.

1. 4.

(a)

(b)

2. 5.

(a)

(b)

3. 6.

(a)

(b)

(a)

(b)

(a)

(b)

(a)

(b)

of 84

Week: Six

Lesson: One

Topic: Types of Angles

Types of Angles Images Description

1. Acute angles

Measures less than 90o

2. Right angles

Measures 90o

3. Straight angles

Measures 180o

4. Obtuse angles

Measures between 90o and 180o

5. Reflex angles

Measures between 180o and 360o

Draw the time indicated below on the following clocks and state which angle is formed by the

hands of each clock.

1. 3 o clock

of 84

2. 2 o clock

3. 5 o clock

4. 6 o clock

5. 7 o clock

of 84

Week: Six

Lesson: Two

Topic: Drawing Angles

Example

Use your protractor to draw an angle whose measure is 40o.

Step 1: draw a horizontal line

Step 2: place the center of the protractor at the vertex.

Step 3: measure 40o and mark using a point.

Step 4: draw a line to connect the vertex to the point marked.

of 84

Use your protractor to draw an angle whose measure is:

1. 25o

2. 60o

3. 90o

4. 125o

5. 150o

6. 180o

7. 200o

of 84

Week: Six

Lesson: Three

Topic: Measuring Angles

Example

Use your protractor to measure the angle below.

Step 1: place the center of the protractor at the vertex of the angle..

Step 2: align the horizontal line of the protractor with one arm of the angle so that the arm points

to zero.

Step 3: mark at which degree the second arm stops.

The angle measures 40o.

of 84

Measure the following angles below.

of 84

xo 55o

Week: Six

Lesson: Four

Topic: Supplementary Angles

Example

Find the value of the unknown angle.

Step 1: equate the sum of the two angles to 180o.

180o = x + 45o

Step 2: subtract the known angle from both sides of the equation.

180o = x + 45o

180o - 45o = x + 45o - 45o

135o = x

Find the value of the unknown angles below.

1.

2.

xo 105o

3.

xo 45o

xo 35o

of 84

35o

xo 55o

4.

xo 90o

5.

6.

7.

8.

xo 155o

xo

28o 46o

116o 28o xo

of 84

xo

55o

Week: Seven

Lesson: One

Topic: Complementary Angles

Example

Find the value of the unknown angle.

Step 1: equate the sum of the two angles to 90o.

90o = x + 15o

Step 2: subtract the know angle from both sides of the equation.

90o = x + 15o

90o - 15o = x + 15o - 5o

75o = x

Find the value of the unknown angles below.

1.

3.

2.

25o

xo

15o xo

xo

35o

of 84

4.

5.

6.

7.

8.

xo

79o

xo

15o

xo

36o

xo

46o

xo

28o

of 84

Week: Seven

Lesson: Two

Topic: Convex and Concave Polygons

Example

Determine which of the polygons below is convex and which is concave.

Step 1: examine the interior angles of each polygon.

Step 2: determine if there is a reflex angle present.

Step 3: the polygon with reflex interior angle/ s is concave and those without reflex interior

angles are convex.

of 84

Concave polygon Convex polygon

State whether the following polygons are convex or concave.

1. 4.

2. 5.

3. 6.

of 84

Week: Seven

Lesson: Three

Topic: Regular and Irregular Polygons

Example

Determine which of the polygons below is regular and irregular.

Step 1: measure the length of sides and the interior angles of the polygons

All sides and angles equal unequal sides and angles

Step 2: differentiate the polygons as regular polygons (all sides and angles equal) and irregular

polygons (unequal sides and angles).

Regular Polygon Irregular Polygon

State whether the polygons below are regular or irregular.

1. .

of 84

2.

3.

4. .

5. .

6. .

of 84

Week: Seven

Lesson: Four

Topic: Triangles 1

Examples

Classify the following triangles as equilateral, scalene or isosceles.

Step 1: measure the sides of each triangle.

all three sides are unequal

All sides are equal Two sides are equal

Step 2: classify the triangles base on the properties of their sides.

All three sides are unequal

All sides are equal Two sides are equal Scalene triangle

Equilateral triangle Isosceles triangle

of 84

Classify the following triangles as equilateral, scalene or isosceles.

1. .

2. .

3.

4. .

5. .

6. .

of 84

Week: Eight

Lesson: One

Topic: Triangles 2

Examples

Classify the following triangles as acute, obtuse or right triangles.

Step 1: measure the interior angles of each triangle.

At least one Obtuse angle

All angles are acute At least one angle is 90o

Step 2: classify the triangles based on the properties of their sides.

At least one obtuse angle

All the angles are acute At least one 90o angle Obtuse triangle

Acute triangle Right triangle

of 84

Classify the following triangles as acute, obtuse or right triangles.

1. .

2. .

3.

4. .

5. .

6. .

of 84

Week: Eight

Lesson: Two

Topic: Polygons

Example

Classify the following polygons based on the number of sides.

Step 1: count the number of sides on each polygon.

6 sides 4 sides 5 sides 3 sides

Step 2: classify each polygon.

6 sides 4 sides 5 sides 3 sides

hexagon quadrilateral pentagon triangle

of 84

Classify the following polygons based on the number of sides.

1. .

2. .

3. .

4. .

5. .

6.

of 84

Week: Eight

Lesson: Three

Topic: Constructing 60o Angles

Example

Construct an angle measuring 60o.

Step 1: draw a line and mark off a point A

Step 2: open you compass to a suitable radius. With center A, draw an arc to intersect the line at

a point O

Step 3: use the point O as center and the same radius, draw an arc to intersect the first arc at the

point P.

Step 4: draw a straight line to pass through the points A and P.

of 84

Construct the following 60o angles below.

1.

2.

3. Construct a triangle with one angle measuring 60o.

4. Construct a parallelogram with one angle measuring 60o.

60o

60o

of 84

Week: Eight

Lesson: Four

Topic: Constructing 90o Angles

Example

Construct an angle measuring 90o.

Step 1: draw a line and mark off a point A

Step 2: open you compass to a suitable radius. With center A, draw an arc to intersect the line at

two points

Step 3: use the two points as center and a radius greater than half the line, draw two arcs to

intersect at a point above the first arc.

Step 4: draw a straight line to pass through the points A and the intersecting arcs.

of 84

Construct the following 90o angles below.

1.

2.

3. Construct a triangle with one angle measuring 90o.

4. Construct a parallelogram with one angle measuring 90o.

90o

90o

of 84

Week: Nine

Lesson: One

Topic: Converting Units of Measurement

Note

kilometer hectometer decameter meter decimeter centimeter millimeter

× 10

× 10

× 10

× 10

× 10

× 10

Example

Convert 5.2 km to meters.

Step 1: determine whether you are converting from a large unit to a smaller unit or from a small

unit to a larger unit.

Kilometers (km) to meters (m) is largest to smallest.

Step 2: count the number of spaces it takes to reach from kilometers (km) to meters (m).

The table above shows that it takes 3 spaces to reach from km to m

Step 3: because you are converting from a larger unit to a smaller unit, multiply 10 by itself 3

times to get how much 1 km is equivalent to in meters

1 km = (10 × 10 × 10) m

1 km = 1000 m

Step 4: multiply 5.2 by 1000 to convert 5.2 km to meters

1 km = 1000 m

5.2 km = 5.2 × 1000m

Shift the decimal point 3 places to the right

of 84

5.2 km = 52 00 m

Convert each of the following lengths to meters

1. 5 km 3. 2.5 hm 5. 10.4 dam

2. 0.75km 4. 10 hm 6. 19 dam

Convert each of the following lengths to millimeters

1. 4 m 3. 4.5 dm 5. 2.4 cm

2. 0.55m 4. 11 dm 6. 13 cm

of 84

Week: Nine

Lesson: Two

Topic: Converting Units of Measurement 2

Note

kilometer hectometer decameter meter decimeter centimeter millimeter

× 1

10 ×

1

10 ×

1

10 ×

1

10 ×

1

10 ×

1

10

Example

Convert 5319 m to kilometers.

Step 1: determine whether you are converting from largest to smallest or smallest to largest.

meters (m) to kilometers (km) is smallest to largest .

Step 2: count the number of spaces it takes to reach from meters (m) to kilometers (km)

The table above shows that it takes 3 spaces to reach from m to km

Step 3: because you are converting from a smaller unit to a larger unit, multiply 1

10

by itself 3

times to get how much 1 m is equivalent to in kilometers

1 m = ( 1 × 1 10 10

1 m = 1 km 1000

× 1 ) km 10

Step 4: multiply 5319 by 1

1000 to convert 5319 m to kilometers

1 m = 1 km 1000

of 84

5319 m = 5319 × 1 km 1000

5319 m = 5319

km 1000

5319 m = 5319 ÷ 1000 km

Shift the decimal point 3 places to the left

5319 m = 5. 319 km

Convert each of the following lengths to kilometers

1. 5012 m 3. 251 hm 5. 104 dam

2. 7531 m 4. 1010 hm 6. 1945 dam

Convert each of the following lengths to meters

1. 468 mm 3. 451 dm 5. 246 cm

2. 6355 mm 4. 1112 dm 6. 1367 cm

of 84

Week: Nine

Lesson: Three

Topic: Perimeter of Regular Shapes

Example

Calculate the perimeter of a regular pentagon of side 5 cm

Step 1: draw and label the shape with dimensions.

5 cm

Step 2: add all the sides of the shape to calculate the perimeter.

P = 5 cm + 5cm + 5 cm + 5cm + 5cm

P = 25 cm

1. Calculate the perimeter of a regular hexagon of side 6 cm.

2. Determine the perimeter of a regular pentagon of side 16 mm.

3. Calculate the perimeter of a regular quadrilateral of side 14 cm.

4. Determine the perimeter of a regular triangle of side 3 cm.

5. Calculate the perimeter of a regular heptagon of side 13 mm.

6. Determine the perimeter of a regular octagon of side 10 cm.

7. Calculate the perimeter of a regular nonagon of side 5 cm.

8. Determine the perimeter of a regular decagon of side 4 cm.

9. Calculate the perimeter of a regular pentagon of side 15mm.

10. Determine the perimeter of a regular icosagon of side 1 cm.

5 cm 5 cm

5 cm 5 cm

of 84

Week: Nine

Lesson: Four

Topic: Perimeter of Irregular Shapes

Example

Calculate the perimeter of the shape below 3 cm

6 cm

4 cm

Step 1: determine the length of the missing side.

The length of the missing side is parallel to the length 3cm and 4 cm. Therefore the length of the

missing side is 3 cm + 4 cm = 7 cm

Step 2: add all the sides of the shape to calculate the perimeter.

P = 6 cm + 3cm + 4 cm + 4cm + 7cm

P = 24 cm

Calculate the perimeter of the following shapes

1. 2.

4 cm

2 cm

7 cm

7 cm

10 cm

2 cm

4 cm

4 cm

4 cm

of 84

3. 4.

12 cm

8 cm

3 cm

5. 6.

3 cm

of 84

Week: Ten

Lesson: One

Topic: Area of Squares

Example

Calculate the area of the square below

6 m

Step 1: state the formula to calculate the Area of a Square.

Area of a Square = l × l

Step 2: substitute the value for the length of one side into the formula

Area of a Square = l × l

Area of a Square = 6 m × 6 m

Area of a Square = 36 m2

Calculate the area of each of the following Squares.

3 cm

2 m

of 84

7 cm

10 mm

12 mm

11 cm

8 cm

3.5 cm

Week: Ten

Lesson: Two

Topic: Area of Rectangles

Example

Calculate the area of the triangle below

3 cm

8 cm

Step 1: state the formula to calculate the Area of a Rectangle.

Area of a Rectangle = bh

Area of a Rectangle = b × h

Step 2: substitute the valu for the length of one side into the formula

Area of a Rectangle = b × h

Area of a Rectangle = 8 cm × 3 cm

Area of a Rectangle = 24 cm2

Calculate the area of the following rectangles

1. 2.

8 cm

3 m 12 cm 5.

9 m

3. 2 cm

5 cm

4.

1 cm

6 cm

9 cm

7 cm of 84

of 84

Week: Ten

Lesson: Three

Topic: Area of Triangles

Example

Calculate the area of the triangle below

8 cm

Step 1: state the formula to calculate the Area of a Triangle.

Area of a Triangle = 1bh

2

Area of a Triangle = 1 × b × h 2


Area of a Triangle = 1 × b × h

2

Area of a Triangle = 1 × 8 cm × 3 cm 2

Area of a Triangle = 4 cm × 3 cm

Area of a Triangle = 12 cm2

Calculate the area of the following triangles.

5m 4cm

10m 12cm 14cm

3 cm

3cm

of 84

6cm

30mm

26cm 16cm

22 cm 20 mm

24 cm

2cm

10mm

8 cm

6cm

4 cm

2 mm

7 mm

Week: Ten

Lesson: Four

Topic: Area of Parallelogram

Example

Calculate the area of the parallelogram below

8 cm

Step 1: state the formula to calculate the Area of a parallelogram

Area of a parallelogram = bh

Area of a parallelogram = b × h


Area of a parallelogram = b × h

Area of a parallelogram = 8 cm × 3 cm

Area of a parallelogram = 24 cm2

Calculate the area of the following parallelograms.

7 cm

8 cm 4 cm 15 mm

2 cm

9 cm

of 84

3 cm

3 cm

15 mm

25 mm

of 84

Mathematics Grade 7

Week: Eleven

Lesson: One

Topic: Expressing a Fraction as a Decimal and as a Percentage

Example

Express 3 as a percentage

4

Step 1: divide the numerator by the denominator to obtain the equivalent decimal

= 3 ÷ 4

= 0 . 75

Step 2: multiply the decimal obtained by 100 (move the decimal point two places to the right)

0 .75 × 100 = 75%

Express the following as decimals then percentages.

1. 1

2

2. 1 4

3. 2 5

4. 3 6

5. 3 8

6. 7 15

7. 5 16

8. 13

20

9. 18

25

10. 37 50

of 84

Week: Eleven

Lesson: Two

Topic: Percentage of a Quantity

Example

Find 10 % of 250

Step 1: express the percentage as a fraction in its lowest terms

10 % = 10

= 1

100 10

Step 2: multiply the fraction obtained by quantity

1 × 250

10

= 250

10

= 250 25

10 1

= 25

Calculate the following.

1. 2% of 50 11. 20.5% of 36 metres

2. 8% of 150 12. 8.2% of 40 grams

3. 5% of 60 13. 371% of 40 litres 2

4. 9% of 200 14. 81% of 36 grams 3

5. 3% of 16 15. 81% of $150 2

6. 15% of 25

7. 8% of 40

8. 20% of 36

9. 3.5% of 16

10. 15.8% of 25 litres

of 84

Week: Eleven

Lesson: Three

Topic: Expressing one quantity as a Percentage of Another Quantity

Example

27 grams is what percentage of 150 grams

Step 1: express the two quantities as a fraction

27

150

Step 2: if possible, reduce the fraction to its lowest term.

Divide both numerator and denominator by the number 3.

27 9

150 =

50

Step 3: multiply the equivalent fraction by 100

9

× 100 50

= 9 × 1002

50

1 = 9 × 2

= 18

1. 8 is what percentage of 25?




5. What percentage of 96 grams is 36 grams?

6. What percentage of 80 grams is 63 liters?

7. What percentage of 85 grams is 34 kilograms?

8. What percentage of 154 grams is 77 centimeters?

of 84

Week: Eleven

Lesson: Four

Topic: Expression ratios as Fractions

Example

Write the ratio 8 to 32 as a fraction

Step 1: identify the first term

First term = 8

Step 2: identify the second term

Second term = 32

Step 3: write a fraction using the first term as the numerator and the second term as the

denominator.

𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚

𝑠𝑒𝑐𝑜𝑛𝑑 𝑡𝑒𝑟𝑚

= 8

32

Step 4: write the fraction in its simplest form

8

32

= 8

÷ 8

32 8

= 1

4

Step 5: rewrite the ratio in the form first term: second term.

first term: second term

1 : 4

of 84

Write the following ratios as fractions.

1. 40 to 8

2. 50 to 30

3. 49 to 21

4. 25 to 45

5. 27 to 45

6. 48 to 36

7. 90 to 75

8. 30 to 42

9. 28 to 70

10. 57 to 38

of 84

Week: Twelve

Lesson: One

Topic: Equivalent Ratios

Example

Write a ratio equivalent to 6 : 15

Step 1: identify any number.

4

Step 2: multiply each term by the number identified.

6 × 4 : 15 × 4

24 : 60

OR

Step 1: identify a factor common to both terms.

3 is a common factor

Step 2: divide each term by the factor identified.

6 ÷ 3 : 15 ÷ 3

2 : 5

Write an equivalent ratio for each of the following ratios.

1. 40 : 8

2. 50 : 30

3. 49 : 21

4. 25 : 45

5. 27 : 45

6. 48 : 36

7. 90 : 75

8. 30 : 42

9. 28 : 70

10. 57 : 38

of 84

Week: Twelve

Lesson: Two

Topic: Dividing Quantities in a Given Ratio

Example

Share $75 in the ratio 2 : 3

Step 1: add the terms

2 + 3 = 5

Step 2: divide the quantity by the sum of the terms

$75 ÷ 5 = $15

Step 3: multiply the quotient by each term

$15 × 2 $15 × 3

= $30 = $45

1. Share $600 in the following ratios:

a) 1 : 4

b) 2 : 3

c) 3 : 7

d) 7 : 13

e) 11 :19

2. There are 30 students in a class. State the number of boys and the number of girls in the

class if the ratio of boys: girls are the following:

a) 4 : 2

b) 1 : 2

c) 2 : 3

d) 3 : 7

e) 6 : 9

of 84

Week: Twelve

Lesson: Three

Topic: Average

Example

John completed 4 in class test this term. His scores are 20, 25, 10 and 15. What is John’s

average score?

Step 1: add all of the scores

Sum of scores = 20 + 25 + 10 + 15

= 60

Step 2: count the number of scores.

1 20

2 25

3 10

4 15

A total number of 4 scores.

Step 3: divide the sum of the scores by the total number of scores.

Sum of scores ÷ number of scores

= 60 ÷ 4

= 15

1. The amount of money spent by Sarah in a school week are: $240, $200, $160, $120, $60.

Determine the average money spent.

of 84

2. In seven 100-meter events a sprinter clocked the following times: 10.20s, 10.10s, 10.18s,

9.86s, 9.79s, 10.24s, and 9.94s. What is the average time for the seven events?

3. The rates of interest charged by banks in Guyana are: 9.9%, 10%, 10.1% and 10.4%. find

the average rate of interest charged by the banks.

4. The marks awarded to a student at the end of the term tests are: 43, 100, 95, 69, 100, 52,

84 and 73. What is the student’s average mark?

5. In a Caribbean country the total number of COVID-19 cases for the last six months were

recorded as 112, 150, 230, 298, 190 and 118. What is the average COVID- 19 cases for

the period?

6. The heights of 10 men in cm are recorded as: 162, 160, 163, 160, 165, 167, 170, 167,

174, and 176. Determine the average height of the men.

7. A motorist covered the following distances during one week: 185, 145, 155, 90, 175, 95

and 240 (km).

of 84

Week: Twelve

Lesson: Four

Topic: Unit Price of Items

Example

Sarah bought 10 apples at a cost of $300. What is the cost of 1 apple?

Step 1: identify the number of items.

The number of items = 10 apples

Step 2: identify the total cost of the items.

Total cost = $300

Step 3: divide the total cost by the number of items to obtain unit price.

Unit price = total cost ÷ number of items

Unit price = $300 ÷ 10

Unit price = $30

1. The cost of two sodas is $48. What is the cost of one soda?

2. A bag of 12 pens costs $240. What is the cost of one pen?

3. Three bags of cherries cost $636. What is the cost of one bag of cherries?

4. Nedd bought 6 basketballs for $1248. How much did he pay for one basketball?

5. A pair of cricket bats cost $360. What is the price for one bat?

6. Kelly paid $1080 for six dolls. How much did she pay for one doll?

7. Sean bought a dozen eggs for $60. What is the cost of one egg?

8. Mary bought half a dozen books for $960. What is the cost of one book?

9. A 3 pairs of shoes with 2 pairs of socks cost $108 and $50 respectively. What is the cost

one pair of shoes and one pair socks?

10. A dozen eggs cost $24, three bags of bread cost $18 and two boxes of milk cost $36.

What is the unit price for each item?

of 84

Week: Thirteen

Lesson: One

Topic: Profit

Example

A computer was bought for $6890 and sold for $8268. Calculate the profit made on the

computer.

Step 1: identify the cost price.

Cost price = $6890

Step 2: identify the selling price.

Selling price = $8268

Step 3: state the formula to calculate Profit.

Profit = selling price – cost price

Step 4: substitute the relevant values and simplify.

Profit = selling price – cost price

Profit = $8268 - $6890

Profit = $1378

1. A pot was sold for $228. If the cost price is $190, find the profit.

2. A toy car was sold for $230. Assuming the cost price was $200 calculate the profit made.

3. A doll house was bought for $250 and sold for $290. Determine the profit.

4. Carl bought a Vacuum cleaner for $600 and sold it for $728. How much money did he

gain?

5. Jenny bought a bicycle for $892 and sold it for $1052.56. how much money did she gain?

of 84

6. A gold chain was sold for $300 USD. If the cost price was $195 USD, what is the profit

in USD?

7. A car was sold for $3100 Euro. If its cost price is $2700 Euro calculate the expected

profit.

8. A CD player costs $600 and was sold for $825. What is the estimated profit?

9. Liam bought a television for $35 000. He sold it for twice the cost price. What is his

estimated profit?

10. Mr. Tanner sells a house for 1 ½ times the cost of it. If the cost for the house is $3 million

what is the estimated profit?

of 84

Week: Thirteen

Lesson: Two

Topic: Loss

Example

A computer was bought for $9890 and sold for $8268. Calculate the loss made on the computer.


Cost price = $9890



Step 3: state the formula to calculate Loss.

Loss = cost price – selling price


Loss = cost price – selling price

Loss = $9890 - $8268

Profit = $1622

1. A pot was sold for $118. If the cost price is $190, find the loss.

2. A toy car was sold for $230. Assuming the cost price was $300 calculate the loss.

3. A doll house was bought for $250 and sold for $190. Determine the loss.

4. Carl bought a Vacuum cleaner for $600 and sold it for $528. How much money did he

lose?

5. Jenny bought a bicycle for $892 and sold it for $852.56. How much money did she lose?

6. A gold chain was sold for $300 USD. If the cost price was $495 USD, what is the loss in

USD?

7. A car was sold for $3100 Euro. If its cost price is $3700 Euro calculate the expected loss.

8. A CD player costs $600 and was sold for $525. What is the estimated loss?

of 84

9. Liam bought a television for $35 000. He sold it for half the cost price. What is his

estimated loss?

10. Mr. Tanner sells a house for two thirds times the cost of it. If the cost for the house is $3

million what is the estimated loss?

of 84

Week: Thirteen

Lesson: Three

Topic: Cost Price

Example

A profit of $1622 was gained after a computer was sold for $8268. Calculate the cost price of the

computer.

Step 1: identify the profit (or loss)

Profit = $1622



Step 3: state the formula to calculate Cost price.

Cost price = selling price – profit OR Cost price = selling price + loss


Cost price = selling price – profit

Cost price = $8268 - $1622

Cost price = $6646

1. A pot was sold for $118. If the profit is $90, find the cost price.

2. A toy car was sold for $230. Assuming the loss was $30 calculate the cost price.

3. A doll house was sold for $190. Assuming the profit was $30 Determine the cost price.

4. Carl sold a Vacuum cleaner for $600 and lost $58. What was the initial cost?

5. Jenny gained $92 and after selling her bicycle for $852.56. How much money did she pay

for it?

6. A gold chain was sold for $300 USD. If the loss incurred was $495 USD, what was the

cost of the chain in USD?

7. A car was sold for $3100 Euro. If the profit is $3700 Euro calculate the cost price.

of 84

Week: Thirteen

Lesson: Four

Topic: Selling Price

Example

The cost price of a computer is $8268. A profit of $1622 was gained after selling it. Calculate the

selling price of the computer.

Step 1: identify the profit (or loss)

Profit = $1622


Cost price = $8268

Step 3: state the formula to calculate Selling price.

Selling price = cost price + profit OR Selling price = cost price - loss


Selling price = cost price + profit

Selling price = $8268 + $1622


1. A pot was bought for $118. If the profit is $90, find the selling price.

2. A toy car was bought for $230. Assuming the loss was $30 calculate the selling price.

3. A doll house was bought for $190. Assuming the profit was $30, determine the cost price.

4. Carl bought a Vacuum cleaner for $600 and lost $58 after selling it. How much did he

sell it for?

5. Jenny gained $92 and after selling her bicycle. If the cost price of the bicycle is $852.56

How much money did she sell it for?

6. A gold chain was bought for $300 USD. If the loss incurred after selling it was $95 USD,

what was the selling price of the chain in USD?

of 84

Week: Fourteen

Lesson: One

Topic: Parts of an Algebraic Term/ Expression

Example

Identify the parts of the expression below

3x + 5

Step 1: identify the constant by looking for the number that stands by itself.

The number that stands by itself is +5

Step 2: identify the variable by looking for the letter/s.

The letter in the expression is x

Step 3: identify the coefficient by looking for the number that stands in front of the variable.

The number that stands in front of the variable is +3 or 3

Complete the table below.

Algebraic Expression Coefficient Variable Constant

1. 2x + 3

2. 5y – 2

3. 2a – 9

4. 3b + 11

5. -7a + 5

6. -10b – 4

7. -13y + 5

8. a + 2

9. –x - 2

10. 6 x

11. -12x

of 84

Week: Fourteen

Lesson: Two

Topic: Expanding Algebraic Term

Example

Expand the term below

3x

Step 1: identify the variable and the coefficient

Variable = x coefficient = 3

Step 2: add the variable to itself the number of time indicated by the coefficient

x + x + x = 3x

Expand the following terms.

1. 4x

2. 7y

3. 9a

4. 2b

5. 13c

6. 14x

7. 12y

8. 3a + 2b

9. 7x + 9y

10. 5a - 2b

of 84

Week: Fourteen

Lesson: Three

Topic: Addition of Algebraic Terms

Example

3x + 7 + 5x

Step 1: group the like terms.

3x + 5x + 7

Step 2: add the like terms. (add the coefficients and rewrite the variable)

3x + 5x + 7

= 8x + 7

Simplify the following

1. 8𝑥 + 7𝑥

2. 5𝑥𝑦 + 4𝑥𝑦

3. 10𝑥 + 7𝑥

4. 9𝑥𝑦 + 4𝑥𝑦

5. 6𝑥 + 3𝑥 + 2𝑥

6. 9𝑥 + 7𝑥 + 2𝑥

7. 5𝑥 + 3 + 7𝑥

8. 9𝑥 + 5 + 4𝑥

9. 8𝑥 + 5 + 3𝑥 + 2

10. 6𝑥 + 3 + 4𝑥 + 2

of 84

Week: Fourteen

Lesson: Four

Topic: Subtraction of Algebraic Terms

Example

5x + 7 - 3x

Step 1: group the like terms. (make sure to move terms with the sign in front of them)

5x - 3x + 7

Step 2: subtract the like terms. (subtract the coefficients and rewrite the variable)

5x - 3x + 7

= 2x + 7


1. 8𝑥

2. 5𝑥𝑦

− 7𝑥

− 4𝑥𝑦

3. 10𝑥 − 7𝑥

4. 9𝑥𝑦 − 4𝑥𝑦

5. 6𝑥 + 3𝑥 − 2𝑥

6. 9𝑥 + 7𝑥 − 2𝑥

7. 7𝑥 + 3 − 5𝑥

8. 9𝑥

9. 8𝑥

+ 5 − 4𝑥

+ 5 − 3𝑥 −

2

10. 6𝑥 + 3 − 4𝑥 − 2

of 84

Week: Fifteen

Lesson: One

Topic: Multiplication of Algebraic Terms

Example

5x x 3y

Step 1: multiply the coefficients

5 x 3

= 15

Step 2: multiply the variables

x × y = xy

Step 3: rewrite the product as one.

5x × 3y

= 15 xy


1. 8𝑥 × 7𝑦

2. 5𝑥 × 4𝑦

3. 10𝑏 × 7𝑎

4. 9𝑎 × 4𝑏

5. 6𝑥 × 2𝑦

6. 9𝑥 × 7𝑦 × 2𝑧

7. 7𝑥 × 3𝑦 × 5𝑧

8. 9𝑎 × 5𝑏 × 4𝑐

9. 8𝑥 × 5𝑦 × 3𝑧 × 2

10. 6𝑎 × 3𝑏 × 4𝑐 × 2

of 84

Week: Fifteen

Lesson: Two

Topic: Division of Algebraic Terms

Example

8x ÷ 2x

Step 1: Divide the coefficients

8 ÷ 2

= 4

Step 2: divide the variables

x ÷ x = 1

Step 3: multiply the two quotients

8 × 1

= 8


1. 8𝑥 ÷ 4𝑥

2. 10𝑥 ÷ 2𝑥

3. 14𝑎 ÷ 7𝑎

4. 9𝑎 ÷ 3𝑎

5. 6𝑦 ÷ 2𝑦

6. 49𝑥 ÷ 7𝑥

7. 27𝑥 ÷ 3𝑥

8. 90𝑎 ÷ 5𝑎

9. 8𝑥 ÷ 2𝑥

10. 6𝑎 ÷ 3𝑎

of 84

Week: Fifteen

Lesson: Three

Topic: Division of Algebraic Terms 2

Example

8xy ÷ 2x

Step 1: Divide the coefficients

8 ÷ 2

= 4

Step 2: divide the variables

xy ÷ x = 1y

Step 3: multiply the two quotients

8 × 1y

= 8y


1. 8𝑥𝑦 ÷ 2𝑥

2. 10𝑥𝑦 ÷ 5𝑥

3. 14𝑎𝑏 ÷ 2𝑎

4. 9𝑎𝑏 ÷ 9𝑎

5. 6𝑥𝑦 ÷ 3𝑦

6. 49𝑥𝑦 ÷ 7𝑦

7. 27𝑥𝑦 ÷ 9𝑥

8. 90𝑎𝑏 ÷ 5𝑏

9. 8𝑥𝑦 ÷ 𝑥

10. 6𝑎𝑏 ÷ 𝑏

of 84

Week: Fifteen

Lesson: Four

Topic: Substitution

Example

If x = 3 and y = 5,

find the value of 4x +

y Step 1: rewrite the

expression

4x + y

Step 2: replace the value of x and y with the stated

values and simplify 4(3) + (5)

= 12 + 5

= 17

1. If x = 2 and y = 3 find the

value of the following a) 𝑥

+ 𝑦

b) 𝑥 – 𝑦

c) 3𝑥 + 𝑦

d) 𝑥 + 4𝑦

e) 5𝑥 + 3𝑦

2. If a = 5 and b =2, find the

value of the following a) 𝑎

+ 𝑏

b) 𝑎 – 𝑏

c) 2𝑎 – 𝑏

d) 𝑎 + 3𝑏

e) 4𝑎 – 5𝑏

week: one lesson: one topic: verbal statements and

Documents