# Lesson Notes By Weeks and Term - Junior Secondary School 1

SOLVING QUANTITATIVE APTITUDE PROBLEMS ON THE USE OF SYMBOLS AND BRACKETS

SUBJECT: MATHEMATICS

CLASS:  JSS 1

DATE:

TERM: 2nd TERM

REFERENCE BOOKS

• New General Mathematics, Junior Secondary Schools Book 1
• Essential Mathematics for Junior Secondary Schools Book 1

WEEK TEN

TOPIC: SOLVING QUANTITATIVE APTITUDE PROBLEMS ON THE USE OF SYMBOLS AND BRACKETS

CONTENT:

• Substitution in algebra
• Inserting brackets
• Simplifying algebraic expression containing brackets.

SUBTRACTION IN ALGEBRA

If a = -2, b = -5, c = ½  , x = 8 and y = 0, evaluate the following:

1. x + y + c
2. 5yc – c + a
3. 7x + c

Solution

1. x + y + c = 8 + 0 + ½ =  8½
2. 5yc-c + a = 5 x 0 x ½ - ½ + ( -2) = -2½
3. 7x + 5c = 7 x 8 + 5 x ½  = 58½

EVALUATION

If x = 8, y = 5, z = 10. Simplify the following:

1. 5y2- 10x2z      (b) – ( x+ y) + 2z    (c) ( zy –xy) – z   (d) 2y x  (-zy)

Simplify expressions containing brackets.

Step 1: Remove the brackets by using the number ( if any ) outside the bracket to multiply each term in the bracket.

Step 2 : Collect like terms and simplify.

Example 1

Remove bracket and simplify this expression 5 ( x -6) + ( 2x – 8)

Solution

5 ( x -6) + ( 2x – 8) = 5x – 30 + 2x – 8

Collect like terms

5x + 2x – 30 – 8

7x – 38 ( 38 cannot be subtracted from 7x because 38 does not have x and so, they are not like terms)

The answer is 7x – 38

Example 2

Remove the bracket and simplify: 4 ( x -1) – ( x – 4)

Solution

4 ( x -1) – ( x – 4)

4x – 4 – x + 4

Collect like terms

4x – x – 4 + 4

3x

Evaluation:

Expand the brackets and simplify

1. 2( x + y) + 3 (x + y)
2. 5y- (-6x – 3y)
3. 5k + ( 7t – k)( 5t + 4k)
4. (2x + 5)- ( 3x – 1)- (3x + 2 ) + 5x

Essential Mathematics for JSS1 pages 158 – 161

General Evaluation

1. Simplify the following
1. 4s – 4y + p – 2p + 7s + 5p + 8y
2. 6x – 3y – 5y + 9y – 4x-y
1. Simplify the following
1. 3a + 5b –a – 2b
2. 4d + 7e – 3d + 6e
1. Simplify the following expressions
1. 2z x 5zb
2. 5xy xy 2x
3. 4y xy

Weekend Assignment

1. The length of a rectangle is 2x metres and its width is 2m shorter than its length. What is the area of the rectangle? (a) ( 4x2 + 8)m2   (b) ( 4x2 – 6)m2    (c) ( 4x2 – 4x) m2  (d) ( 2x2 – 4) m2
2. If x= -2, y= -4 and z = 0, what is the value of 2x – ( 2xz – 4y)? (a) 12  (b) -12   (c) -20  (d) 16
3. Subtract x -7 from x + 9 (a) 16   (b) 2x + 16  (c) 6  (d) 2
4. Simplify 4y – ( 6- y). (a) 5y – 6   (b) 3y – 6   (c) 4y – 6   (d)  24y2
5. The smaller of two consecutive numbers is x – 5. What is the sum of the two numbers? (a) 2x – 9  (b) 2x + 11 (c) – 9   (d) 1

Theory

1. Simplify ( 2x – y- y) – ( 5x – 3y) + 5
2. The parallel sides of a trapezium are ( 3x + 2)m and ( 2x-1)m and they are 4m apart. Calculate the area of the trapezium.