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:

- x + y + c
- 5yc – c + a
- 7x + c

Solution

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

EVALUATION

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

- 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

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

**Reading Assignment**

Essential Mathematics for JSS1 pages 158 – 161

**General Evaluation**

- Simplify the following

- 4s – 4y + p – 2p + 7s + 5p + 8y
- 6x – 3y – 5y + 9y – 4x-y

- Simplify the following

- 3a + 5b –a – 2b
- 4d + 7e – 3d + 6e

- Simplify the following expressions

- 2z x 5zb
- 5xy xy 2x
- 4y xy

**Weekend Assignment**

- 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
- If x= -2, y= -4 and z = 0, what is the value of 2x – ( 2xz – 4y)? (a) 12 (b) -12 (c) -20 (d) 16
- Subtract x -7 from x + 9 (a) 16 (b) 2x + 16 (c) 6 (d) 2
- Simplify 4y – ( 6- y). (a) 5y – 6 (b) 3y – 6 (c) 4y – 6 (d) 24y2
- 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**

- Simplify ( 2x – y- y) – ( 5x – 3y) + 5
- 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.

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