Algebraic substitution involves replacing variables in a mathematical expression with their specific numerical values to calculate a final answer. In the West African Senior School Certificate Examination ( WAEC) and National Examinations Council (NECO) Senior Secondary School 1 (SS1 , SS2 and SS3) curriculum, substitution is a fundamental skill. It is heavily tested in both paper 1 (objectives) and paper 2 (theory), appearing in formula evaluation, change of subject of formulae, and simultaneous equations.
Below are 10 unique examples designed to match WAEC and NECO standards, moving from basic evaluations to complex fractional and root expressions. Each example includes long, step-by-step structural explanations optimized to keep your blog readers engaged and maximize your ad impressions.
1. Basic Multi Variable Substitution
Question: Given that a = 3, b = -2, and c = 5, evaluate the algebraic expression: 4a - 3b + 2c
Solution
Step 1: Insert the Numerical Values
To evaluate the expression, replace every occurrence of the variables a, b, and c with their assigned numbers. Always place negative numbers in protective parentheses to prevent basic sign errors, Note:
= 4(3) - 3(-2) + 2(5)
- First term: 4 × 3 = 12
- Second term: -3 × -2 = 6
- Third term: 2 × 5 = 10
= 12 + 6 + 10
Step 3: Compute the Final Sum
Add the remaining numbers together to find the final value:
= 12 + 6 + 10
= 18
Always remember to multiply the operators I mean "Mathematical" sign
2.Question: If p = 7, q = 2 and r =- 4 find the value of the expression: √ p²q - 2p
--------------
√ r
Solution
The first thing we need to do is substituting each value,
√7² × 2 - 2(7)
= ----------------------------
√ 4
√ 49× 2 - 14
= ----------------------
√4
√ 98 - 14
= -------------------
2
√84
= -------------
2
9.1652
= ----------------
2
= 4.5826
That was a great solving, remember the square root of 4 is 2 and since 84 is not a perfect square, so we right it as decimals.
3. Given that a = -2 , b = 4 , c = 1/2 and d= -1.
Fine the value of:
ab² + c³
----------------
a( d² - a)
Solution
ab² + c³
-------------------
a( d² - a)
Insert the numerator values
To evaluate the expression, replace every occurrence of the variables a, b, c and d with their assigned values. Always place negative numbers in protective parentheses to prevent basic sign errors, Note:
1
-2(4²) + (-------)²
2
------------------------------------
- 2(-1)² - (- 1)
Now let multiply the available powers.
1
- 2(16) + ----------
4
---------------------------
-2(1) - ( - 1 )
Simplify the numerator
1
- 32 + ---------
4
- 32 1
--------- + ---------
1 4
- 128 + 1
= -------------------
4
- 127
= ------------------
4
3
= 31 -------
4
Numerator
- 127
= ------------------
4
Now simplify the denominator
-2(1) - ( - 1 )
= - 2 + 1
= -1
Simplify the whole equation
- 127
= ------------------
4
-----------------------------
-1
4
- 127 ÷ ----------
-1
-127 -1
=----------- x --------
1 4
Minus multiply by minus is plus , then divide 127 by 4
127
---------------
4
3
= 31 ---------
4
That wasa great working by Simplemethod11 Series lesson, this is a direct guides students should study. It is well explained, with clear steps that involves.
That is how to substitute a letter for a number.please it is always important to ask questions,if have any question put them in the comments box.
Class Work
Simplify the following:
If p = 4 , q = -- 2 and r = 5
(a) p +pr³ + 4
-------------------
qr
(b) √p² + √16 (pr)
(c) p²q² 2/7
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