Mathematics for Science Streams

😁Food for thought for Grade 12's. Application of calculus proves that any parabolic function f(x) = ax² + bx + c will have a minimum/maximum value at x = - b/2a. That's where the gradient of f, defined by f'(x) is 0.

21/05/2022| As we approach the end of term 2, are you ready to ace your mid-year/june examinations ? 😊

Test your knowledge on:

Grade 10
Functions

Grade 11
Euclidean Geometry

Grade 12
Trigonometric functions

Solutions @ 23:00

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09/03/2022| Are you ready to ace your term 1 test? 😊

Test your knowledge on:

Grade 10
Exponential equations

Grade 11
Quadratic equations

Grade 12
General solutions

Solutions @23:00

05/03/2022 | Evaluate yourself 😊

✅Got it? Good for you.👊🏻
❌Didn't get it? Don't worry, read the explanation below and you'll do better next time😎

Grade 10

1) The first thig we do when we have a fraction raised to a negative exponent, we invert the fraction then make the exponent positive. In other words, we swap the numerator and the denominator and make the exponent positive.

2) When we have a fraction a/b as an exponent, it means we take the b-th root and raise to the power of a. That is why we took the 4-th root and raised to the power of 3.

3) Simplify inside the brackets by getting rid of the 4-th roots and raise the answer to the power of 3.

Grade 11:

1) First thing we do when we solve quadratic inequalities is to simplify our equation to a standard form, that is: ax² + bx + c, and make sure that we only have 0 on our right hand side.

Thus, 3x² + x — 4 ≤ 0 is in standard form.

2) Factorise

(3x + 4)(x — 1) ≤ 0

Just like when you solve for x, without the inequality sign, i.e (3x + 4)(x - 1) = 0, our critical values will be our roots or our x-intercepts of the graph y = 3x² + x — 4. Hence:

x = —4/3 or x = 1

3) Draw your parabola or number line.

Since we are only looking for the x-values where y ≤ 0, it means we want the x-values where the graph is below the x-axis (y = 0 line). Hence, those x-values are between —4/3 and 1.

4) Thus, our solution:

—4/3 ≤ x ≤ 1

Grade 12

1) A geometric convergent series is a series that has a limit or approaches a certain constant. This happens only when the constant ratio of the series is between —1 and 1, that is —1 < r < 1

2) Find your constant ratio, substitute in the inequality

—1 < r < 1 then solve for x

3) After solving for x:

—1 < 2x + 3 < 1, we find that the series will converge when x is between —2 and 1.

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05/03/2022| Are you ready to ace your term 1 test? 😊

Test your knowledge on:

Grade 10
Exponents

Grade 11
Quadratic inequalities

Grade 12
Sequences & series

Solution @23:00

Solutions for Dailly challenge 01/01/2022. Continue reading for explanations.




Grade 10:

1st step: Let x = 5.4`3`2`

x = 5.432432432...

2nd step: Multiply both sides by 1000. Why? Because we have 3 recurring digits aftet the coma. (4`3`2`) 3 digits > 1000 (3 zeros).

Then we have:
1000x = 5432.432432432...

3rd step: Subtract the first equation from the second equation:

1000x — x = 5432.432432432... — 5.432432432...


We remain with :

999x = 5427 then solve for x.
..................

Grade 11

1st step:
Expand the bases on the numerator. Why? Because we have addition of exponents and we know that they are as a result of same bases multiplying.

2nd step:
Factor out the common factor 3ⁿ. Then simplify
..................

Grade 12:


1st step:

You know that it's a quadratic sequence (given).
You know that the general n-th term of a quadratic sequence is given by: Tn = an² + bn + c
Where:
2a = second difference (common)
3a + b = first term of the first difference
a + b + c = first term of the sequence

2nd step:
Solve for a, b and c to find the Tn of the sequence.

3rd step:
Substitute n = 26 to find the 26th term of the sequence.
😊☺️
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Daily Challenge 01/02/2022.


Exercise your mind by solving the problem corresponding to your grade.


Post your answers in the comment box. Solutions will be posted at 21:00😊

Grade 10 — 12 Mathematics pace setters! Make sure not to fall behind the schedule 😊

Lol, I like the examiner 🔥🔥🔥Did you get it? Please if you didn't get it forget about it😭