Los op vir x:
1.1.1
$x^2 - 7x + 12 = 0$
1.1.2
$x(3x + 5) = 1$ (korrek tot TWEE desimale syfers)
1.1.3
$x^2 - 2x + 15$
1.1.4
$ ext{√}(2(1-x)) = x - 1$
Los gelijktidig vir x en y op:
1.2
$3^{x+y} = 27$ en $x^2 + y^2 = 17$
1.3
Bepaal, sonder die gebruik van 'n sakrekenaar, die waarde van:
$ rac{1}{ ext{√}1 + ext{√}2 + ext{√}3 + ext{√}4 + ext{...} + rac{1}{ ext{√}99 + ext{√}100}$ - NSC Mathematics - Question 1 - 2023 - Paper 1
Question 1
Los op vir x:
1.1.1
$x^2 - 7x + 12 = 0$
1.1.2
$x(3x + 5) = 1$ (korrek tot TWEE desimale syfers)
1.1.3
$x^2 - 2x + 15$
1.1.4
$ ext{√}(2(1-x)) = x - 1$
Lo... show full transcript
Worked Solution & Example Answer:Los op vir x:
1.1.1
$x^2 - 7x + 12 = 0$
1.1.2
$x(3x + 5) = 1$ (korrek tot TWEE desimale syfers)
1.1.3
$x^2 - 2x + 15$
1.1.4
$ ext{√}(2(1-x)) = x - 1$
Los gelijktidig vir x en y op:
1.2
$3^{x+y} = 27$ en $x^2 + y^2 = 17$
1.3
Bepaal, sonder die gebruik van 'n sakrekenaar, die waarde van:
$ rac{1}{ ext{√}1 + ext{√}2 + ext{√}3 + ext{√}4 + ext{...} + rac{1}{ ext{√}99 + ext{√}100}$ - NSC Mathematics - Question 1 - 2023 - Paper 1
Step 1
1.1.1
$x^2 - 7x + 12 = 0$
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Answer
To solve for x, we can factor the quadratic expression:
(x - 3)(x - 4) = 0
ext{Thus, } x = 3 ext{ or } x = 4.
\end{align*}$$
Step 2
1.1.2
$x(3x + 5) = 1$ (korrek tot TWEE desimale syfers)
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Answer
Rearranging gives:
3x^2 + 5x - 1 = 0
\end{align*}$$
Using the quadratic formula:
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
Where $a = 3$, $b = 5$, and $c = -1$:
$$\begin{align*}
b^2 - 4ac & = 5^2 - 4(3)(-1) = 25 + 12 = 37,
\end{align*}$$
So:
$$x = \frac{-5 \pm \sqrt{37}}{6}$$
Calculating gives:
$$x \approx 0.18 ext{ or } x \approx -1.85.$$
Step 3
1.1.3
$x^2 - 2x + 15$
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Answer
Since this is a quadratic that does not factor nicely, we can find the vertex or simply identify that the discriminant (D) is negative:
D=(−2)2−4(1)(15)=4−60=−56,
This indicates no real roots.
Step 4
1.1.4
$ ext{√}(2(1-x)) = x - 1$
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Answer
Rationalizing the expression breaks this down:
The sum reduces to:
=−1+2−2+3−3+4+...+101
Adding terms leads to the conclusion that the overall result sums to 9.
