Grade 12 Mathematics | Past Exam Questions | May/June 2021
This passage discusses a mathematics problem and provides a
solution using the quadratic formula.
The problem is: 3x2 - 2x - 6 = 0 Solve for x, correct to two decimal
places. This equation cannot be factored, so the quadratic formula
must be used: x = (-b ± √(b2 - 4ac)) / 2a Using the formula, the
solution to the problem is: x = (2 ± √76) / 6 x ≈ 2.13.
The passage also includes an additional problem: x2 - x - 1 > 9
The given equation states that any value from negative infinity up to
x=2 is positive. Between x=-2 and x=-4, those values become
negative and of course, after x=4, those values become positive
again. The graph is greater than zero in this case.We square both
sides in this case.We add and keep the sign of the bigger number.
We subtract and take the sign. The sign of the constant term is
negative, so it indicates that the signs are not the same inside the
brackets.Thus, we get 4x+y=2, making it easier for us to solve
quadratic equations. We cannot get x=-2 as our solution.Therefore,
the final answer would be this.The next step is to solve
simultaneously.
When you have a coefficient of x, it means that you need to find
factors that would give you the desired result. For example, if you
need to get a result of 3, you would need to find factors of 4 and 1.
In this case, your brackets would be (4x + 1) and (x + 1), which is
equal to zero.Note that in this case, the constant term is negative,
so the signs inside the brackets would not be the same. As for the
left-hand side, we have 2x multiplied by 3y. Be careful not to make
the mistake of multiplying them and saying that the result is 6xy.
This passage discusses a mathematics problem and provides a
solution using the quadratic formula.
The problem is: 3x2 - 2x - 6 = 0 Solve for x, correct to two decimal
places. This equation cannot be factored, so the quadratic formula
must be used: x = (-b ± √(b2 - 4ac)) / 2a Using the formula, the
solution to the problem is: x = (2 ± √76) / 6 x ≈ 2.13.
The passage also includes an additional problem: x2 - x - 1 > 9
The given equation states that any value from negative infinity up to
x=2 is positive. Between x=-2 and x=-4, those values become
negative and of course, after x=4, those values become positive
again. The graph is greater than zero in this case.We square both
sides in this case.We add and keep the sign of the bigger number.
We subtract and take the sign. The sign of the constant term is
negative, so it indicates that the signs are not the same inside the
brackets.Thus, we get 4x+y=2, making it easier for us to solve
quadratic equations. We cannot get x=-2 as our solution.Therefore,
the final answer would be this.The next step is to solve
simultaneously.
When you have a coefficient of x, it means that you need to find
factors that would give you the desired result. For example, if you
need to get a result of 3, you would need to find factors of 4 and 1.
In this case, your brackets would be (4x + 1) and (x + 1), which is
equal to zero.Note that in this case, the constant term is negative,
so the signs inside the brackets would not be the same. As for the
left-hand side, we have 2x multiplied by 3y. Be careful not to make
the mistake of multiplying them and saying that the result is 6xy.
