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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
2. | GCSE Higher |
Find the highest common factor of the following two expressions:
$$ 8x^5y^3 $$ $$ 6x^2y $$3. | GCSE Higher |
Simplify then find the square root of this expression:
$$\frac{y}{(1-y)^2} - \frac{y}{1-y}$$4. | GCSE Higher |
(a) Simplify \( \left(\dfrac{3a}{a^3 - 3}\right)^0 \)
(b) Simplify \( \dfrac{9(2b-1)}{(2b-1)^2}\)
(c) Simplify \( (2c^3d^4)^5 \)
5. | GCSE Higher |
(a) Simplify the following expression.
$$ \frac{x^2 - 4}{3x^2 + 13x + 14}$$(b) Make b the subject of the following formula.
$$ a = \frac{7(3b-c)}{b}$$7. | GCSE Higher |
The expression below can be written as a single fraction in the form \( \dfrac{a-bx}{x^2-25} \) where \(a\) and \(b\) are integers.
$$ \frac{x-4}{x-5} - 2 + \frac{x+1}{x+5}$$Work out the value of \(a\) and the value of \(b\).
8. | A-Level |
The function \(f\) is defined as \(f(x) = 12x^3 - 5x^2 -11x + 6 \).
(a) Use the Factor Theorem to show that \( (4x-3) \) is a factor of \(f(x)\)
(b) Express \(f(x)\) as a product of linear factors.
(d) Hence solve the equation \( g(\theta ) = 0 \), giving your answers, in radians, in the interval \(0 \le \theta \le 2 \pi \).
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