Mathematics
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Fluency · Pack A

Algebra

Answer each question. Show working where needed.

Bronze

  1. Simplify $5x + 3x - 2x$.

  2. Simplify $5a + 3b + 2a - b$.

  3. Expand $3(x + 4)$.

  4. Expand $-2(x - 5)$.

  5. Factorise $6x + 9$.

  6. Factorise $4x^2 + 6x$.

  7. Simplify $(4x)^2$.

  8. Simplify $\sqrt{12}$.

  9. Find the value of $3x + 2y$ when $x = 4$ and $y = 5$.

  10. Solve $3x + 5 = 17$.

Silver

  1. Expand $(x + 3)(x + 5)$.

  2. Expand $(x - 4)(x + 3)$.

  3. Expand $(x + 5)^2$.

  4. Expand $(x + 6)(x - 6)$.

  5. Factorise $x^2 + 7x + 12$.

  6. Factorise $x^2 + 3x - 10$.

  7. Simplify $\sqrt{6} \times \sqrt{24}$.

  8. Simplify $\sqrt{8} + \sqrt{18}$.

  9. Solve $3(x - 4) = 9$.

  10. When $a = 3$ and $b = -2$, find the value of $a^2 - 3ab + 2b$.

Gold

  1. Factorise $x^2 - 49$.

  2. Factorise $2x^2 + 7x + 3$.

  3. Simplify $(3 + \sqrt{5})(3 - \sqrt{5})$.

  4. Rationalise the denominator of $\dfrac{6}{\sqrt{3}}$.

  5. Solve the system: $\begin{cases} y = 2x + 1 \\ y = -x + 7 \end{cases}$

  6. Solve the system: $\begin{cases} 2x + 3y = 15 \\ 2x + 1y = 9 \end{cases}$

  7. Factorise fully $2x^2 - 18$.

  8. Solve $\dfrac{x + 3}{4} = 5$.

  9. Expand and simplify $(x + 2)(x + 5) - (x + 3)^2$.

  10. The sum of two numbers is $30$ and their difference is $6$. Find both numbers.

Platinum

  1. Solve the system: $\begin{cases} 3x + 2y = 12 \\ 2x - 5y = -11 \end{cases}$

  2. Factorise fully $6x^2 - 5x - 4$.

  3. Rationalise the denominator of $\dfrac{2}{3 + \sqrt{5}}$.

  4. If $x + \dfrac{1}{x} = 3$ (with $x > 0$), find $x^2 + \dfrac{1}{x^2}$.

  5. A cinema sells adult tickets at £$12$ and child tickets at £$8$. One evening it sold $80$ tickets for £$832$. How many adult and child tickets were sold?

  6. Solve $x^2 + 7x + 12 = 0$.

  7. Simplify $\dfrac{x^2 - 25}{x + 5}$.

  8. Solve simultaneously: $y = x^2$ and $y = 3x + 4$.

  9. Simplify $(\sqrt{3} + \sqrt{12})^2$.

  10. Find $x$ such that $x^2 = 50$, giving exact answers in surd form.