Mathematics
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Fluency · Pack B

Algebra

Answer each question. Show working where needed.

Bronze

  1. Simplify $7y + 2y - 4y$.

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

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

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

  5. Factorise $8x + 12$.

  6. Factorise $9x^2 + 12x$.

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

  8. Simplify $\sqrt{18}$.

  9. Find the value of $3x + 2y$ when $x = 6$ and $y = 3$.

  10. Solve $4x + 2 = 18$.

Silver

  1. Expand $(x + 4)(x + 7)$.

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

  3. Expand $(x + 6)^2$.

  4. Expand $(x + 8)(x - 8)$.

  5. Factorise $x^2 + 9x + 20$.

  6. Factorise $x^2 + 2x - 15$.

  7. Simplify $\sqrt{5} \times \sqrt{20}$.

  8. Simplify $\sqrt{12} + \sqrt{27}$.

  9. Solve $5(x - 2) = 25$.

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

Gold

  1. Factorise $x^2 - 100$.

  2. Factorise $3x^2 + 8x + 4$.

  3. Simplify $(4 + \sqrt{3})(4 - \sqrt{3})$.

  4. Rationalise the denominator of $\dfrac{10}{\sqrt{5}}$.

  5. Solve the system: $\begin{cases} y = 3x + 2 \\ y = -x + 14 \end{cases}$

  6. Solve the system: $\begin{cases} 3x + 4y = 26 \\ 3x + 2y = 16 \end{cases}$

  7. Factorise fully $2x^2 - 50$.

  8. Solve $\dfrac{x + 2}{3} = 7$.

  9. Expand and simplify $(x + 1)(x + 6) - (x + 2)^2$.

  10. The sum of two numbers is $50$ and their difference is $10$. Find both numbers.

Platinum

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

  2. Factorise fully $4x^2 - 4x - 3$.

  3. Rationalise the denominator of $\dfrac{4}{5 + \sqrt{3}}$.

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

  5. A cinema sells adult tickets at £$15$ and child tickets at £$10$. One evening it sold $60$ tickets for £$750$. How many adult and child tickets were sold?

  6. Solve $x^2 + 8x + 15 = 0$.

  7. Simplify $\dfrac{x^2 - 36}{x + 6}$.

  8. Solve simultaneously: $y = x^2$ and $y = 5x + 6$.

  9. Simplify $(\sqrt{2} + \sqrt{8})^2$.

  10. Find $x$ such that $x^2 = 72$, giving exact answers in surd form.