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Fluidité · Pack B

8.7 Algebra Expressions

Répondez à chaque question. Montrez les calculs si nécessaire.

Bronze

  1. Find the value of $3x + 4$ when $x = -2$.

  2. Simplify $5x \times 6$.

  3. Expand $6(x + 5)$.

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

  5. Factorise $12x + 18$.

  6. Factorise $10x^2 + 25x$.

  7. Simplify $\dfrac{18x}{6}$.

  8. Identify which is equivalent to $5(x + 7)$: $(5x + 7)$ or $(5x + 35)$?

  9. Substitute $a = 4, b = -2$ into $ab + 5$.

  10. Simplify $5p + 2q + 8p$.

Silver

  1. Substitute $x = -3, y = 4, z = 7$ into $2x + 3y - z$.

  2. Expand and simplify $3(x + 5) + 2(x - 7)$.

  3. Factorise $15x^2 - 9xy$.

  4. Simplify $\dfrac{15x^2}{5x}$.

  5. Simplify $\dfrac{10x + 15}{5}$ by factorising.

  6. Expand and simplify $-5(x - 2) - 3(x + 1)$.

  7. Simplify $\dfrac{6ab}{9a}$ by cancelling common factors.

  8. Show that $4(x + y) + 2(x - y)$ is equivalent to $(c)x + (d)y$. Find $c$ and $d$ for $a = 4, b = 2$.

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

  10. Pete has three times as many songs on his phone as Sabrina. Sabrina has 75 fewer songs than Elena. Elena has $x$ songs. Write expressions for (a) Sabrina, (b) Pete.

Gold

  1. Expand $-4(x - 2) - (7x + 1)$.

  2. Factorise fully $27x^2 + 18x$.

  3. Simplify $\dfrac{12x^2 + 8x}{4x}$.

  4. Show that the expressions $(x + 3)^2 - 9$ and $x^2 + 6x$ are equivalent by expanding the first.

  5. Factorise $a^2 b + a b^2$.

  6. Substitute $x = -3, y = 2$ into $2x^2 - 3xy + y^2$.

  7. Factorise $4(x + 3) + y(x + 3)$.

  8. Simplify $\dfrac{7}{x} + \dfrac{4}{x}$.

  9. Simplify $\dfrac{x}{3} + \dfrac{x}{4}$.

  10. A rectangle has length $(2x + 3)$ and width $(x - 1)$. Find a simplified expression for the perimeter, and evaluate when $x = 4$.

Platinum

  1. Expand and simplify $4x(x + 2) - 3(5x - 7)$.

  2. Factorise $3x^2 + 12x + 9$ by first taking out a common factor.

  3. Simplify $\dfrac{10x^2 - 15x}{6x^2 + 9x}$.

  4. In a rectangle, the two long sides are labelled $3y$ cm and $(y + 3)$ cm; the two short sides are labelled $z$ cm and $(4z - 6)$ cm. (a) Find $y$. (b) Find $z$.

  5. Two similar triangles have a side ratio of $\dfrac{x+2}{15} = \dfrac{x}{10}$. Find $x$.

  6. A student won 300 of his first 500 games and then won the next $x$ games. He has now won 80% of all games. Find $x$.

  7. Factorise $a^2 - b^2$ (difference of squares).

  8. A field has dimensions $(x + 5)$ m by $(x + 2)$ m. Write an expression for its area, expand, and find the area when $x = 8$.

  9. Find the value of $x$ for which the area of a square of side $x$ is equal to the perimeter $4x$.

  10. Simplify $\dfrac{x + 3}{2} - \dfrac{x - 1}{3}$.