Mathematics
EN FR
← Retour à la révision

Fluidité · Pack A

8.7 Algebra Expressions

Répondez à chaque question. Montrez les calculs si nécessaire.

Bronze

  1. Find the value of $3x + 4$ when $x = 5$.

  2. Simplify $7x \times 4$.

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

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

  5. Factorise $10x + 15$.

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

  7. Simplify $\dfrac{12x}{4}$.

  8. Identify which is equivalent to $3(x + 4)$: $(3x + 4)$ or $(3x + 12)$?

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

  10. Simplify $4p + 7q + 3p$.

Silver

  1. Substitute $x = 5, y = 10, z = -1$ into $2x + 3y - z$.

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

  3. Factorise $20x^2 - 4xy$.

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

  5. Simplify $\dfrac{6x + 9}{3}$ by factorising.

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

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

  8. Show that $3(x + y) + 5(x - y)$ is equivalent to $(c)x + (d)y$. Find $c$ and $d$ for $a = 3, b = 5$.

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

  10. Pete has three times as many songs on his phone as Sabrina. Sabrina has 120 fewer songs than Elena. Elena has $x$ songs. Write expressions for (a) Sabrina, (b) Pete.

Gold

  1. Expand $-3(x - 4) - (5x + 6)$.

  2. Factorise fully $24x^2 + 16x$.

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

  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 $\dfrac{3}{x} + \dfrac{5}{x}$.

  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 $6x(x + 3) - 5(4x - 2)$.

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

  3. Simplify $\dfrac{6x^2 - 9x}{4x^2 + 6x}$.

  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 $(3z - 4)$ cm. (a) Find $y$. (b) Find $z$.

  5. Two similar triangles have a side ratio of $\dfrac{x+2}{15} = \dfrac{x}{12}$. Find $x$.

  6. A student won 370 of his first 500 games and then won the next $x$ games. He has now won 75% 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 $\dfrac{x + 3}{2} - \dfrac{x - 1}{3}$.