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Fluidité · Pack B

8.5 Directed Number and Algebra Basics

Répondez à chaque question. Montrez les calculs si nécessaire.

Bronze

  1. Calculate $6 + (-9)$.

  2. Calculate $-5 - (-8)$.

  3. Calculate $-7 \times -3$.

  4. Calculate $-36 \div -9$.

  5. Simplify $7x + 4y + 3x - 6y$.

  6. Simplify $8a + 4b - 6a$ and identify the coefficient of $b$.

  7. Write $a \times a \times 7 \times a$ using exponent notation.

  8. Calculate $12 + -4 \times 2$ using the correct order of operations.

  9. Write the algebraic product correctly: $3 \times a \times a$.

  10. Expand $4(7 + x)$ using the distributive rule.

Silver

  1. Calculate $8 - -2 \times -3$.

  2. Calculate $\dfrac{20 - -5}{8 + -3}$.

  3. Calculate $({a})^2$ and $-{a}^2$ for $a = 6$.

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

  5. Simplify $-4(x - 7)$.

  6. Simplify $7p \times 5q$.

  7. Simplify $(5x)^2$.

  8. Calculate $(8) + (-3) \times -4 - (6)$.

  9. Expand $-(7x - 2y + 4)$.

  10. Order from smallest to largest: $-8, 3, -2, 0, 5, -7$.

Gold

  1. Expand $5x(2x - 7)$.

  2. Simplify $4x - [2(5 - x) - 3]$.

  3. Find the value of $a^2 - 3b$ when $a = 5$ and $b = -3$.

  4. Find $xw^2$ when $x = -3$ and $w = 4$.

  5. Calculate the value of $\dfrac{10^2 - 6^2}{8}$.

  6. Substitute and simplify: $3(x + 2y) - 2(x - y)$ when $x = 5, y = -1$.

  7. Simplify $7(x + y) - 2(x - y)$.

  8. A square has side $-2x + 5$. Write an expression for its perimeter and simplify.

  9. Calculate $(-5)^3$.

  10. Simplify $(5xy)(2x^2 y)$.

Platinum

  1. Simplify $-4(3x - 2) - (7x + 1)$.

  2. Find the value of $-(p - q)^2$ when $p = -3$ and $q = 5$.

  3. The temperature in a town drops by 3°C each hour for 4 hours starting at $-2°C$. Find the temperature after 4 hours, showing each step.

  4. Expand and simplify $(5x - 2)(x + 3)$ where this is the product of two single-variable expressions. (Apply the area model / FOIL.)

  5. Substitute $a = -3, b = 2, c = -1$ into $a^2 b - bc + ac^2$.

  6. A bank account has balance $-£320$. Three deposits of £100, £75 and £90 are made, then a withdrawal of £50. Find the final balance.

  7. Investigate: is $(-a)^2 = -a^2$? Find a case where they differ and a case where they agree (with a reason).

  8. Simplify $4(x + 2y) - 3(4x - y) + 2(3x + y)$.

  9. A directed-number table game: each player rolls a die, and the result is multiplied by $-1$ if odd, $+1$ if even. After 5 rolls a player has scores 3, 4, 2, 5, 6. Find the player's total.

  10. Simplify $8x^2 - 2xy + 1x^2 + 5xy - 6y^2$.