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Fluency · Pack A

8.5 Directed Number and Algebra Basics

Answer each question. Show working where needed.

Bronze

  1. Calculate $-7 + (-5)$.

  2. Calculate $4 - (-3)$.

  3. Calculate $-6 \times 4$.

  4. Calculate $-20 \div 4$.

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

  6. Simplify $5a + 3b - 7a$ and identify the coefficient of $b$.

  7. Write $a \times a \times 5 \times a$ using exponent notation.

  8. Calculate $-5 + 3 \times 4$ using the correct order of operations.

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

  10. Expand $5(3 + x)$ using the distributive rule.

Silver

  1. Calculate $-3 - -4 \times 5$.

  2. Calculate $\dfrac{-12 - 4}{-3 + 7}$.

  3. Calculate $({a})^2$ and $-{a}^2$ for $a = 5$.

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

  5. Simplify $-3(x - 5)$.

  6. Simplify $4p \times 3q$.

  7. Simplify $(3x)^2$.

  8. Calculate $(-3) + (-4) \times 2 - (-5)$.

  9. Expand $-(3x - 5y + 2)$.

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

Gold

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

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

  3. Find the value of $a^2 - 3b$ when $a = -4$ and $b = -2$.

  4. Find $xw^2$ when $x = 5$ and $w = -2$.

  5. Calculate the value of $\dfrac{7^2 - 3^2}{4}$.

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

  7. Simplify $5(x + y) - 3(x - y)$.

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

  9. Calculate $(-4)^3$.

  10. Simplify $(3xy)(4x^2 y)$.

Platinum

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

  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 $(2x - 3)(x + 4)$ 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 $-£250$. Three deposits of £80, £60 and £120 are made, then a withdrawal of £40. 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 $3(x + 2y) - 2(3x - y) + 5(2x + y)$.

  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 $5x^2 - 3xy + 2x^2 + 7xy - 4y^2$.