Practice Maths

Topic Review — Further Algebra

Mixed Practice — L46 – L48

This review covers substitution and formulas, rearranging formulas, and mixed algebraic problems. Try each question before checking your answers.

Review Questions

  1. Substitution fluency. Fluency

    1. Evaluate 5x − 2y when x = 4 and y = −3.
    2. Find A using A = ½bh when b = 14 and h = 9.
    3. Find v using v = u + at when u = 6, a = 4 and t = 5.
    4. Find I using I = Prt ÷ 100 when P = 3000, r = 4 and t = 2.
    5. Evaluate 3a² − 2a + 5 when a = −3.
    6. Find V using V = πr²h when r = 3 and h = 10. Give exact and decimal (1 d.p.) answers.

  2. Rearranging formulas. Fluency

    1. Make w the subject of P = 2(l + w).
    2. Make a the subject of v = u + at.
    3. Make r the subject of C = 2πr.
    4. Make r the subject of A = πr².
    5. Make x the subject of y = 4x − 3.
    6. Make h the subject of A = ½bh.

  3. Mixed algebra — identify and apply the correct technique. Understanding

    1. Expand and simplify: (x + 5)(x − 3) − 2(x + 4)
    2. Factorise fully: 3x² − 27
    3. Solve: 2x² − 8x = 0
    4. Rearrange F = 9C⁄5 + 32 to make C the subject.
    5. Find two consecutive integers whose product is 182. (Form and solve a quadratic.)
    6. Simplify (2x − 1)² and verify by substituting x = 3 into both sides.

  4. Applying formulas in context. Understanding

    1. A triangle has area 42 cm² and base 12 cm. Use A = ½bh to find the height.
    2. A car accelerates from rest (u = 0) to 30 m/s over 10 seconds. Use v = u + at to find the acceleration.
    3. A sphere has volume 905 cm³. Use V = ¾πr³ to find r (round to 1 d.p.).
    4. $2500 is invested at simple interest. After 4 years, the interest earned is $400. Use I = Prt ÷ 100 to find the annual interest rate.

  5. Problem solving. Problem Solving

    1. A rectangular swimming pool has a length 4 m more than its width. The area is 96 m².
      1. Let the width be w. Write an expression for the length.
      2. Form a quadratic equation and solve for w.
      3. Find the perimeter of the pool.
    2. A ball is kicked and follows the path h = −4t² + 16t where h is height (m) and t is time (s).
      1. Factorise the expression.
      2. When does the ball land?
      3. What is the maximum height and when does it occur?
    3. The formula for the area of a trapezium is A = ½(a + b)h. A trapezium has area 55 cm², one parallel side of 8 cm and height 5 cm. Find the length of the other parallel side.
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