How to Take This Test

You have 15 minutes for 25 questions. That is the pace of the real Tier 1 Maths section, about 36 seconds a question, so you will need the quick methods as well as the full working: k2−2k^2 - 2 and k3−3kk^3 - 3k when x+1x=kx + \frac{1}{x} = k is given, the conjugate surd for 1x\frac{1}{x} (if x=a+bx = a + \sqrt{b} and a2−b=1a^2 - b = 1, then 1x=a−b\frac{1}{x} = a - \sqrt{b}), spotting three brackets that add up to zero so that a3+b3+c3=3abca^3 + b^3 + c^3 = 3abc, putting easy values such as a=2a = 2, b=1b = 1 to test the options, and the remainder theorem (for a divisor x−ax - a, just work out the value at x=ax = a). The questions jump from topic to topic, as they do in a real shift.

  • Run a 15-minute timer and do the test in one go, with your notes closed.
  • A right answer earns +2 and a wrong one costs −0.50. A skipped question scores 0.
  • If a question looks long, leave it for the end. Getting stuck on one high-power or two-equation question can cost you three quick ones.
  • Open the explanations only when the time is up.

Working out your score. Take 2 × (number right) − 0.5 × (number wrong); the most you can get is 50. For example, 21 right, 3 wrong and 1 skipped gives 42 − 1.5 = 40.5.

Score (out of 50) What it tells you
40 or more Your algebra is exam-ready. Redo the two PYQ Practice Sets against the clock a week before the exam.
30 to 39.5 Look at what the misses have in common. Wrong signs and wrong roots point to Reciprocal Forms (x + 1/x) and Surd Values; slow bracket work points to Three-Variable Identities and Special Conditions. Redo the quiz of the section with the most misses.
20 to 29.5 You know the methods but take too long over them. Practise the one-line formulas in Shortcuts & Speed Methods, mainly the ones for x+1xx + \frac{1}{x} and for three brackets that add to zero, then do Practice Sets 1 and 2 and take this test again after a few days.
Below 20 Go back to the five topic sections, Square and Cube Identities, Three-Variable Identities and Special Conditions, Reciprocal Forms (x + 1/x) and Surd Values, Polynomials and Quadratic Equations and Linear Equations and Maximum or Minimum Values, before you try more timed tests.

The tag on each question tells you where to look: square identities, cube identities, and factorisation and simplification are in Square and Cube Identities; three-variable identities, a+b+c=0a + b + c = 0 and special conditions are in Three-Variable Identities and Special Conditions; x+1xx + \frac{1}{x}, its special values and surd values are in Reciprocal Forms (x + 1/x) and Surd Values; polynomials and quadratic equations are in Polynomials and Quadratic Equations; and linear equations, word problems, and maximum and minimum are in Linear Equations and Maximum or Minimum Values.

More than 3 wrong usually means rushing, often a sign lost in a cube or a root taken the wrong way, so go a little slower next time. On guessing: a wrong answer costs only a quarter of what a right one earns, so in Tier 1 even a blind guess is very slightly in your favour on average, and once you can rule out one option a guess is clearly worth taking. Chapter 0 shows the numbers.