How the Algebra and Functions test works
Algebra and Functions comes first on test day, before a short break and Reading Comprehension. It is a test of solving problems with algebra: 33 questions in 46 minutes, each with four answers and one right. There is no calculator, and you do not need to memorise any formulas, because every question that needs one gives it to you.
The official sample shows five kinds of question. You put given values into a formula and work out the result. You pick the expression that is equivalent to a given one. You find the next number in a pattern. You decide whether a formula comes out positive, negative or zero under stated conditions. And you read a table of values and choose the formula that links the two columns, or fill in a missing value.
Your score is the number you get right, with nothing taken off for a wrong answer. An unfinished test is scored on what you answered, and it cannot be finished another day.
A method for each kind of question
Most marks are lost to slips, not to hard algebra, so use a fixed routine for each kind:
- Formula: copy it down, then put each value in brackets where its letter was. Work brackets, then powers, then multiplying and dividing, then adding and subtracting.
- Equivalent expression: multiply out every bracket and collect like terms. If that stalls, put x = 2 into the original and into each option; only the right one gives the same number.
- Number pattern: write the gaps between neighbouring terms underneath. Try a constant gap, then a constant multiplier, then gaps that themselves grow, in that order.
- Positive or negative: try one easy number of each sign allowed by the conditions. A squared term is never negative, and a negative times a negative is positive.
- Table: see how much y changes when x goes up by one; that is the number in front of x. Then check the whole rule against every row, not just the first.
Worked examples
Formula: If A = 3b² − 2c, what is A when b = −2 and c = 5? A: 2. B: −22. C: 22. D: −2. Put the values in brackets: A = 3(−2)² − 2(5) = 3 × 4 − 10 = 2. The answer is A. B comes from squaring −2 as −4, and C from adding 10 instead of taking it away.
Table: x is 1, 2, 3 and 4, and y is 7, 11, 15 and 19. Which formula gives y? A: y = 3x + 4. B: y = 4x + 3. C: y = x + 6. D: y = 4x + 7. Each step of 1 in x adds 4 to y, so the rule starts with 4x, and 4 × 1 + 3 = 7 fixes the + 3. The answer is B. A and C both fit the first row and fail on the second, which is why every row needs checking.
Tips for the real test
- Practise fractions, negative numbers and squaring by hand for a week before the test. Without a calculator, these are where the time goes.
- Keep to about 80 seconds a question. Mark your best answer on anything slower and come back to it at the end.
- Substituting the options back into the question is often faster than solving, especially for equivalent expressions and tables.
- Write every step on scratch paper. A dropped minus sign is the most common wrong answer, and the options are built to catch it.
- Answer every question before time is called. A guess costs nothing.
Practise Algebra and Functions on CogniPrep
Our Algebra and Functions game is free. It gives 33 questions in 46 minutes, generated fresh each time in the five kinds the official sample shows: seven each of formulas, equivalent expressions and patterns, and six each of positive or negative and tables. The mix is ours, because a real form’s mix is not published. Every question has four answers and there is no calculator. You can move back and forth and change answers, and hand in from a review grid or let the clock hand in at 0:00. You get your number right and how you did on each kind of question, not a pass or a fail, because the qualifying score is set by each JATC.