Algebra & Functions Practice

This page describes the electrical training ALLIANCE battery. If your local uses the GAN battery instead, its subtests and timings are different and none of the format below applies to you — see the GAN aptitude test guide.

What gets tested

• Linear equations. Solve for x. Multiple variables.
• Word problems. Translate English into equations.
• Formula substitution. Put given values into a stated formula.
• Equivalent expressions. Expand or factor and pick the match.
• Number series. Sequences built on an alternating rule — two operations taking turns.
• Variable relationships. What has to be true about one variable when the other changes.
• Tables and graphs. Match a table of x/y values to its equation.
• Ratios, percentages, and rates. Always show up.

Pacing

~84 seconds average per question. If a problem takes more than 90 seconds, mark a guess and move on. Coming back is allowed; running out of time isn't.

Sample questions

1. Linear equation

If 3x − 7 = 2x + 5, what is the value of x?

Add 7 to both sides: 3x = 2x + 12. Subtract 2x: x = 12. Six seconds.

2. Formula substitution

Using d = ½at², what is d when a = 6 and t = 4?
A) 24   B) 48   C) 96   D) 192

Square first: t² = 16. Then ½ × 6 = 3, and 3 × 16 = 48. Answer: B. A = 24 is 6 × 4 — dropping the ½ and forgetting to square. C = 96 is 6 × 16 — squaring correctly but dropping the ½. D = 192 is 2 × 6 × 16 — doubling where the formula halves.

3. Equivalent expression

Which expression is equivalent to (2x − 5)(x + 3)?
A) 2x² + x − 15   B) 2x² − x − 15   C) 2x² + 11x − 15   D) 2x² + x + 15

Multiply out: 2x·x = 2x², 2x·3 = 6x, −5·x = −5x, −5·3 = −15. Combine the middle terms: 6x − 5x = x. So 2x² + x − 15. Answer: A. B = −x in the middle, which is 5x − 6x — the two products swapped signs. C = 11x is 6x + 5x, treating −5 · x as positive. D keeps the correct middle term but makes the last term +15, which is −5 · 3 with the sign dropped.

4. Number series with an alternating rule

3, 7, 5, 9, 7, 11, ?
A) 8   B) 9   C) 13   D) 15

Two rules take turns: add 4, then subtract 2. 3 + 4 = 7, 7 − 2 = 5, 5 + 4 = 9, 9 − 2 = 7, 7 + 4 = 11. The next step is a subtraction: 11 − 2 = 9. Answer: B. D = 15 is 11 + 4, assuming the +4 repeats instead of alternating. C = 13 is 11 + 2, adding the 2 instead of subtracting it. A = 8 follows from neither rule.

5. Variable relationship

For a = ½b − 4, which statement is true?
A) When b < 8, a is negative   B) When b = 0, a is positive   C) When b > 8, a is negative   D) a is always greater than b

a is zero exactly when ½b = 4, that is b = 8. Below that, ½b is less than 4 and a is negative. Answer: A. B fails at b = 0, where a = −4. C reverses the inequality: at b = 10, a = 1, which is positive. D fails at b = 10 as well, where a = 1 and b = 10.

6. Table matched to an equation

Which equation describes this table?
x: 1, 2, 3, 4
y: 1, 4, 7, 10
A) y = 2x − 1   B) y = 3x − 2   C) y = 4x − 3   D) y = 3x + 2

y climbs by 3 each time x climbs by 1, so the coefficient is 3. At x = 1, 3(1) − 2 = 1, and the rest follow: 4, 7, 10. Answer: B. A gives 1, 3, 5, 7 — right at x = 1, wrong after. C gives 1, 5, 9, 13 — also right at x = 1 only, which is why checking one row is not enough. D gives 5, 8, 11, 14 — the right slope with the sign of the constant flipped.

What's in our practice bank

Every question type above is in the practice bank, in the same proportions the official sample suggests. The bank deliberately contains no exponent-rule or geometry questions: the electrical training ALLIANCE's published sample has neither, and drilling them would cost you time you need elsewhere.

Study plan

1. Take a free test today. Identify your weakest sub-topic.
2. Drill that sub-topic for 30 minutes a day.
3. Run a full timed simulator once a week.
4. Repeat until you're finishing the section inside the time limit with answers you'd defend.

Sources

• electrical training ALLIANCE — published test format and sample questions