IBEW math practice, worked step by step.

01Put values into a formula

If R = 3b² − 2c, b = −4 and c = 5, what is R?

Step by step

1. Write each value in its place, with the negative number in parentheses: R = 3(−4)² − 2(5).

2. Powers come first: (−4)² = (−4) × (−4) = 16.

3. Then multiply: 3 × 16 = 48 and 2 × 5 = 10.

4. Then subtract: 48 − 10 = 38. So R = 38.

Where it goes wrong

• −58

  The square was taken as −16. A negative number times itself is positive: (−4)² = 16.

• 134

  3 × (−4) was squared. The power belongs to b alone: square first, then multiply by 3.

• 58

  2c was added. The formula subtracts it: 48 − 10.

Check A square is never negative, so 3b² has to be positive. If your first term came out negative, a sign went wrong.

02Find the equal expression

Which expression is equal to 2(x + 3)(x − 5)?

Step by step

1. Multiply the two sets of parentheses first. Every term in the first meets every term in the second: x × x = x², x × (−5) = −5x, 3 × x = 3x and 3 × (−5) = −15.

2. Join the like terms: −5x + 3x = −2x. That gives x² − 2x − 15.

3. Now multiply every term by 2: 2x² − 4x − 30.

Where it goes wrong

• 2x² − 30

  Only the first terms and the last terms were multiplied. The two middle terms, −5x and 3x, are missing.

• 2x² − 4x − 15

  The 2 reached the first two terms and stopped. It multiplies all three.

• 2x² + 4x − 30

  The middle terms were joined with the wrong sign: −5x + 3x is −2x.

Check Try x = 1. The question gives 2 × 4 × (−4) = −32. The answer gives 2 − 4 − 30 = −32. A choice that gives any other number is out.

03Continue a pattern

40, 43, 37, 40, 34, 37. What comes next?

Step by step

1. Write the change under each gap: +3, −6, +3, −6, +3.

2. The two changes take turns. After +3 comes −6.

3. 37 − 6 = 31.

Where it goes wrong

• 40

  +3 was used twice in a row. The last change was +3, so −6 is due.

• 34

  This goes back by 3. The pattern moves by +3 and by −6, never by −3.

• 43

  This adds 6. In this pattern the 6 is taken away.

Check Test your rule on every gap in the list, not only on the first two.

04Say when a result is negative

For p = 12 − q/2, when is p negative?

Step by step

1. Find where p is zero: 12 − q/2 = 0, so q/2 = 12 and q = 24.

2. Test a value above it. q = 26 gives 12 − 13 = −1, which is negative.

3. Test a value below it. q = 20 gives 12 − 10 = 2, which is positive.

4. So p is negative when q is greater than 24.

Where it goes wrong

• q < 24

  The direction is turned around. q/2 is taken away, so a bigger q makes p smaller.

• q > 12

  12 is where p starts, not where its sign changes. At q = 14, p = 12 − 7 = 5.

• q > 6

  12 was halved. q/2 = 12 means q is twice 12.

On the test This kind comes as four statements, such as “When q is greater than 24, p is negative.” Try one number in each statement and see whether it holds.

05Read a rule from a table

The same linear rule continues. What is y when x = 10?

Step by step

1. See how far y moves for one step of x: 7 − 4 = 3, and again 10 − 7 = 3. Each step adds 3.

2. See where it starts: at x = 0, y = 4.

3. So the rule is y = 3x + 4.

4. At x = 10: 3 × 10 + 4 = 34.

Where it goes wrong

• 30

  This is 3 × 10 and nothing more. The table starts at 4, so the 4 still has to be added.

• 40

  The starting value 4 was used as the step. y moves 3 for each step, not 4.

• 37

  One step too far: 37 is y when x = 11.

Check Test the rule on a pair you were given. At x = 3: 3 × 3 + 4 = 13. It fits the table.

On the test The sample asks which choice shows the same relationship as the table, and the choices are a formula, a sentence, another table and a graph. Find the rule first, then look for it.