Expressions and equations test

Read a letter as a number, tidy the expression, then solve it — the whole move from arithmetic to algebra on one paper.

Expressions and equations test

The answer key prints on a separate page.

What's on this test

The jump into algebra is one idea repeated: a letter stands for a number you do not know yet. Evaluating comes first because it makes that concrete — put 4 where the x is and the expression is just arithmetic again. The reliable error appears the moment nothing is substituted: 3x read as 3 + x, or 3x + 2 collapsed to 5x. Those are not careless; they are a child treating letters like the digits they replaced.

How the paper is put together

Like terms and the distributive property are the two rules that keep the letters honest, and two-step equations are where they get used in reverse. 3x + 2 and 5x are different quantities until x is known, and 2(x + 4) is 2x + 8, not 2x + 4 — the second term is the one that gets left behind. A child fluent in the first three sections and stuck in the last has not met an equation problem; they have met undoing done in the wrong order.

Math test

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1. Evaluate expressionsPut the number in place of the letter, then work each one out.6 questions

1a = 2, b = 24a + b =

2x = 114x − 20 =

3x = 122x − 12 =

4x = 68x − 3 =

5a = 6, b = 72a + b =

6x = 39x − 11 =

2. Collect like termsCollect the like terms. Write the x-term and the number.5 questions

75x + 6x + 6x

86x + 10 − 5x − 2x

96 + 4x + 3 + 6xx

109x + 15 − 5x − 3x

115 + 7x + 10 + 5xx

3. Multiply out bracketsMultiply out each bracket. Write the x-term and the number.5 questions

128(4x + 2)x

137(3 + 2x)x

142(3x − 2)x

155(x − 10)x

163(4 + 7x)x

4. Solving equationsSolve each equation for x.5 questions

1711x + 10 = 21

1810x − 8 = 42

193x + 22 = 25

203x − 24 = 24

217x − 28 = 7

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Answer key

Evaluate expressions

1. 4a + b (a = 2, b = 2) → 102. 4x − 20 (x = 11) → 243. 2x − 12 (x = 12) → 124. 8x − 3 (x = 6) → 455. 2a + b (a = 6, b = 7) → 196. 9x − 11 (x = 3) → 16

Collect like terms

7. 5x + 6x + 6 → 11x + 68. 6x + 10 − 5x − 2 → 1x + 89. 6 + 4x + 3 + 6x → 10x + 910. 9x + 15 − 5x − 3 → 4x + 1211. 5 + 7x + 10 + 5x → 12x + 15

Multiply out brackets

12. 8(4x + 2) → 32x + 1613. 7(3 + 2x) → 14x + 2114. 2(3x − 2) → 6x − 415. 5(x − 10) → 5x − 5016. 3(4 + 7x) → 21x + 12

Solving equations

17. 11x + 10 = 21 → x = 118. 10x − 8 = 42 → x = 519. 3x + 22 = 25 → x = 120. 3x − 24 = 24 → x = 1621. 7x − 28 = 7 → x = 5

Expressions and equations test

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