Topics › KS3 › Algebra

Notation & simplifying

not-01 Present from here

Simplify $5x + 2x$

Option A: $7x^2$

Option B: $10x$

Option C: $7x$

Option D: $7$

Answer and misconceptions

Option A: $7x^2$ ✗
Multiplies the letters when adding like termsAdds 5 and 2 but treats x + x as x times x, giving x squared.

Option B: $10x$ ✗
Multiplies coefficients instead of addingCalculates 5 × 2 instead of 5 + 2 when collecting like terms.

Option C: $7x$ ✓ Correct

Option D: $7$ ✗
Drops the letter when collecting termsAdds the numbers and thinks the x terms cancel or disappear.
not-02 Present from here

Which is the same as $m \times m \times m$?

Option A: $3m$

Option B: $m^3$

Option C: $m + 3$

Option D: $3m^3$

Answer and misconceptions

Option A: $3m$ ✗
Treats repeated multiplication as repeated additionConfuses m × m × m with m + m + m = 3m.

Option B: $m^3$ ✓ Correct

Option C: $m + 3$ ✗
Adds the number of factors to the letterCounts three m's and writes "m and 3" as m + 3.

Option D: $3m^3$ ✗
Writes the count as coefficient and powerUses the 3 twice: once as a multiplier and once as an index.
not-03 Present from here

Simplify $3a + 4b - a + 2b$

Option A: $4a + 6b$

Option B: $8ab$

Option C: $3a + 6b$

Option D: $2a + 6b$

Answer and misconceptions

Option A: $4a + 6b$ ✗
Ignores the sign in front of a termAdds the a instead of subtracting it: 3a + a = 4a.

Option B: $8ab$ ✗
Combines unlike termsAdds all the numbers (3 + 4 − 1 + 2) and joins the letters into ab.

Option C: $3a + 6b$ ✗
Thinks a on its own means 0aTreats a as having no coefficient, so 3a − a stays 3a.

Option D: $2a + 6b$ ✓ Correct
not-04 Present from here

Simplify $2a \times 3b$

Option A: $5ab$

Option B: $23ab$

Option C: $6$

Option D: $6ab$

Answer and misconceptions

Option A: $5ab$ ✗
Adds coefficients when multiplying termsCalculates 2 + 3 instead of 2 × 3 for the number part.

Option B: $23ab$ ✗
Writes the numbers side by sideThinks writing 2 and 3 next to each other shows multiplication, giving 23.

Option C: $6$ ✗
Drops the letters when multiplying termsMultiplies 2 × 3 but thinks the letters disappear.

Option D: $6ab$ ✓ Correct
not-05 Present from here

Simplify $x^2 + x^2$

Option A: $2x^2$

Option B: $x^4$

Option C: $2x^4$

Option D: $4x$

Answer and misconceptions

Option A: $2x^2$ ✓ Correct

Option B: $x^4$ ✗
Adds the powers when adding termsApplies the multiplication index law to addition: x² + x² = x⁴.

Option C: $2x^4$ ✗
Adds both coefficients and powersCorrectly gets 2 lots but also adds the indices to get x⁴.

Option D: $4x$ ✗
Reads x squared as 2xThinks x² means 2 × x, so works out 2x + 2x = 4x.