Topics › KS3 › Algebra

Substitution

sub-01 Present from here

Find the value of $3n$ when $n = 4$

Option A: $34$

Option B: $12$

Option C: $7$

Option D: $81$

Answer and misconceptions

Option A: $34$ ✗
Writes the digits side by sideReplaces n with 4 and reads 3n as the two-digit number 34.

Option B: $12$ ✓ Correct

Option C: $7$ ✗
Thinks 3n means 3 + nDoes not know that a number next to a letter means multiply.

Option D: $81$ ✗
Reads 3n as 3 to the power nCalculates 3⁴ = 81 instead of 3 × 4.
sub-02 Present from here

Find the value of $2a^2$ when $a = 3$

Option A: $18$

Option B: $36$

Option C: $12$

Option D: $11$

Answer and misconceptions

Option A: $18$ ✓ Correct

Option B: $36$ ✗
Squares the coefficient as wellWorks out (2 × 3)² = 36 instead of 2 × 3².

Option C: $12$ ✗
Thinks squaring means multiplying by 2Calculates a² as 3 × 2 = 6, then 2 × 6 = 12.

Option D: $11$ ✗
Reads 2a squared as 2 + a squaredAdds the coefficient instead of multiplying: 2 + 9 = 11.
sub-03 Present from here

Find the value of $a - b$ when $a = 2$ and $b = -5$

Option A: $-3$

Option B: $-7$

Option C: $7$

Option D: $3$

Answer and misconceptions

Option A: $-3$ ✗
Treats subtracting a negative as subtractingWorks out 2 − 5 = −3, ignoring that b is negative.

Option B: $-7$ ✗
Adds the numbers but keeps a negative signSees two minus signs, adds 2 and 5, then thinks the answer must be negative.

Option C: $7$ ✓ Correct

Option D: $3$ ✗
Subtracts the smaller number from the largerIgnores signs and order, calculating 5 − 2 = 3.
sub-04 Present from here

Use $v = u + at$ to find $v$ when $u = 5$, $a = 2$ and $t = 3$

Option A: $21$

Option B: $10$

Option C: $28$

Option D: $11$

Answer and misconceptions

Option A: $21$ ✗
Works left to right, ignoring order of operationsAdds 5 + 2 first, then multiplies by 3.

Option B: $10$ ✗
Thinks letters next to each other mean addReads at as a + t, so calculates 5 + 2 + 3.

Option C: $28$ ✗
Joins substituted digits into one numberReads at as the number 23, so calculates 5 + 23.

Option D: $11$ ✓ Correct
sub-05 Present from here

Find the value of $3x^2$ when $x = -2$

Option A: $-12$

Option B: $12$

Option C: $36$

Option D: $-6$

Answer and misconceptions

Option A: $-12$ ✗
Thinks a negative number squared is negativeWorks out (−2)² as −4, giving 3 × −4 = −12.

Option B: $12$ ✓ Correct

Option C: $36$ ✗
Multiplies by the coefficient before squaringCalculates (3 × −2)² = 36 instead of 3 × (−2)².

Option D: $-6$ ✗
Ignores the powerCalculates 3 × −2 and forgets to square.