Course Support. Past Paper Questions by Topic. For Free.
13
| Answer | Mark | Mark scheme |
|---|---|---|
| \(n^3\) | B1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| 6 | M1 | for isolating \(k\) terms, eg \(5k = 26 + 4\) or \(5k = 30\) or \(k - \dfrac{4}{5} = \dfrac{26}{5}\) oe or \(26 + 4 \div 5\) |
| A1 | cao |
For M mark step must be carried out not just intention shown.
For example, if you see
\(5k - 4 = 26\)
\(+4 \qquad +4\)
award M1 for \(5k = r\) where \(r \gt 26\)
2 Simplify \(2 \times 3n\) (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(6n\) | B1 |
Allow \(n6\) but not \(6 \times n\) or \(6.n\)
1 Simplify \(e + e + e + e + e\) (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(5e\) | B1 | cao |
11
| Answer | Mark | Mark scheme |
|---|---|---|
| \(6xy\) | B1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| \(5d - 3e\) | M1 | for \(5d\) or \(-3e\) |
| A1 | for \(5d - 3e\) |
An answer of \(5d + -3e\) scores M1 A0
14 Match each description to the correct expression.
One has been done for you. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| All 4 correct matches \(2n\) \(n^2\) \(\dfrac{n}{2}\) \(n - 2\) | B4 | B1 for each correct match |
Accept any unambiguous indication
More than one line from a box on the left is incorrect for that box
11 Here are two expressions, A and B.
| A | B |
|---|---|
| \(7(x - 2) + 4x + 6\) | \(5(3x + 2) - 4x - 18\) |
Show that A and B are equivalent. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: expands brackets and simplifies | ||
| \(7x - 14\) or \(15x + 10\) | M1 | |
| \(7x - 14\ (+ 4x + 6)\) and \(11x - 8\) or \(15x + 10\ (- 4x - 18)\) and \(11x - 8\) | M1dep | A or B fully correct |
| \(7x - 14\ (+ 4x + 6)\) and \(11x - 8\) and \(15x + 10\ (- 4x - 18)\) and \(11x - 8\) | A1 | A and B fully correct SC1 \(11x - 8\) for one or both of A and B with no working seen |
| Alternative method 2: shows the \(x\) terms and constant terms are the same | ||
| Any one of \(7x + 4x = 11x\) or \(15x - 4x = 11x\) or \(-14 + 6 = -8\) or \(10 - 18 = -8\) | M1 | |
| Any two of \(7x + 4x = 11x\) or \(15x - 4x = 11x\) or \(-14 + 6 = -8\) or \(10 - 18 = -8\) | M1dep | |
| \(7x + 4x = 11x\) and \(15x - 4x = 11x\) and \(-14 + 6 = -8\) and \(10 - 18 = -8\) | A1 | SC1 \(11x - 8\) for one or both of A and B with no working seen |
| M1 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| Use the scheme that favours the student | |
| Alt 2: \(7x + 4x = 11x\) and \(-14 + 6 = -8\) | M1M1 |
| Alt 2: \(7x + 4x = 11x\) and \(15x - 4x = 11x\) | M1M1 |
| Alt 2: \(11x\) only | M0 |
| Alt 2: \(-8\) only | M0 |
| Do not ignore subsequent incorrect work such as \(11x - 8 = 3\), which may be awarded up to M2 if working shown | |
| Substituting values into the two expressions | M0 |
4
| Answer | Mark | Comments |
|---|---|---|
| \(ab\) or \(ba\) | B1 |
Allow upper case A and/or B
Do not accept \(a \times b\) or \(b \times a\) or \(a^b\) or \(b^a\)
| Answer | Mark | Comments |
|---|---|---|
| \(3c\) | B1 |
Do not accept \(c3\) or \(3 \times c\) or \(c \times 3\)
| Answer | Mark | Comments |
|---|---|---|
| \(p^3\) | B1 |
Do not accept \(p3\)
| Answer | Mark | Comments |
|---|---|---|
| 1 | B1 |
Do not accept \(\dfrac{1}{1}\)
25 Here are three terms.
\(xy\) \(x^2\) \(5y^2\)
Alec multiplies two of these terms.
Work out the three possible fully simplified answers. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(x^3y\) or \(yx^3\) | B1 | |
| \(5xy^3\) or \(5y^3x\) | B1 | |
| \(5x^2y^2\) or \(5y^2x^2\) | B1 |
Mark the answer lines unless blank
Do not allow transcription errors
17 Match the algebra to the correct description.
One has been done for you. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| All correct | B3 | B2 for 2 or 3 correct B1 for 1 correct |
Two or more lines from one box on the left is choice so incorrect for that box
Accept any unambiguous indication
10
| Answer | Mark | Comments |
|---|---|---|
| \(6m + 11\) or \(11 + 6m\) | B2 | B1 \(6m\) or \((+)11\) |
| Do not ignore further work for B2 eg \(6m + 11 = 17m\) eg \(6m + 3 = 9m\) | B1 B1 |
| Answer | Mark | Comments |
|---|---|---|
| \(3cd\) or \(3dc\) | B2 | B1 3 or \(cd\) or \(dc\) |
| \(cd3\) | B1 |
| Use of multiplication signs is max B1 eg \(3 \times cd\) eg \(c \times d\) | B1 B0 |
| \(6\dfrac{1}{2}cd\) | B1 |
| \(\dfrac{1}{2}c6d\) | B0 |
| \(\dfrac{1}{2}c3d\) | B0 |
2 Simplify fully \(\quad y + y + y\) [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| \(3y\) | B1 |
| \(3 \times y\) or \(y \times 3\) | B0 |
| \(y3\) | B0 |
15 Complete these statements. [3 marks]
\(\ldots\ldots\ldots\) \(+\; 5x \;=\; 9x\)
\(y \;\times\) \(\ldots\ldots\ldots\) \(=\; y^2\)
\(\ldots\ldots\ldots\) \(-\; 2t \;=\; t\)
| Answer | Mark | Comments |
|---|---|---|
| \(4x\) | B1 | oe |
| \(y\) | B1 | oe |
| \(3t\) | B1 | oe |
2
| Answer | Mark | Comments |
|---|---|---|
| \(5x\) | B1 |
| \(5 \times x\) or \(x \times 5\) or \(x5\) | B0 |
| Answer | Mark | Comments |
|---|---|---|
| \(10w\) | B1 |
| \(10 \times w\) or \(w \times 10\) or \(w10\) | B0 |
| Answer | Mark | Comments |
|---|---|---|
| 2 | B1 |
| \(\dfrac{2}{1}\) or \(2 \div 1\) | B0 |
| Answer | Mark | Comments |
|---|---|---|
| \(y^3\) | B1 |
| \(y^2 \times y\) or \(y \times y^2\) | B0 |
28 Here is the term-to-term rule for a sequence.
| Double the previous term and add 3 |
The first three terms of the sequence are \(\quad a + 1 \quad 2a + 5 \quad 4a + 13\)
Show that the sum of the first four terms is a multiple of 3 [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(8a + 29\) | B1 | oe eg \(2(4a + 13) + 3\) |
| \(15a + 48\) | B1ft | correct or ft B0 only their \(8a + 29\) must be in the form \(na + c\) where \(n \ne 0\) and \(c \ne 0\) implied by \(3(5a + 16)\) |
| \(3(5a + 16)\) or \(15 = 5 \times 3\) and \(48 = 16 \times 3\) | B1 | oe eg \(5a + 16\) so it divides by 3 |
| Ignore use of substitution as an attempt to show divisibility | |
| Ignore further non-contradictory statements | |
| Further simplification eg \(15a + 48 = 63\) which is \(21 \times 3\) | B1B1B0 |
| For the 1st B1 accept \(8a + 29\) embedded in a calculation for the sum of the first four terms eg \(a + 1 + 2a + 5 + 4a + 13 + 8a + 29\) | |
| For the 2nd B1 accept \(15a + 48\) embedded in a calculation to show divisibility eg \(\dfrac{15a + 48}{3} = 5a + 16\) | |
| For the 3rd B1 accept 15 is a multiple of 3 and 48 is a multiple of 3 | |
| \(8a + 29\) \(a + 2a + 4a + 8a = 15a \quad 1 + 5 + 13 + 29 = 48\) but \(15a + 48\) not seen \(15 = 5 \times 3\) and \(48 = 16 \times 3\) | B1 B0 B1 |
11
| Answer | Mark | Comments |
|---|---|---|
| \(10x + 4y - 6\) or \(2(5x + 2y - 3)\) | B3 | any order B2 two terms correct B1 one term correct |
| B1 may be awarded for correct work, with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| Further incorrect work after a B3 response is B2 eg1 \(10x + 4y - 6 = 8xy\) eg2 \(10x + 4y - 6\) and \(10x = -10\) eg3 \(10x + 4y - 6\) and \(2(5x + 2y - 6)\) | B2 |
| Further incorrect work after a B2 or B1 response is B1 eg1 \(10x + 4y + 6 = 20xy\) eg2 \(10x - 4y + 6\) and \(10x = -2\) eg3 \(10x + 4y + 6\) and \(2(5x + 2y + 6)\) | B1 |
| \(10x + 4y + 6\) and \(2(5x + 2y + 3)\) | B2 |
| \(10x\) and \(4y\) and \(-6\) | B2 |
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{a^2}{2}\) | B1 | accept any indication |
5
| Answer | Mark | Comments |
|---|---|---|
| \(a^3 + 2b\) | B2 | B1 for \(a^3\) (+) or (+) \(2b\) |
| Do not accept \(2 \times b\) or \(b2\) for \(2b\) | |
| Do not accept \({}^3a\) for \(a^3\) | |
| Do not accept further working for B2 eg \(a^3 + 2b = a^32b\) | B1 |
| Do not accept further working for B1 eg \(3a + 2b = 5ab \quad\) or \(\quad a^3 \quad b^2 = a^3b^2\) | B0 |
| \(a^3 + b^2\) | B1 |
| \(3a + 2b\) | B1 |
| \(a^3 \quad 2b\) | B1 |
| \(a^3 \quad 2b = a^32b\) | B1 |
| \(a^3 \times 2b\) or \(a^32b\) without working for B1 | B0 |
| \(a^3 \times b^2\) or \(a^3b^2\) | B0 |
| \(3a \times 2b\) | B0 |
| \(3a - 2b\) | B0 |
| Answer | Mark | Comments |
|---|---|---|
| \(5x\) (+) 15 | B1 | Implied by correct answer |
| \(4x + 17\) | B2ft | B2ft their \(5x + 15\) in the form \(5x + b\) or \(ax + 15\), both their terms with correct ft in final answer B1ft \(4x\) or (+)17 B1ft their \(5x + 15\) in the form \(5x + b\) or \(ax + 15\), one of their terms with correct ft in final answer |
| ft \(4x\) or (+)17 or must use \(5x + b - x + 2\) or \(ax + 15 - x + 2\) | |
| \(4x + 17\) with no expansion seen | B1B2 |
| Ignore further working with an attempt to solve after their \(4x + 17\) eg \(4x + 17 = 0\) followed by \(x = -4.25\) | B1B2 |
| Do not ignore further working with an attempt to simplify after their \(4x + 17\) eg \(4x + 17\) followed by \(21x\) | B1B1 |
| \(5x + 15 - x + 2\) followed by \(4x + 15 = -2\) | B1B1 |
| \(5x + 3\) followed by \(4x + 5\) also \(5x - 15\) followed by \(4x - 13\) | B0B2ft |
| Ignore further working after \(5x + 15\) for first B1 eg \(5x + 15\) followed by \(20x\) and \(20x - x + 2\) followed by \(19x + 2\) | B1B0 |
| \(5x \quad 15\) | B1 |
| \(4x + k,\ k \ne 17\), with no expansion seen | B0B1ft |
| \(kx + 17,\ k \ne 4\), with no expansion seen | B0B1ft |
| \(5x + 15 - 5x + 10\) followed by 25 | B1B0 |
| \(5x + 3\) followed by \(4x + 1\) | B0B1ft |
| \(5x^2 + 15\) followed by \(5x^2 - x + 17\) | B0B1ft |
| \(5x + 3\) followed by \(4x + 1\) followed by \(5x\) | B0B0ft |
| \(5x + 3\) followed by \(6x + 1\) | B0B0ft |
| \(5x^2 + 3\) followed by \(5x^2 - x + 5\) | B0B0ft |
2 Circle the expression that is four times bigger than \(n\). [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| \(4n\) | B1 |
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