Paper 2 - Marking Schedule

Question

Answer

Mark

Partial Marks

M1 for $2 \times 3^3$ and $2^3 \times 3^2$
or $2 \times 3 \times 3$ as final answer
or B1 for 2, 3, 6, 9 as final answer

$>$

M1 for $\dfrac{10 \times 60}{\sqrt[3]{1000}}$

$3\sqrt{3}$

M1 for $5\sqrt{3} - 2\sqrt{3}$

M1 for $\dfrac{1}{9}$ or $9$

$4\sqrt{3}$

M1 for $a^2 + (-4)^2 = 8^2$ or equivalent

8(a)

$600

M1 for $\dfrac{5}{10} \times 1200$ or equivalent

8(b)

$960

M1 for $1200 \div 1.25$ or equivalent

$x^3 - 2x^2 -15x$

M2 for $x^3 - 5x^2 + 3x^2 -15x$
or 2 correct terms.
B1 for $x^2-2x-15$ or $x^2-5x$

$\dfrac{12}{5}$ or 2.4

M1 for $y = \dfrac{k}{\sqrt{x-4}}$
M1 for $k=12$

11(a)

B1 for correct $y$-intercept
B1 for correct gradient

11(b)

$y=-2x+3$ or equivalent

B1 for -2
B1 for 3

M1 for open circle on -4
or closed circle on 3.

Correct triangle with arcs

B1 Correct triangle, no arcs

$15x^{\frac{11}{2}}$

B1 for $15x^k$ or $ax^{\frac{11}{2}}$

$a=-3$ and $b=5$

M1 for $1+a+b=-1$ or equivalent
M1 for $8+4a+2b=-2$ or equivalent
M1 for attempting to use elimination or substitution to solve
B1 for $a=-3$ or $b=5$

$y=3x-3$ or
$3x-y=-3$ or equivalent

B1 for midpoint $\left(-1,-6\right)$
M1 for gradient = $\dfrac{-5- -7}{-4-2}$ or equivalent
M1 for $-1 \div$ gradient or equivalent
M1 for substituting perp gradient and midpoint into $y=mx+c$
or $y-y_1 = m(x-x_1)$ or equivalent

17(a)

Correct shape through (0,1), (180,-1), and (360,1).

B1 Correct shape through (0,1) only.

17(b)

60, 300

M1 $x = \cos^{-1}\left(\dfrac{1}{2}\right)$ seen or implied
A1 for 60

M1 for $\sin x = \dfrac{2\sqrt{3}}{4}$
M1 for $x = \sin^{-1}\left(\dfrac{\sqrt{3}}{2}\right)$

19(a)

Triangle at (-3,-1), (0, -3), (-4, -4)

B1 for translation by $\begin{pmatrix} -7 \\ k \end{pmatrix}$ or $\begin{pmatrix} k \\ 2 \end{pmatrix}$

19(b)

Reflection in the line $y=x$

B1 for reflection
B1 for $y=x$

0.725

M1 for $7250 \div 10\,000$ or equivalent
B1 for 72.5

21(a)

$\dfrac{x(x+2x+1)}{2} = 0.125$ or equivalent

$x(x+2x+1) = 0.25$

Clears the fraction

$3x^2+x = 0.25$

Expands and simplifies bracket

[$3x^2 + x - 0.25$]
$12x^2+4x-1$

21(b)

$(2x+1)(6x-1)$

M1 for $6x(2x+1)-(2x+1)$
or $2x(6x-1)+(6x-1)$

21(c)

$x=-\frac{1}{2}$ or $x=\frac{1}{6}$

Must have both solutions

FT their positive solution

Exponential curve through (0,2) with asymptote $y=1$

B1 for correct asymptote or $y$-intercept

23(a)

Straight line with about half the points above it

23(b)

Negative

24(a)

24(b)(i)

$h^2 + 5^2 = 13^2 $

24(b)(ii)

$100\pi$

M1 for $\dfrac{1}{3}\pi(5)^2(12)$ or equivalent

25(a)

$\dfrac{9}{20}$

25(b)

$\dfrac{6}{90} = \dfrac{1}{15}$ or equivalent

M2 for $\dfrac{3}{10} \times \dfrac{2}{9}$
B1 for either $\dfrac{3}{10}$ or $\dfrac{2}{9} $

26(a)

26(b)

26(c)

M2 for $15 \times \sqrt[3]{\dfrac{54}{250}}$ or equivalent

M1 for use of opposite angles cyclic quad (seen or implied)
B1 for $q=20$

29(a)

29(b)

3.5

29(c)

3.5 or $\dfrac{15}{4}$

M1 for $1 \times 4 + 2 \times 4 + 3 \times 11 + 4 \times 8 + 5 \times 5 + 6 \times 8$ or equivalent

$23\,25$ or 11:25 pm

B1 for $03\,25$ or equivalent
or $12\,40$ or equivalent

31(a)

$x^2-4x-12$

B1 for any two correct terms

31(b)

7, -3

M1 for $x^2-4x-12=9$ or better
M1 for $(x-7)(x+3)$
B1 for 7 or 3

M1 for $24 \div \dfrac{3}{5}$ or $24 \times \dfrac{5}{3}$

Question 1 Marks: 1

Question 2 Marks: 2

for $2 \times 3^3$ and $2^3 \times 3^2$

or $2 \times 3 \times 3$ as final answer

or B1

for 2, 3, 6, 9 as final answer

Question 3 Marks: 1

$>$

Question 4 Marks: 2

for $\dfrac{10 \times 60}{\sqrt[3]{1000}}$

Question 5 Marks: 2

$3\sqrt{3}$

for $5\sqrt{3} - 2\sqrt{3}$

Question 6 Marks: 2

for $\dfrac{1}{9}$ or $9$

Question 7 Marks: 3

$4\sqrt{3}$

for $a^2 + (-4)^2 = 8^2$ or equivalent

Question 8(a) Marks: 2

$600

for $\dfrac{5}{10} \times 1200$ or equivalent

Question 8(b) Marks: 2

$960

for $1200 \div 1.25$ or equivalent

Question 9 Marks: 3

$x^3 - 2x^2 -15x$

for $x^3 - 5x^2 + 3x^2 -15x$

or 2 correct terms.

for $x^2-2x-15$ or $x^2-5x$

Question 10 Marks: 3

$\dfrac{12}{5}$ or 2.4

for $y = \dfrac{k}{\sqrt{x-4}}$

for $k=12$

Question 11(a) Marks: 2

for correct $y$-intercept

for correct gradient

Question 11(b) Marks: 2

$y=-2x+3$ or equivalent

for -2

for 3

Question 12 Marks: 2

for open circle on -4

or closed circle on 3.

Question 13 Marks: 2

Correct triangle with arcs

Correct triangle, no arcs

Question 14 Marks: 2

$15x^{\frac{11}{2}}$

for $15x^k$ or $ax^{\frac{11}{2}}$

Question 15 Marks: 5

$a=-3$ and $b=5$

for $1+a+b=-1$ or equivalent

for $8+4a+2b=-2$ or equivalent

for attempting to use elimination or substitution to solve

for $a=-3$ or $b=5$

Question 16 Marks: 5

$y=3x-3$ or
$3x-y=-3$ or equivalent

for midpoint $\left(-1,-6\right)$

for gradient = $\dfrac{-5- -7}{-4-2}$ or equivalent

for $-1 \div$ gradient or equivalent

for substituting perp gradient and midpoint into $y=mx+c$

or $y-y_1 = m(x-x_1)$ or equivalent

Question 17(a) Marks: 2

Correct shape through (0,1), (180,-1), and (360,1).

Correct shape through (0,1) only.

Question 17(b) Marks: 3

60, 300

$x = \cos^{-1}\left(\dfrac{1}{2}\right)$ seen or implied

for 60

Question 18 Marks: 3

for $\sin x = \dfrac{2\sqrt{3}}{4}$

for $x = \sin^{-1}\left(\dfrac{\sqrt{3}}{2}\right)$

Question 19(a) Marks: 2

Triangle at (-3,-1), (0, -3), (-4, -4)

for translation by $\begin{pmatrix} -7 \\ k \end{pmatrix}$ or $\begin{pmatrix} k \\ 2 \end{pmatrix}$

Question 19(b) Marks: 2

Reflection in the line $y=x$

for reflection

for $y=x$

Question 20 Marks: 2

0.725

for $7250 \div 10\,000$ or equivalent

for 72.5

Question 21(a) Marks: 4

$\dfrac{x(x+2x+1)}{2} = 0.125$ or equivalent

$x(x+2x+1) = 0.25$

Clears the fraction

$3x^2+x = 0.25$

Expands and simplifies bracket

[$3x^2 + x - 0.25$]

$12x^2+4x-1$

Question 21(b) Marks: 2

$(2x+1)(6x-1)$

for $6x(2x+1)-(2x+1)$

or $2x(6x-1)+(6x-1)$

Question 21(c) Marks: 2

$x=-\frac{1}{2}$ or $x=\frac{1}{6}$

Must have both solutions

FT their positive solution

Question 22 Marks: 2

Exponential curve through (0,2) with asymptote $y=1$

for correct asymptote or $y$-intercept

Question 23(a) Marks: 1

Straight line with about half the points above it

Question 23(b) Marks: 1

Negative

Question 24(a) Marks: 1

Question 24(b)(i) Marks: 1

$h^2 + 5^2 = 13^2 $

Question 24(b)(ii) Marks: 2

$100\pi$

for $\dfrac{1}{3}\pi(5)^2(12)$ or equivalent

Question 25(a) Marks: 1

$\dfrac{9}{20}$

Question 25(b) Marks: 3

$\dfrac{6}{90} = \dfrac{1}{15}$ or equivalent

for $\dfrac{3}{10} \times \dfrac{2}{9}$

for either $\dfrac{3}{10}$ or $\dfrac{2}{9} $

Question 26(a) Marks: 1

Question 26(b) Marks: 1

Question 26(c) Marks: 1

Question 27 Marks: 3

for $15 \times \sqrt[3]{\dfrac{54}{250}}$ or equivalent

Question 28 Marks: 3

for use of opposite angles cyclic quad (seen or implied)

for $q=20$

Question 29(a) Marks: 1

Question 29(b) Marks: 1

3.5

Question 29(c) Marks: 2

3.5 or $\dfrac{15}{4}$

for $1 \times 4 + 2 \times 4 + 3 \times 11 + 4 \times 8 + 5 \times 5 + 6 \times 8$ or equivalent

Question 30 Marks: 2

$23\,25$ or 11:25 pm

for $03\,25$ or equivalent

or $12\,40$ or equivalent

Question 31(a) Marks: 2

$x^2-4x-12$

for any two correct terms

Question 31(b) Marks: 4

7, -3

for $x^2-4x-12=9$ or better

for $(x-7)(x+3)$

for 7 or 3

Question 32 Marks: 2

for $24 \div \dfrac{3}{5}$ or $24 \times \dfrac{5}{3}$