Foundation PP2 May 2016 Mark Scheme

Question 1

(a) / 65 / 1 / B1 cao
(b) / 127 / 1 / B1 cao
(c)
(d) / 30
22 / 1
1 / B1 cao
M1 for 140 – 118 (=22) or 10 + 10 + 2 (=22) or 11 × 2 (=22)
A1 cao
Total 5 marks

Question 2

Question 3

Question 4

Q

/ Working / Answer / Mark / Notes
(a) / 13 / 1 / B1
(b) / 3(2w + 5) / 1 / B1
(c) / x2 + 4x + 7x + 28 / 2 / M1 / for 3 correct terms out of 4 or for 4 correct terms ignoring signs
or for x2 + 11x + c for any non-zero value of c
or for ... + 11x + 28
x2 + 11x + 28 / A1
Total 4 marks

Question 5

(a) / / 1 / B1
(b) / 6 x 5 +1 / 31 / 2 / M1
A1
(c) / (61 – 1) ÷ 5 / 12 / 2 / M1brackets not necessary
A1
Total 5 marks

Question 6

(3 x 7.50) + (2 x 1.35) +1.20 (=26.4)
30 – “26.4” / 3.6(0) / 3 / M13 correct “products” listed
M1 dep on 1st M1
A1Accept 3.6
Total 3 marks

Question 7

(a) / 450 x 1.4(0) / 630 / 2 / M1
A1
(b) / 840 ÷ 1.4(0) / 600 / 2 / M1
A1
(c) / 100 ÷ 1.4(0) (=71.4...) / 71 / 2 / M1or 1 ÷ 1.4(0)
A1 awrt 71
Total 6 marks

Question 8

(a) / 6 / 1 / B1
(b) / 8 / 1 / B1
(c) / 0.5 x (11 + 7) x 10 / 90 / 2 / M1 M1 for (0.5 x 2 x 10) + (7 x 10) + (0.5 x 2 x 10)
A1
(d) / “90” x 12 / 1080 / 2 / M1 ftTheir area in (c) x 12
A1 ft
Total 6 marks

Question 9

(a) / x = 6 oe / 1 / B1Accept x – 6 =0
(b) / Shape P in correct position / 2 / B2Vertices at (8,2) (8,4) (9,4) (9,3) (11,4) & (11,2)
If not B2 then:

B1 for correct reflection in line x = k where k ≠ 6
or at least 2 vertices in correct position.

(c) / rotation
90° clockwise or −90°
(centre) (0,0) or O or origin / 3 / B1
B1 accept 270° or 270° anticlockwise.
B1condone lack of brackets around 0,0
Award no marks if multiple transformations.
Total 6 marks

Question 10

Question 11

(a) (i) / correct line / 1 / B1 / Parallel to y-axis through x = 2 / Lines must pass through at least two correct grid intersections.
(a) (ii) / correct line / 1 / B1 / Parallel to x-axis through y = 3
(a) (iii) / / correct line drawn from between x = 2 and x = 3 / 3 / B3 / For a correct line between x = 2 and x = 3.
If not B3, then B2 for:

at least 2 correct points plotted or
for a line passing through at least 2 correct points or
for a line drawn with positive gradient through (0,2) and clear intention to use a gradient of 3 (e.g. a line through (0,2) and (0.5, 5)

If not B2, then B1 for:

at least 2 correct points stated (may be in a table) or
for a line drawn with a positive gradient through (0 , 2) or
for a line with gradient 3.

(b) / 2 / M1 / ft for a point marked above theirif at least B1 scored in (a)
or
for a point to the right of
correct point / A1 / Point marked above and to the right of (not on lines).
Label P may be omitted if unambiguous.
SCB1 for the correct region identified by either shading in or shading out.
Total 7 marks

Question 12

Question 13

Question / Working / Answer / Mark / Notes
Working with all 12 boxes
12 × 15 (=180) or12 × 12 (=144) / M1 for correct total cost or correct total number of drinks (either may appear as part of another calculation)
/ M1 for revenue from all full price drinks sold
oe (=207) or
180 × 0.15 oe (=27) / M1 for total revenue or total profit
oror / M1 dep on M3
1.25 / 5 / A1 cao
Alternative – working with one box
15 ÷ 12 (=1.25) or / M1 for price of 1 drink or number of full price drinks
/ M1 for revenue from all full price drinks sold
(=17.25) / M1 for total revenue from one box
or / M1 dep on M3
1.25 / 5 / A1 cao
Total 5 marks

Question 14

Question / Working / Answer / Mark / Notes
1 can of soup weighs 0.8 ÷ 4 = 0.2 kg
5 jars of peppers weigh 4.1 - 3 ×0.2 kg = 3.5 kg
1 jar of peppers weigh 3.5 ÷ 5 / 0.7 / 4 / M1 for 0.8 ÷ 4 or 0.2 or 0.6
M1 for 4.1 - 3× "0.2" (=0.35)
M1 for "3.5" ÷ 5
A1
Total 4 marks

Question 15

Ques / Working / Answer / Mark / Notes
AngleDAB = 110 / 4 / B1 can be implied by angle DAX = angle BAX = 55o
Angle BAX =110 ÷ 2 (= 55) or
Angle DAX =110 ÷ 2 (= 55) or
Angle AXD = 55 / M1
Angle AXD = 55 or
Angle CBA = 180 – 110 (=70) or
Angle ADC = 180 – 110 (=70) / M1
125 / A1
Total 4 marks

Question 16

or 7.4 = xcos56 or
sin(90 56) = or 7.4 = xsin(90 56) / 3 / M1 / Correct equation for x. e.g.

( x = ) or / M1 / Correct expression for x. e.g.

13.2 / A1 / awrt 13.2
Total 3 marks

Question 17

(a) / 6 → 6.1 (inclusive) x 5 / 30→ 30.5 inclusive / 2 / M1
A1
(b) / 076 → 080 inclusive / 1 / B1 leading zero not necessary
(c) / 256 →260 inclusive / 1 / B1 ft from (b) if (b) is acute {180 + (b) oe}
(d) / 1 bearing line or 1 arc drawn correctly from A or B / Cross in correct position / 2 / M1
A1 dep on M1 (see overlay)
Total 6 marks

Question 18

(a)

11.5 or 1.96 seen

/ 2 / M1 / Also award for 5 or or answer of 5.9 or 5.87

5.8673(46939...)

/ A1 / for at least first 5 figures (ignore figures after the first five)

(b)

5.9

/ 1 / B1 / ft from (a) if non-trivial
Total 3 marks

Question 19

Ques / Working / Answer / Mark / Notes
a / or / 2 / M1 for a complete method
136 / A1
b / 20  14 (= 6) / 4 / M1
'6'2 + 82or 36 + 64 or 100 / M1 dep on previous M1
/ M1 dep on previous M1
10 / A1
Total 6 marks

Question 20

(19 x1)(=19) + (8x3)(=24) + (3x5)(=15) + (1x 9) (=9) / 67 / 3 / M2 for freqx all correct midpoint values correctly evaluated (condone omission of 4thinterval)
{do not have to see intention to add}
if not M2 then M1 for freqx consistent point in each interval
or M1 for 1 error in list of 19, 24, 15, (0), 9
A1isw if 67 calculated correctly. (2.16.. = M2A1)
Total 3 marks

Question 21

Ques / Working / Answer / Mark / Notes
a / x / –2 / –1 / 0 / 1 / 2 / 3 / 4
y / 9 / 3 / –1 / –3 / -3 / -1 / 3
y = x2 – 3x – 1. / 2 / M1 for at least 2 correct
M2 for all correct
2 / M1 for 2 points plotted correctly on graph
M2 for all points plotted correctly
Total 4 marks

Question 22