Edexcel GCSE Mathematics (Linear) 1380 Higher Tier Paper 4 (Calculator) Time 1 hour 45 minutes

June 2010 Ref: N36762A

Before you start The original paper, without the answers, is at:

http://issuu.com/mathsgeek

120g raspberry jelly for 4 people, so: 120/4 = 30 for 1 person 6 x 30 = 180g for 6 people

How itâ€™s done

8 sponge fingers for 4 people, so 8/4 = 2 for 1 person 6 x 2 = 12 for 6 people

180 120 630 270

How itâ€™s done

420ml for 4 people, so 420/4 = 105 for 1 person 6 x 105 = 630 for 6 people 180g for 4 people, so 180/4 = 45 for 1 person 6 x 45 = 270 for 6 people

.

Upward slope – left to right

Positive

Draw a line of best fit – your answer should be between 6.6 and 7.6

7.1

620 x 1.25 = €775 775

€50 ÷ 1.25 = £40 Difference is £42 - £40 = £2

£2

-2

4

7

y = 3 x -2 + 4 = -6 + 4 = -2 y=3x0+4=0+4=4 y=3x1+4=3+4=7

. . . . .

1120 Angle ANL = 680 (alternate angles) So, angle y = 180 â€“ 68 = 1120 (angles in a straight line = 1800)

2 = 2 1.5 + 2.45 3.95

= 0.506329113 0.506329113

Go to the THIRD integer â€“ it is 5 or more, so increase the SECOND integer by 1 to 1

0.51

The third significant figure is the second 7 â€“ and the next integer is les than 5

Circumference = Ď€ x d = 3.142 x 12 = 37.704 37.7

x = 1 gives 11 x = 2 gives 28 x = 1.5 gives = 18.375 X = 1.6 gives 20.(096) x = 1.7 gives 21.(913) x = 1.8 gives 23.(832) x = 1.9 gives 25.(859) x = 1.85 gives 24.8(316..) x = 1.86 gives 25.(03..) x = 1.87 gives 25.2(3..) x = 1.88 gives 25.4(4..) x = 1.89 gives 25.6(5..)

1.9

84 x 100 = 8400 = 24 350 350 24

Total of probabilities MUST add up to 1, so: 1 – (0.15 + 0.30 + 0.35) = 1 – (0.80) = 0.20 0.2

Number of ribbons = 0.30 x 500 = 150 150

Base angles of an isosceles triangle are equal (AB = AC)

Rearrange x to the left and numbers to the right (of the = sign) 3x â€“ x = 10 + 30 2x = 40 x = 20

20

Area of triangle = ½ x base x perp. Height = ½ x 14 x 6 = 42 cm2

42

By Pythagoras: AB2 = AC2 + BC2 = 142 + 62 = 196 + 36 = 232 232 AB = AB = 15.23154621 15.23

The high edge (at the back of the shape (2cm high)

The narrow edge of the shape (1cm high)

20 X 3 60 X 5 100 X 12 140 X 7 180 X 3

60 300 1200 980 540

Numbers in blue – midpoints of n

Mean number of CDs sold = (60 + 300 + 1200 + 980 + 540) ÷ 30 = 3080 = 102.6666 = 102.7 102.7

n MUST be an INTEGER and BIGGER than -4 and less than or equal to 1, so -3, -2, -1, 0, 1

Re-arrange with x on the left and numbers on the right of the > 3x – x > 7 + 2 2x > 9 x > 4.5

-3, -2, -1, 0, 1

x > 4.5

Draw a line between B and C â€“ find the midpoint and join to A

Square both sides to give r2 = A 3 Multiply BOTH SIDES by 3 to give: 3r2 = A

3r2

1.55 x 104

Remember 10-3 is 1/1000

0.00248

24500 รท 0.000125 = 196000000 = 1.96 x 108

1.96 x 108

x2 – 5x – 2x + 10 x(x – 5) -2(x – 5) (x – 5)(x – 2) (x – 5)(x – 2)

(x – 5)(x – 2) = 0 X – 5 = 0 so x = 5 Or X – 2 = 0 so x = 2

5 2

Cos 580 = AB 16 AB = 16Cos 580 = 8.48

8.48

28.5

Upper bound = 147.5 (to the nearest 5 metres) Upper bound for perimeter = 147.5 + 28.5 + 147.5 + 28.5

352

= 352 metres

p9

p5 x p4 = p5+4 = p9

q3

q5 ÷ q2 = q5-2 = q3

2u

12tu6 ÷ 6tu5 = 2u6-5 = 2u

(9w y ) = 2 6

½

.......... 9w2y6

3wy3

= 3wy

3

x-2

x0

x1/2

x

x2

Ratio of surface area = 50:18 = 25:9 Ratio of length = 5:3 Ratio of volume = 125:27 Mass = 500 x 27 = 108 125 108

Each element has an equal chance of being selected (e.g. All the balls in a bag have an equal chance of being pulled out)

Number each of the stamps and then use the random number generator on a calculator 10 times

50 x 95 = 7.175 662 7.175

12 6

16 12 8 4

REMEMBER: in histograms the measure is the AREA of the bar â€“ not its height:

Area of circle of the whole circle centre 0 = π x r x r = πx8x8 Area of sector of circle = 40 x π x 64 = 1 x 3.142 x 64 = 360 9 22.343 (remember this is the area of the sector – the triangle OSP and the shaded area) The area of the triangle = ½ x 82 x sin 40 = 20.569 So, the area of the shaded segment = 22.343 – 20.569 = 1.774 = 1.77 (to 3 sig figs)

1.77

y = f(x – 5)

x=4

y=3