GCSE Higher June 2013 Non-Calculator

GCSE Higher June 2013 Non-Calculator

Good morning year 11

Once you’ve sat down we’ll begin


Before you start the questions, write all the formulas you need on to the formula sheet


Q1Popular question – the answers are there you just need to move the decimal point. Use an estimatea. (2 x 200=400) 331.705b. (300,000 ÷ 2 = 150,000) 179,300


Q2Find each separately15% - 10% = 24, 5% = 12 so 15% = 36¼ is 60 so ¾ is 180Total so far is 216 so 24 don’t knowOr ¾ is 75% plus 15% = 90% leaving 10% which is also 24


Q3 do as comes first2 4,7,83 5,8,8,3,0,7,34 4,5,1,4,1,2So you have 5 4,7,86 0,3,3,5,7,8,87 1,1,2,4,4,5

Don’t forget the key and the units


Q4 a) 6 + 3tb) 6x2 + 15xc) m2 + 13m + 30


Q5Factor tree which will give3 x 5 x 5 x 7Can be written with powers


Q6If the mean is 10 then they must add to 40The total is 33The other must be 7


Q7


Q7b

Note single transformation which isRotation of 180° with centre of (0,1)


Q8As an estimate use 20 litres and 300 daysSo number of bottles in a day = 40So total is 300 x 40 = 12 000Not asked but actual is 12152


Q9You can do counts of bothMatt: 50,100,150,200,250,300,350,400Dan: 80,160,240,320,400So they meet after 400 seconds Or find the LCM of 50,80 which is 400Answer is how many laps though which is 8 for matt and 5 for dan - RTFQ


Q10Perimeter is length around outside (yes Rose a snail trail!)Add to get 2(4 + 3x + x + 6) = 8x + 20So 8x + 20 = 32

8x = 12 x = 1.5


Q11 Ian went at 66 km/h which for 20 mins is 22 km so we can draw his line which is in red and is below Debbie’s line which means she is faster or find Debbie’s speed – she does 25 km in 20 mins so will do three times that in an hour so her speed is 75km/h

Remember it’s a * question


Q12 Make a table if you want but you only need three points for a straight line so

X = 0 y = 0 + 5 = 5X = 2 y = 1 + 5 = 6X = 4 y = 2 + 5 = 7


Q13 Draw a cricle of 5 cm from the point C and then a line on a bearing of 037 (bearings – clockwise from North)

The line goes inside the circle so the ship will get too close


Q14a

b 8x – 3 ≥ 6x + 48x – 6x ≥ 4 + 32x ≥ 7 x ≥ 3.5


Q15500 sheets will be 500 x 9 x 10-3 highWhich is 500 x 0.009 which is 4.5 cmAs the tray is only 4 cm deep then NO


Q16Reverse percentage ( what was it before)30% off means 70% in sale70% = £35010% = 350 ÷ 7 = 50100% = 50 x 10 = £500


Q17 Shape is a PRISM (formula sheet)Cross section is a trapezium(formula sheet)CSA = ½ (1.3 + 0.5) x 2 = 1.8Volume = CSA x width = 1.8 x 1 = 1.8In first 30 mins it drops 20 cm which is a cuboid so its volume would be 0.2 x 1 x 2 = 0.4 so it can pump 0.8 in an hour Time then is 1.8 ÷ 0.8 = 18 ÷ 8 = 2 ¼ hoursHow much more time = 2 ¼ - ½ which is 1 ¾ hours RTFQC


Q18 eliminating the x eqn 1 x 3 12x + 21y = 3 ③

eqn 2 x 4 12x + 40y = 60 ④Subtract ④-③ 19y = 57

y = 3Put y=3 in eqn 1 4x + 21 = 1

4x = -20 x = -5

Check with eqn 2 3 x -5 + 10x 3 = -15 + 30 = 15OR


Q18 eliminating the y eqn 1 x 10 40x + 70y = 10 ③

eqn 2 x 7 21x + 70y = 105 ④Subtract ③ - ④ 19x = -95

x = -5y = 3Put x=-5 in eqn 1 -20 + 7y = 1

7y = 21 y = 3

Check with eqn 2 3 x -5 + 10x 3 = -15 + 30 = 15


Q19 turn all into decimals

5-1 = 1/5 = 0.2 50 = 1

So order is -5, 5-1 , 0.5, 50


Q20 Easiest way is to find the area of the three triangles and subtract from rectangleMD=MC= 2x and AN is 3x

Δ NMD has sides of x and 2x so area is x²Δ BMC has sides of 4x and 2x so area is 4x²Δ ANB has sides of 3x and 4x so area is 6x²

\ Total white area is 11x²\ Grey area is area of square (16x²) minus

white which gives 5x²


Q21

Cumulative frequencies4,9,25,52,57,60

Median is 172 cmLQ= 166, UQ = 177, IQR = 11 cm


Q22 - similar shapes Lengths of AC and DF show the lengths are twice which means that areas will be four times bigger and volumes eight times

\Δ DEF will have an area of 4 x 10 = 40Prism Q’s length will be twice as long so 30cmThe volume will then be 30 x 40 (formula sheet) which gives 1200cmᶾ


Q23 simplify – the hint is to factorise the top and the bottom

Top 4(x + 5) already so (x + 5) must be in the bottom

Bottom x² + 2x – 15 = (x – 3)(x + 5)

So simplified is


Q24

class width 10 5 5 10 15 frequency d 1.2 3 2.6 1.8 0.2


Q24


Q25 multiply the (x + a)² + b = x² + 2ax + a² + bIf this is to be x² - 8x + 21 then matching give thatThe x’s must be the same so 2a = -8 so a = -4Numbers on end must match so a² + b = 21 so 16+b=21 so b=5

So x² - 8x + 21 = (x – 4)² + 5

This is lowest when bracket is 0 so x = 4 and it will b 0 + 5 = 5So M is (4,5)


Q26 to make £2.50 she could have (5 x 50p) or (3x50P and £1) or (50p and 2 x £1) and only the last is 3 coins

P( £1 then £1 then 50p) = 3/10 x 2/9 x 7/8 = 42/720P( £1 then 50p then £1) = 3/10 x 7/9 x 2/8 = 42/720P(50p then £1 then £1) = 7/10 x 3/9 x 2/8 = 42/720You can say all three the same

Overall P = 126/720 = 63/360=21/120=7/40


Q27

a. PS + SQ = PQ so SQ= PQ-PS which gives a - b

NQ + QR = NR

From the first part and the ratio NQ =2/5 of SQ

QR = PS = b

All together makes

NR = 2/5(a – b) + b

Which is 2/5 a + 3/5 b


Q28 From the graph

a) ¼ the way through the cycle so 90°

b) y = 2 Cos x just doubles all the y values


Grade boundaries (out of 100)

U 0 to 11 D 12 to 23 C 24 to 42 B 43 to 62 A 63 to 79 A* 80 or more

Documents

GCSE Higher June 2013 Non-Calculator