Mathematics AQA. Paper 1 (Non-Calculator) Higher Tier. Churchill Paper 1A Marking Guide. For

Size: px

Start display at page:

Download "Mathematics AQA. Paper 1 (Non-Calculator) Higher Tier. Churchill Paper 1A Marking Guide. For"

Allison Nichols
5 years ago
Views:

For AQA Mathematics Paper (Non-Calculator) Higher Tier Churchill Paper A Marking Guide Method marks (M) are awarded for a correct method which could lead to a correct answer Accuracy marks (A) are

1 For AQA Mathematics Paper (Non-Calculator) Higher Tier Churchill Paper A Marking Guide Method marks (M) are awarded for a correct method which could lead to a correct answer Accuracy marks (A) are awarded for a correct answer, having used a correct method, although this can be implied (B) marks are awarded independent of method Written by Shaun Armstrong This paper is part of a product for use in the single school or college that has purchased the licence. However, this paper is available as a sample that can be used without licence. 07 AHA Marks Page Churchill Maths Limited

2 Churchill Paper A Marking Guide AQA Higher Tier B Total = 35 60p = = = = B Total Next term = 3 5 = B Total 3 0 = 3 0 = 6 0 = B Total 5 (a) chain costs 80 0 = 9 bead costs =.50 spacer costs = 0.90 heart charm costs 0 30 = Total = 9 + (8.50) + ( 0.90) + = = 8.60 Profit on bracelet = =.30 Profit on 5 bracelets = 5.30 = = = Total 5 6 The angles in a triangle add up to 80º so x + 3x x 8 = 80 x + = 80 x = 68 x = x = 56, 3x + 0 = 6 and 5x 8 = 6 As angle ABC = angle ACB the triangle is isosceles The two sides opposite the equal angles are the same length Hence, AB = AC Total 07 AHA Marks Page Churchill Maths Limited

3 7 (a) = 7 6 = ways B Smallest frame sizes: no. of combinations = 7 3 = Largest 3 frame sizes: no. of combinations = = 6 Total no. of combinations = + 6 = 68 Total 3 8 (a) e.g. She can not be sure of this because 0 is a very small number of trials B No. of times red bead picked = = 7 No. of trials = 0 P(Faria picks a red bead) = 7 0 (c) No, she is wrong. We know the probability that one bead will be green is 6 0. However, we don't know the probability that the second will be green, given that the first was green, because we don't know how many beads are in the bag. Her answer assumes that the bag contains 0 beads so that after removing one green bead there are 9 beads left, 5 of which are green. B Total 5 9 p = q 7 p + 7 = q q = p + 7 p + 7 7p p + 7 p + 7 B Total 0 (a) Jeremy marks homework in 60 = 5 minutes Kira marks homework in 0 30 = minutes Liz marks homework in 6 minutes Therefore Kira is the quickest In 0 minutes Jeremy marks homeworks and Kira marks 5 homeworks Together they mark 9 homeworks in 0 minutes 36 9 = so they take 0 = 80 minutes.30 pm + 80 minutes = 5.30 pm + 0 minutes = 5.50 pm They finish marking at 5.50 pm Total 5 Last week = 00% This week = 0% = 0 So, 0% = 0 = 0 00% = 0 0 = 00 Leanne sent 00 s last week Total 07 AHA Marks Page 3 Churchill Maths Limited

4 Angle in semi-circle = 90º a = 80 ( ) a = B Total = = 0 0 = B Total (a) Number of orders (N) Cum. Freq. 0 < N 5 0 < N 50 0 < N < N < N < N < N B3 00 Cumulative Frequency Number of orders (c) (approx, from graph) B Total 6 07 AHA Marks Page Churchill Maths Limited

5 5 Radius of inner circle = 0 = 5 Area of inner circle = π 5 = 5π Radius of outer circle = distance from centre to corner of square: B r 5 cm 5 cm Pythagoras': r = = = 50 Area of outer circle = π 50 = 50π Shaded area = 50π 5π = 5π Therefore shaded area = area of inner circle Total 6 In a normal week, let Henrik earn h and Rob earn r h : r = 3 : so h = 3 r () B h + 0 : r + 0 = : 3 so h + 0 = (r + 0) 3 3(h + 0) = (r + 0) 3h + 60 = r + 80 () Sub () into () 3 3 r + 60 = r r + 60 = r + 80 r = 0 r = 0 so, h = 3 0 = 60 In the week before Christmas, Henrik earns h + 0 = 80 Total 7 (a) 8 seconds B 5 Velocity (m/s) Time (s) Acceleration = gradient of line = 8 6 = 6 = 3 m/s (c) Distance = area under graph = ( 6 8) + [ (8 + ) 6] + (8 ) + ( 6 ) M = = 76 m Total 6 07 AHA Marks Page 5 Churchill Maths Limited

6 8 = 83 = = 8 = B Total 9 5y = ( 0 7 ) + ( 0 6 ) 5y = ( 0 7 ) + ( ) 5y = y = y = Total 3 0 David is not correct e.g. When x = 6 : x = 6 = < x = 6 = making his statement incorrect Total [Any value in the interval 0 < x < can be used] (a) g(5) = = fg(5) = f() = 3 = Let g(x) = x + 3 = x + 3 = x = 7 Therefore g ( ) = 7 Total (a) B sin 0º sin 30º sin 5º sin 60º sin 90º 0 3 Area ABC = 6 8 sin 30º Area PQR = = = cm 3 8 sin 5º = = 6 cm Triangle ABC has the larger area Total 07 AHA Marks Page 6 Churchill Maths Limited

7 3 Sub P (a, a) into equation: (a) + a = 80 5a = 80 a = 6 a = [can't be as positive constant] P is (8, ) Gradient of OP = = Gradient of tangent = = ( ) Equation of tangent: y = x + c = ( 8) + c c = + 6 = 0 Hence, y = x + 0 y-intercept = 0 so R is (0, 0) Crosses x-axis when y = 0: 0 = x + 0 x = 0 x = 0 so Q is (0, 0) Area of OQR = 0 0 = 00 Total 5 (a) XY = XO + OY = OA + 3 OC = p + q BC = BO + OC = OB + OC = (3p + 3q) + 6q = 3p + 3q = 3 XY As BC is a multiple of XY they have the same direction so BC is parallel to XY Total 5 (a) x + x 3 = (x + ) 3 = (x + ) 7 (x + ) 7 = 0 (x + ) = 7 x + = ± 7 x = ± 7 B (c) y = ± y = ± (y ) = y y + = y y = 0 a = and b = Total 6 TOTAL FOR PAPER: 80 MARKS 07 AHA Marks Page 7 Churchill Maths Limited

Mathematics AQA. Paper 1 (Non-Calculator) Foundation Tier. Churchill Paper 1A Marking Guide. For

Mathematics AQA. Paper 1 (Non-Calculator) Foundation Tier. Churchill Paper 1A Marking Guide. For For AQA Mathematics Paper 1 (Non-Calculator) Foundation Tier Churchill Paper 1A Marking Guide Method marks (M) are awarded for a correct method which could lead to a correct answer Accuracy marks (A) are