M1 for a complete method with relative place value correct. Condone 1 multiplication error, addition not necessary.

Transcription

1 = M for a complete method with relative place value correct. Condone multiplication error, addition not necessary. M for a complete grid. Condone multiplication error, addition not necessary. M for sight of a complete partitioning method, condone multiplication error. Final addition not necessary. A for sight of digits 96(00...) A (dep on M, but not previous A) for correct placement of decimal point in their product. [SC:B for digits 96(00...) seen if M0 scored] =.96 MA Practice Papers: Set Regular (H) mark scheme Version. This publication may only be reproduced in accordance with Pearson Education Limited copyright policy. 06 Pearson Education Limited.

2 . 7.5 H < 7.5 B 7.5 B 7.5 MA practice test paper H (Set ) mark scheme: Version.

3 = M for or 480 seen 480 (6 0) = M (dep) for '480' (6 0) oe A cao M for 0 0 (=) or 0 0 (= ) or 8 0 M (dep) for 8 '' or 8 or 8 0 A cao oe or 0 8 oe 0 oe or SC : B for answer of 6 coming from oe 0 6 MA practice test paper H (Set ) mark scheme: Version.

4 , , , (a) (4,0) (, 0) (, ) (, ) (, ) (4, ) (b) Correct order M changing any one correctly or at least in the correct order (ignoring one) or reverse order A for correct order (accept any form) Correct position B for correct shape in correct position Rotation 80 (0,) (B for any incorrect translation of correct shape) B for rotation B for 80 (ignore direction) B for (0, ) B for enlargement B for scale factor B for (0, ) (NB: a combination of transformations gets B0) 6. (a) ( x + ) = ( x + ) x + B x + or ( x + ) x + (b) 6a 5 b B cao (B exactly out of terms correct in a product or a 5 b or 6a + b + ) MA practice test paper H (Set ) mark scheme: Version. 4

5 :80 9 : = 0:60:00 Not enough cement (but enough sand and enough gravel) 5: 5:5 5 =5:45: = 5 (< 80) Not enough cement (to make 80kg of concrete) No + reason 4 M for 80 ( + + 5) ( = 0) or multiples of : : 5 M for 0 or 0 or 5 0 or 0 seen or 60 seen or 00 seen A for (Cement =) 0, (Sand =) 60, (Gravel) = 00 C ft (provided both Ms awarded) for not enough cement oe M for ( 5 and) 5 and 5 5 or 9 5 or sight of the numbers 5, 45, 75 together. M for A for 5 (< 80) C ft (provided both Ms awarded) for not enough cement oe MA practice test paper H (Set ) mark scheme: Version. 5

6 M for (=50) M for (=0) M for A for 5 with supporting working M for (= 6) or (= 6 ) M for (=50) or (=00) or (= 00) M for 50 6 or 00 4 or 50 6 A for 5 with supporting working M for (=6) or (= ) 6 M for = M for A for 5 with supporting working MA practice test paper H (Set ) mark scheme: Version. 6

7 9. (a) 5 9 B for 5 9 oe (e.g. 5 to 9) (b) Frequency polygon through (, 8), (7, ), (, 9), (7, 4) and (, 8) B for a complete and correct polygon (ignore any histograms, any lines below a mark of or above a line of, but award B only if there is a line joining the first to last point) (B for one vertical or one horizontal plotting error for incorrect but consistent error in placing the midpoints horizontally (accept end points of intervals) for correct plotting of mid-interval values but not joined ) Plotting tolerance ± square 0. 5q + 5p = 4 + 8p 5q = 4 + 8p 5p 5q = 4 + p 4 + p q = 5 Points to be joined by lines (ruled or hand-drawn but not curves) 4 + p M for expansion of bracket or 5q + 5p or each term 5 q = 5 M for correct process to aq = bp + c, a, b and c numbers 4 + p A q = oe 5 [SC B for ambiguous answer e.g. 4 + p 5 ] MA practice test paper H (Set ) mark scheme: Version. 7

8 . (a) x² x + 5x 5 x² + x 5 M for four correct terms with or without signs, or out of no more than 4 terms with correct signs. The terms may be in an expression or in a table A cao (b) (x + 9)(x ) = 0 x = or x = 9 M for (x + 9)(x ) (M for (x ± 9)(x ± )) A cao a =, b = 8, c = 9 x = = 8 ± ± 00 (x + 4)² 6 9 (x + 4)² = 5 x = 4 ± 5 M for correct substitution in formula of, 8, ±9 M for reduction to A cao M for (x + 4)² M for 4 ± 5 A cao 8 ± 00 SC: if no marks score then award B for correct root, B for both correct roots. MA practice test paper H (Set ) mark scheme: Version. 8

9 . (a) t + < t + t t < t < t < 5.5 M t t < A t < 5.5 oe (B for t = 5.5 or t > 5.5 or 5.5 or t 5.5 or t 5.5 on the answer line) (b) 5 B for 5 or ft (a). 54 M for any correct use of distance, speed, time formulae, e.g (= 0.5) or 5 min 4. M = kl M 60 k = = L 8 Where L =, = M = (a) 5 (b) M (dep) for a complete method to find speed from G to H, e.g. 8 (5 5 ) 60 oe A cao M for 6 Correct black (cm high between 40 and 60) A k = 0 MαL M for 0 A for 540 cao M = kl M for correct use of frequency density to find a unit of area (for example cm =.5 or small square = 0.) or the area of one block. A cao B for correct black MA practice test paper H (Set ) mark scheme: Version. 9

10 6. (a) 7 B for 7 (accept 7 or ±7) (b) 5 B cao 7. Proof M for (x =) (...) 8. Vertices at ( 6, 7) (, 7) (, ) or 000x = (...), accept 000x = or 00x = (...), accept 00x = or 0x = (...),accept 0x = M for finding the difference between two correct, relevant recurring decimals for which the answer is a terminating decimal A (dep on M) for completing the proof by subtracting and cancelling to give a correct fraction e.g. = or = B fully correct (B correct orientation and correct size or two correct vertices) (B correct size or correct orientation or one correct vertex) MA practice test paper H (Set ) mark scheme: Version. 0

11 9. EE + CC + HH 76 5 M for use of 0 as denominator for nd probability 0 M for or or M for = M (dep on previous M for 4 0 A for Or Or 76 oe 0 EC+EH+CE+CH+HE +HC Or E,not E+ C,not C + H,not H M for use of 0 as denominator for nd probability M for 4 5 or 4 or 5 4 or 5 or 4 or M for (M for at least of these) A for 76 oe Or 0 M for use of 0 as denominator for nd probability M for or or M for (M for two of these added) A for 76 oe 0 MA practice test paper H (Set ) mark scheme: Version.

12 0. Gradient of AB = y = x + 4 M for attempt to find gradient of AB Gradient of perpendicular line = y = x + c = 5 + c c =. (a) Circle, centre O, radius (b) x =.6, y =.6 or x =.6, y =.6 M (dep) for attempt to find gradient of perpendicular line eg use of /m M(dep on M) for substitution of x = 5, y = A for y = x + oe M for a complete circle centre (0, 0) A for a correct circle within guidelines M for x + y = drawn M (dep) ft from (a) for attempt to find coordinates for any one point of intersection with a curve or circle A for x =.6, y =.6 and x =.6, y =.6 all ± 0. MA practice test paper H (Set ) mark scheme: Version.

13 . (a) M for 8 4 A for 0 cao 4 or 8 (b) M for ' ' 4 A for 75 cao MA practice test paper H (Set ) mark scheme: Version.

14 . DE = AE, and AE = EB (tangents from an external point are equal in length) so DE = EB Proof 4 B for DE = AE or AE = EB (can be implied by triangle AED is isosceles or triangle AEB is isosceles or indication on the diagram) AE = EC (given) tangents from an external point are equal in length Therefore AE = DE = EB = EC So DB = AC B for AE = DE = EB = EC If the diagonals are equal and bisect each other then the quadrilateral is a rectangle. If AE = DE = EB = EC then there are four isosceles triangles ADE, AEB, BEC, DEC in which the angles DAB, ABC, BCD, CDA are all the same. B for DB = AC, (dep on B) consideration of 4 isosceles triangles in ABCD C fully correct proof. Proof should be clearly laid out with technical language correct and fully correct reasons Since ABCD is a quadrilateral this makes all four angles 90, and ABCD must therefore be a rectangle. MA practice test paper H (Set ) mark scheme: Version. 4

15 National performance data taken from Results Plus Qu Spec Paper Session YYMM Qu Topic Max score Mean % all ALL A* A B C D E 544 4H 0806 Q0 Four operations NEW Bounds No data available MA0 H 06 Q Volume MA0 H Q0 Standard form MA0 F 06 Q6 Translations H 0 Q5cd Simplify expressions MA0 H Q Ratio MA0 H 4 Q4 Ratio H 006 Q08 Frequency diagrams H 09 Q6 Rearranging equations H 0 Q Solve quadratic equations H 0906 Q0 Solve inequalities MA0 H 506 Q4 Compound measures H 0906 Q Direct and inverse proportion H 08 Q Histograms and grouped frequency H 08 Q5 Index notation MA0 H 506 Q Recurring decimals MM H 06 Q Enlargement MA0 H 0 Q4 Selection with and without replacement MB0 H Q6 Equations of lines H 0 Q8 Graphs of circles H 0806 Q4 Congruence and similarity MB0 H 0 Q6 Proof No grade data available 80 MA practice test paper H (Set ) mark scheme: Version. 5