PiXL Pre Public Examination, November 2016, 1H, Edexcel Style Mark Scheme

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1 PiXL Pre Public Examination, November 016, 1H, Edexcel Style Mark Scheme Qn Working Answer Mark Notes 1 for isolating term in t, e.g. 3t = w 11 or dividing all terms by 3. for oe = 57 11, 44 and 38 3 P1 for correct process to set up algebraic expressions for each number and set up an inequality. e.g. x + 4x + 4x - 6 > 57 or for a correct trial with a prime number. e.g. P1 for a correct process to solve the inequality. e.g. x > (57+6)/9 (=7) or for a correct trial with a prime number as 7 resulting in a sum of /(7-) (=16) P1 for strategy to start to solve the problem, e.g. 80/(7-) (=16) P1 for full process to solve the problem, e.g B1 Rounds appropriately using two of 5, or a x x for x +P() = 1 oe for 0.6 x oe

2 PiXL Pre Public Examination, November 016, 1H, Edexcel Style Mark Scheme Qn Working Answer Mark Notes 5 b B1 5 c 300x 1 B1 for 300x, x 300 oe 6a 48 4 P1 start to process e.g (=40) P1 40 /5 6b C1 e.g. she may drive a different distance and therefore her average speed could be different 7 More than C1 makes reference to different number of boys and girls C1 Completes reasoning e.g. there are more (boys) with 80% than (girls) with 70% or correct mean ( )/5 = 76

8a Venn Diagram Correct Diagram 3 P1 to begin to interpret given information, e.g. 3 overlapping labelled ovals with central region correct. P1 to extend interpretation of given information, e.g. 3 overlapped labelled ovals with at least 5 regions correct C1 for correct process to communicate given information, e.

3 8a Venn Diagram Correct Diagram 3 P1 to begin to interpret given information, e.g. 3 overlapping labelled ovals with central region correct. P1 to extend interpretation of given information, e.g. 3 overlapped labelled ovals with at least 5 regions correct C1 for correct process to communicate given information, e.g. 3 overlapped ovals with all regions correct, including outside. 8b 1 B1 ft from diagram 8c for probability with denominator of x x 3x = Reasoning to reach x 5 oe 3 Starts reasoning to find volume in terms of x. Gives inequality 6x or substitutes 5 and 6 into 6x 3 completes reasoning to show x 5

4 10 5 P1 using sides of length 4 P1 Method to find fraction or area of one unshaded triangle P1 Method to complete fraction or area for total unshaded region P1 Method to find total fraction or area for shaded region oe or a 1 1 B1 11b for two of cube root, square, reciprocal P1 for simplifying left hand side or right hand side correctly, e.g y-1 or P1 For equating the indices e.g. y-1 = 5

5 13a 4 3 for correct expansion to 3x 8 or multiplying both sides by 3x or dividing both sides by 4. for complete and correct method to isolate the x terms and the number terms (condone one arithmetic error in multiplying out the bracket). 13b ( y 6) ( y + 3) y 15 3 ( y + 3)( y 6) ( y + 3)( y 6) 14 3 for common denominator of (y+3)(y-6). ( y 6) y + 3 for oe ( y + 3)( y 6) ( y + 3)( y 6) (condone expanding bracket in denominator) 1 k for yα or y = or k = yx x x 5 15 (=375) oe 15 (x + 1)( x 5) x (x + 1) ( x 5) 3 for factorising the numerator correctly x for fully factorising the denominator correctly ( x 5) 5 + x for oe e.g. x x

6 16 n - n + 1 oe 3 for correct deduction from differences, e.g. nd difference of implies 1n or sight of 1,, 3 for sight of 1,, 3 linked with 1,, 3 for n - n + 1 oe 17 x > 4, x < -1 3 rearrange and factorise for critical values 4 and -1 found 18 a 4b 3 for expansion of brackets or 4 b = b for a or (-4b) 19 A) x + (x+1) = (x+) x + x + 1 = x + 4x + 4 x x 3 = 0 (x 3)(x + 1) = P1 for a process beginning to use Pythagoras, e.g. x + (x+1) = (x+) P1 for correct expansion and simplification leading to x + x + 1 = x + 4x + 4 P1 for rearranging and factorising x x 3 = 0 leading to (x - 3)(x + 1) = 0

7 0 Proof 5 1 3y 4x = 11 5 P1 process to start to solve the problem e.g. draw a diagram, find gradient of AB (0.5) P1 process to use the gradients e.g. find gradient of BC (-) P1 process to find coordinate of C (9) P1 process to find equation of AC Proof 4 for any two consecutive integers expressed algebraically e.g. n and n + 1 (dep) for the difference between the squares of two consecutive integers expressed algebraically e.g. (n + 1) - n for correct expansion and simplification of difference of squares, e.g. n + 1 C1 For showing the statement is correct, e.g. n + n + 1 = n + 1

Not drawn accurately

Q1. A trapezium has parallel sides of length (x + 1) cm and (x + 2) cm. The perpendicular distance between the parallel sides is x cm. The area of the trapezium is 10 cm 2. Not drawn accurately Find the