Core Mathematics 1 Tracking Test - STELLA'S CLASSROOM
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30727658636000Tracking Test 1- Version A Time allowed: 60 minutes. 50 marksAttempt ALL questions. Show working-out clearly and triple check for errors1 Write 4x+x4x2 in the form axn+bxm (3) 2Find the set of values for k, for which 2x2+4kx-5k=0 has no real roots. Give your answer in set notation. (2) 3 Solve the equation 5-x4-3x-26=0. (3) 4 (a) Express y=x2+10x-4 in the form y=(x+a)2+b, where a and b are constants. (2) (b) Hence or otherwise, sketch the curve with equation y = x2+10x-4, giving the coordinates of : (i) The point where it meets the y-axis. (ii) The coordinates of its minimum point. (3)5 (a) A line l passes through the points A (5, -1) and B (7, 3). Find the equation of the line in the form ax + by + c = 0 where a, b, and c are integers. (4) (b) A second line is perpendicular to l and passes through the origin. Find the coordinates of the point where the two lines meet. (5) 6 A triangle has vertices (0, 3), (0, p) and (2, -5) where p > 3. Given that the area of the triangle is 5, find the value of p. (3)PLEASE TURN OVER7 Complete the square to solve 2x2-6x+3=0, giving your solutions in the form p±rq (4)8 Sketch the following curves, clearly showing the x and y intercepts (if they exist) and stating the equations of any asymptotes. (a) y=1x-3 (b) y=x-23 (6) 9 The circle C has equation x2+y2-12x+8y+16=0 (a) Find the centre and radius of C. (3) (b) Show that the line y-2x=0 does not touch the circle, C. (4) 10 A ball is thrown vertically downwards from the top of a tower with speed 6 ms-1. The ball strikes the ground with speed 25 ms-1. Find the time the ball takes to move from the top of the tower to the ground. (3)11 In a student group, a record was kept of the number of days of absence each student had over one particular term. The results are shown in the table:Number of Days Absent01234Frequency12201075 Use your calculator to work out the mean and the standard deviation of the number of days absent. (2) 12A person throws a ball in a sports hall. The height of the ball, h m, can be modelled in relation to the horizontal distance from the point it was thrown from by the quadratic equation: h=-310x2+52x+32 The hall has a sloping ceiling which can be modelled with equation h=152-15x. Determine whether the model predicts that the ball will hit the ceiling. (3)5772153429000 Total Marks for Test: (50) MarksAS Tracking Test 1 Mark Scheme A1x-1+14x-32 M1 for splitting into two separate fractions A1 for first term correctA1 for second term correct2-52 <k< 0k: -52 <k< 0)B1 caoB1 cao in set notation365-x-43x-2=0 30-6x-12x+8=0 38-18x=0 18x=38x=199M1 for common denominator/multiplying equation by denominatorsM1 for correct linear equationA1 cao4(a) y= x+52-29 (b) -444519812000 A (0,-4) B (-5,-29) , (a) M1 for (x ± 5)2 minus 52 seen. 5 could be 102 A1 cao (b) B1ft Shape: Quadratic with TP in correct quadrant (follow through their completed square)B1 for A B1ft for B (follow through from their completed square)5(a) m=3--17-5=2 y+1=2(x-5) 2x-y-11=0 (b) Gradient = -12 y-0=-12(x-0)y=-12x2x--12x-11=0 4x+x-22=0 5x=22 ∴x=225, y=-115 (a) B1 for m=2M1A1 for substituting into construction formulaA1 for k(2x-y-11)=0(b) M1 ft for perpendicular gradient (follow through their gradient)A1 for correct equationM1 ft for substituting into their part (a)A1, A1 for (x,y)612p-32=5 p-3=5 p=8 M1 for ?(b)(h)=5 where b and h are vaguely sensible. Must say = 5 for this mark.A1 for (p-3) as the base and 2 as the height (M0A0 if it doesn’t say =5)A1 for p=872x-322-32=0 x=32±123 M1 for bracket squared minus something squared. A1 for correct completed square OK if y = 2x-322-32 seenM1 for taking to other side and square rooting A1 cao8(a)(b)(a) B1 ShapeB1 for both x = 0 and y = -3B1 (1/3, 0)(b) B1 ShapeB1 (0, -8)B1 (2, 0)9(a) x2-12x+y2+8y+16=0(x-6)2-36+y+44-16+16=0(x-6)2+y+44=36Centre (6, -4), radius = 6(b) y=2xx2+(2x)2-12x + 8 (2x) +16 =0x2+4x2-12x + 16x +16 =05x2+4x +16 =0b2-4ac=(4)2-4(5)(16) = 16-320b2-4ac = -304 <0So the line y- 2x = 0 does not touch the circle.(a) M1 for trying to complete the square (must have at least one bracket squared minus something squared)B1 for correct centre B1 for radius(b) M1 for substituting y=2x into the circleA1 for correct quadratic equationM1 for use of b2-4acA1 for -304<0 and a final conclusion (either QED or final conclusion in words)10u = 6, v=25, a= gv= u + at25 = 6 + gtt= 199.8t = 1.9387755102t=1.94s (or 1.9s)B1 for u = 6, v = 25 and a = g (all three)M1for v = u + at with correct values for v, u and a. A1 for awrt 1.94 or 1.911Mean = 1.5SD = 1.228519133 B1 for the mean caoB1 for the sd (accept awrt 1.23)12M1 for solving simultaneous equationsM1 ft for using the discriminant for their quadraticA1 for a correct conclusion including >0 and a correct final statement using the words model, ball and ceiling ................
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