GCSE Maths - Practice Calculator Paper (Answered + Marked)

Alternative transcript:

of 40 and 56 4 40 56 2 10 14 5 1 4x2x5x7 = 28x10 = 280 A=2³×3×5 B=2² × 3 × 5² (b) Write down the highest common factor (HCF) of A and B. 8 x3 = 24 x 5 = 120 =2×3×5=10×6=60 A=2²x3x B = ² x 5² 4 x3 =12 x 25 = 60x5-300 1 m 125m² p. 60 (2) (Total for Question 1 is 5 marks) 280 (1) (2) (2) (1) (Total for Question 2 is 3 marks) 3 The line L is shown on the grid. Find an equation for L. Ду : H ។ · 2 6 = C 1 -1 0 -2- -3 L +3x+c y=-3x-6 =+3 (2) 0·3(2-6 76-6=0 +0 +6+0 yog 3 4 5 X y=3x-6 (Total for Question 3 is 3 marks) lonely 4 Raya buys a van for £8500 plus VAT at 20% Raya pays a deposit for the van. She then pays the rest of the cost in 12 equal payments of £531.25 each month. Find the ratio of the deposit Raya pays to the total of the 12 equal payments. Give your answer in its simplest form. 531.25 12 106250 531250 6375.00 6375 8500÷10-850 x2 1700 8500 +1700=10200 6375 3825 deposit payments 38256375 7651275 1.53 255 51:85 ксер дау 17 F11 3:5 51:85 (Total for Question 4 is 5 marks) 5 (a) Complete the table of values for y=x²-x-6 x 0 = y -3 -2 9 y=-(-2)²-(-2)-6 - 4 + 2-6 -1 NB be careful (go through points) 9-1+1 = -4 0 -4 -6-6-40 y = (²-1) ² - (-1) ²6 y = 1²-1-6 =1-1-6 y q 6 (b) On the grid, draw the graph of y=x²-x-6 for values of x from -3 to 3 5 4 3 1 -2 0 -3 4 1 -5 2 3 y= 2²-2-6 4-2-6 y=3²-3-6 =9-3-6 (2) (2) 6 (c) Use your graph to find estimates of the solutions to the equation x²-x-6--2 Solve the simultaneous equations 2x = 19+4y x= = = 19+4y² =95+2y 3/9.5+29) + 5y = 1 2 28.5+69+5=1 28.5+11=1 11y=1-28,5 5-27.5 y=-27.5 2=-16 ~ = 9 ī 2x - 4y = 19 3x + 5y = 1 3x+5y=1 3x + 5 (-1/2) - 1 3x-12.5=1 3x = 13.5 x=135 ou x = 2.6 (2) (Total for Question 5 is 6 marks) lovey. 9/2 -5./2 X=....... y=.. 95 God wor (Total for question 6 is 4 marks) 16 15 4 marks) 9 Jean invests £12 000 in an account paying compound interest for 2 years. In the first year the rate of interest is x% At the end of the first year the value of Jean's investment is £12 336 In the second year the rate of interest is What is the value of Jean's investment at the end of 2 years? 12000 12336 x=2.7% > 250 257 =0.9728... * = 0.0136...% 12336 × 1.0130 % -12 504 12336 = 1.028 12000 £= 2.8 → 2.2.3, 1.47. 1.0.9728 -0.027.. x 100 = 2.1% 1.028-10.028 0.028×100 2.8% 12336 x+4% (100+1.4%) -12336 x 1.014 (12508.70) explar bett 12,504.00 £.... (Total for Question 9 is A marks) 10 Graph A Graph C K 0 Type of proportionality yox Graph B ya √x 1 Graph D 0 2. The graphs of y against x represent four different types of proportionality. Match each type of proportionality in the table to the correct graph. 0 Graph letter B + D A с (Total for Question 104s 2 marks) t 11 (a) On the grid, draw the graph of -6 -2 6 YA 4 x² + y² = 12.25 0 -2 -6 23 1-82.759921135/271 1.8 4 (b) Hence find estimates for the solutions of the simultaneous equations = 1-2x y=1 x² + y² = 12.25 2x+y=1 -220+1 6 X celler (2) (x=1₁9, y=-2.9), (x == -1-1, y = 3.3) (3) (Total for Question 11 is 5 marks) 12 ABCDEFGH is a cuboid. AB = 7.3 cm CH=8.1 cm Angle BCA = 48° A F Find the size of the angle between AH and the plane ABCD. Give your answer correct to 1 decimal place. 7.3 A 9.823 D 8.1 Sin (48)=13 AC AC= 7.3 sin (48) tan (A). 2 A = 9.823 = tan¹ (8.1 9.823 H 9.823. 2 8.1 39.51 395 excellent! 39.5 (Total for Question 12 is 4 marks) 13 Martin did this question. Rationalise the denominator of Here is how he answered the question. 14x (2-√3) (2+√3)(2-√3) 28-14√3 4+2√3-2√3+3 14 2+√√3 14 2+√3 28-14√3 7 = 4-2√3 Rationalise the denominator of √12 Martin's answer is wrong. (a) Find Martin's mistake. Martin thought (+57) x ( -53) would equal (+3) but it's actually (-3), so the answer is (28-1953) Sian did this question. 5 √12 Here is how she answered the question. 5√12 √12x√12 5x3√2 12 5√2 4 14 (2-55) (2+57) (2-√7) = 14 (2-√3) 2(2-53) + √2/2-53) -28-1453 4-255+253-37 √12 √12 X Sian's answer is wrong. (b) Find Sian's mistake. She thought equal to (253), so the final 28-1453-28-1453 5.J2 5√2-5√4√3 12 5×253 12 TOP 12 S53 4 · (√√2) equalled (752) but & its answer is 513 (Total for Question 18 is 2 marks) TOTAL FOR PAPER IS 50 MARKS