Mathematics GCSE. Paper 1 Higher tier. Materials. Time allowed: 1 hour 30 minutes

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1 GCSE Mathematics H Paper Higher tier Materials Time allowed: hour 30 minutes For this paper you must have: mathematical instruments You may not use a calculator. Instructions Use black ink or black ball-point pen. Draw diagrams in pencil. all questions. You must answer the questions in the space provided. In all calculations, show clearly how you work out your answer. Information The marks for questions are shown in brackets. The maximum mark for this paper is 80. Name: Practice Exam Paper

2 Practice Exam Paper Circle the formula for calculating pressure, where F = Force, A = Area and D = Density. P = F A P = D F P = A F P = A D What is the value of sin 30? Circle your answer Expand (x + )(x + )(x + 3) Circle your answer. x 3 + 6x + 8x + 6 x 3 + 6x + x + 6 x 3 + 6x + 6 x + 3x + 4 Here is a sequence: Circle the expression for the nth term of the sequence. n + 3 3n n + 5 n GCSE Maths Workbook

3 Workbook 5 (a) What is one million minus one? (b) 3,, 5, 5, 7, 60 From the numbers above choose: (i) the cube number (ii) the square number (iii) the LCM of and 5. [3 marks] (c) Sandra says, If I double a prime number and then add three, the answer will always be a prime. Give two prime numbers for which this statement is true and two prime numbers for which this statement is not true (do not use or 3). True: and Not True: and 6 Work out TURN OVER FOR THE NEXT QUESTION Practice Exam Paper

4 Practice Exam Paper 7 (a) If a =, b = 4 and c = 8, work out the value of a b c (b) Solve the equation (m + 3) m = (c) 6 p = 4 4 Work out the value of p. 8 y The diagram shows two regular hexagons. Work out the size of angle y. You must show your working. [4 marks] GCSE Maths Workbook

5 Workbook 9 y x (a) On the grid draw triangle A with vertices ( 3, 0), ( 3, 3) and (, 3). (b) Reflect triangle A in x = 0 to form triangle B. (c) Rotate triangle B clockwise 90 about the origin. Label the image C. (d) What transformation maps triangle A onto triangle C? TURN OVER FOR THE NEXT QUESTION Practice Exam Paper

6 Practice Exam Paper 0 Two men invest 8000 and 6000 into a business. In the first year, the business makes a profit of 064. The profit is divided in the ratio of the original amounts invested. Work out the value of each share of the profit. [4 marks] Tick whether each statement is true or false. TRUE FALSE (a) A parallelogram has rotational symmetry of order. (b) A rhombus has rotational symmetry of order 4. (c) A hexagon can be drawn with only one line of symmetry. (d) An isosceles triangle with more than one line of symmetry is an equilateral triangle. GCSE Maths Workbook

7 Workbook (a) Estimate the answer to ( ) ( ) (b) If x = and y =.3 0 5, work out the value of x + y in standard form. (c) Write correct to 3 significant figures. (d) Work out TURN OVER FOR THE NEXT QUESTION Practice Exam Paper

8 Practice Exam Paper 3 (a) Draw the graph of y = x 4x + using values of x from to 5. 6 y x (b) Use your graph to solve x 4x + = 0 (c) Work out the equation of the line of symmetry for y = x 4x + GCSE Maths Workbook

9 Workbook 4 (a) Simplify y + y + y (b) Expand 4 m(m + 3) (c) Expand and fully factorise p(p t) + t(p t) (d) Expand and simplify (3a + )(a 4) TURN OVER FOR THE NEXT QUESTION Practice Exam Paper

10 Practice Exam Paper 5 A bag contains eight marbles. Two marbles are yellow and six marbles are blue. A marble is selected and not replaced. A second marble is selected. What is the probability of obtaining: (a) Two yellow marbles? [3 marks] (b) One marble that is yellow and one marble that is blue? [3 marks] GCSE Maths Workbook

11 Workbook 6 Write down the value of: (a) 4 0 (b) 64 (c) 7 (d) 8 ( ) (e) 0. 3 TURN OVER FOR THE NEXT QUESTION Practice Exam Paper

12 Practice Exam Paper 7 The owner of an aquarium likes to regularly measure the length (y) of all his fish that are smaller than one metre. The lengths of 00 fish are shown below. Length (cm) Frequency Cumulative Frequency 0 y y y y y y y y y y 00 5 (a) Complete the cumulative frequency column in the table. GCSE Maths Workbook

13 Workbook (b) Plot a cumulative frequency curve for this data. (c) Estimate the median length of the 00 fish. (d) Estimate the interquartile range. TURN OVER FOR THE NEXT QUESTION Practice Exam Paper

14 Practice Exam Paper 8 Write down as a fraction in its lowest terms: a + a + a + 6a + 8 [4 marks] END OF QUESTIONS GCSE Maths Workbook

15 s. P = F A. [] [] 3. x 3 + 6x + x + 6 [] 4. n [] 5. (a) [] (b) (i) 7 [] (ii) 5 [] (iii) 60 [] (c) True: mark for any two correct answers, e.g. 5 and 7 []; Not true: mark for any two correct answers, e.g. and 3 [] [] (only award mark if decimal point is in incorrect place) 7. (a) a b = 6 []; 3 6 [] (b) m = 3 [] (c) p = [] 8. Exterior angle of hexagon = = 60 []; Interior angle = = 0 []; y = 80 0 = 60 []; y = 0 [] 9. (a) Correct drawing of triangle A (see diagram). [] (b) Correct reflection in y-axis to produce triangle B (see diagram). [] (c) Correct rotation of triangle B to produce triangle C (see diagram). [] A y x C (d) Reflection in y = x [] B in the ratio of 8 : 6 []; part = = 76 []; One man receives 76 8 = 608 []; The other receives 76 6 = 456 [] This could also have been solved using the ratio 4 : 3, where part = 5. (a) True [] (b) False [] (c) True [] (d) True []. (a) (50 00) (80 + 0) [] = 50 (or estimate reasonably near to this) [] (b) x = 3 000, y = []; x + y = [] (c) [] (d) 0 [] 3. (a) Correct y-intercept (0, ) []; all other points accurately plotted. [] y x (b) x = 3.7 (+/ 0.) []; x = 0.3 (+/ 0.) [] (c) x = [] 4. (a) 3y [] (b) 4 m 6m [] (c) p pt + tp t []; (p + t)(p t) [] (d) 3a + a a 8 []; 3a 0a 8 [] 5. (a) 8 7 []; 56 = 8 [] (b) = 3 7 [] []; []; GCSE Maths Workbook

16 6. (a) [] (b) 8 [] (c) [] 7 (d) 8 [] (e) 0 3 []; = 000 [] 7. (a) 6, 0, 9, 9, 4, 60, 74, 88, 95, 00 [] (b) Correct scale and labels on axes []; Correct plotting of cumulative frequency curve. [] (c) Median = 55cm (+/ 5cm) [] (d) Interquartile range = 34cm (+/ 6cm) [] Cumulative Frequency Fish Length (cm) a + a + a + a 4 = = ( )( + ) []; ( a + 4) + a ( a + ) ( a + 4 ) []; = a + 4 ( a + ) ( a + 4) a + 4 [] []; s