TUTOR WORLD ASHFORD GCSE MATHEMATICS. Sample Test 1 (Non-Calculator)

Transcription

1 TUTOR WORLD ASHFORD GCSE MATHEMATICS Sample Test 1 (Non-Calculator) Time: 1 hour 30 minutes Higher Tier Read the following carefully o o o o o o INSTRUCTIONS Use black ink only. Calculators must not be used. Fill in your name at the bottom of the page before you start the test. Answer all questions. Answer the questions in the space provided. You must show all your working out. INFORMATION o The total mark for this paper is 80. o The marks for each question are displayed in brackets. o o ADVICE Read each question carefully before answering it. Check your answers at the end if you have time NAME: MARK: GRADE:

2 QUESTION 1 The diagram shows three shapes joined together along their edges. Shape A is a regular hexagon, shape B is a square, and shape C is a parallelogram. Work out the size of the angle marked x? A C x B DIAGRAM NOT ACCURATELY DRAWN Total for Question 1 is 4 marks

3 QUESTION 2 f(x) = x+7 2 Find the value of a such that f(a) = 3 4 Total for Question 2 is 3 marks QUESTION 3 Sketch the graph of y = sin(x) + 1 on the grid below, for 0 o x 450 o. Total for Question 3 is 3 marks

4 QUESTION 4 Find the gradient of the line which passes through the coordinates (0,1) and ( 5, 5). Give your answer as a fraction in its simplest form. Total for Question 4 is 3 marks QUESTION 5 Prove that (3n + 1) 2 (n 1) 2 is always even, where n is an integer. Total for Question 5 is 3 marks

5 QUESTION 6 The two solid cones on the right are mathematically similar. Cone A has a radius of 4 cm and a volume of 32π cm 3. Cone B has a height of 3 cm. A B 3cm Find the volume of Cone B. Give you answer in terms of π. 4cm DIAGRAMS NOT ACCURATELY DRAWN Total for Question 6 is 5 marks

6 QUESTION 7 The value (V), in pounds, of a certain car is inversely proportional to one more than its age (A), in years. The value of the car is 5000, when it is 4 years old. (a) Find a formula for V in terms of A. (b) How old is the car when its value is 2500? [2] [2] Total for Question 7 is 4 marks

7 QUESTION 8 Solve the equation 2x 2 = 5x + 3. Total for Question 8 is 3 marks QUESTION 9 On Adam s Farm, the ratio of the number of cows, pigs and sheep is 2:3:4 The ratio of the number of pigs and goats is 4:5 If there are 60 goats on the farm, how many animals are there altogether? Total for Question 9 is 3 marks

8 QUESTION 10 (a) What type of sequence is the following? bx, b, b x b x 2 [1] (b) Find a formula for the n th term of the following quadratic sequence. 1, 5, 13, 23, [3] Total for Question 10 is 4 marks

9 QUESTION 11 Toby has a stamp collection. The Venn diagram shows information about his stamp collection. ξ = {Toby s full collection of 720 stamps} B = {British stamps} C = {stamps from the 20 th century} ξ B C 3x + 2 x 7x 9 11x + 1 (a) How many British stamps does Toby own? [3] Toby chooses a stamp at random from his collection. (b) Find the probability that the stamp is in the set B C, simplifying your answer. [3] Total for Question 11 is 6 marks

10 QUESTION 12 The speed of an average snail is m/s. How long does it take an average snail to travel 65cm, in seconds? Total for Question 12 is 4 marks QUESTION 13 g(x) = 2x 2 9x + 1 Express g(x 3) in the form ax 2 + bx + c. Total for Question 13 is 3 marks

11 QUESTION 14 OABC is a parallelogram. M is the midpoint of OA. M A N B OA = a OC = c The ratio of MN:NB is 1:2 Show that the ratio of AN:NC is also 1:2 O C Diagram NOT accurately drawn Total for Question 14 is 5 marks

12 QUESTION 15 (a) Write y = x 2 + 8x 15 in completed square form. [3] (b) Hence, state the coordinates of the turning point of the graph of y = x 2 + 8x 15. Total for Question 15 is 4 marks [1] QUESTION 16 The line of equation y = (k + 2)x is perpendicular to the line of equation y = kx. Find the value of k. Total for Question 16 is 3 marks

13 QUESTION 17 Calculate, giving your answer as a mixed number in its simplest form. Total for Question 17 is 2 marks QUESTION 18 Work out an estimate for ( ) 0.5 Total for Question 18 is 2 marks

14 QUESTION 19 Simplify ( x2 +2x+1 y 2 ) 0.5 Total for Question 19 is 3 marks QUESTION 20 Expand and simplify, ( m + 2m)( m + 3 2m). Total for Question 20 is 3 marks

15 QUESTION 21 The diagram shows 3 identical rectangles connected together to form a new shape. The perimeter of this new shape is 66cm. Calculate its area. 10cm DIAGRAM NOT ACCURATELY DRAWN Total for Question 21 is 4 marks

16 QUESTION 22 1 x = y z Make z the subject of the formula above. Total for Question 22 is 3 marks QUESTION 23 A straight line with the equation y + 3x = c passes through the points (1, 4) and (5, q). Find the value of q. Total for Question 23 is 3 marks END OF TEST