Higher tier unit 6a check in test. Calculator

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1 Higher tier unit 6a check in test Calculator Q1. The point A has coordinates (2, 3). The point B has coordinates (6, 8). M is the midpoint of the line AB. Find the coordinates of M. Q2. The points A, B and C lie on a straight line. The coordinates of A are (9, 0). The coordinates of B are (7, 4). The coordinates of C are (1, q). Work out the value of q. GCSE Mathematics (9 1) Higher tier Unit 6a check in test

2 Q3. In the diagram, the points A, B and C lie on the straight line y = 2x 1 The coordinates of A are (2, 3). The coordinates of B are (5, 9). Given that AC = 3AB, find the coordinates of C. GCSE Mathematics (9 1) Higher tier Unit 6a check in test

3 Q4. You can use the graph below to find out how much Lethna has to pay for the units of electricity she has used. Lethna pays at one rate for the first 100 units of electricity she uses. She pays at a different rate for all the other units of electricity she uses. Lethna uses a total of 900 units of electricity. Work out how much she must pay. GCSE Mathematics (9 1) Higher tier Unit 6a check in test

4 [Q5 6 linked] Q5. Water is leaking out of two containers. The water started to leak out of the containers at the same time. The straight line P shows information about the amount of water, in litres, in container P. The straight line Q shows information about the amount of water, in litres, in container Q. Work out the gradient of line P. Q6. One container in question 5 will become empty first. Which container empties first, and how much water is left in the other container at that point? GCSE Mathematics (9 1) Higher tier Unit 6a check in test

5 [Q7 8 linked] Q7. At 9 am, Bradley began a journey on his bicycle. From 9 am to 9.36 am, he cycled at an average speed of 15 km/h. From 9.36 am to am, he cycled a further 8 km. Draw a travel graph to show Bradley's journey. Q8. From am to 11 am, Bradley cycled at an average speed of 18 km/h. Work out the distance Bradley cycled from am to 11 am. GCSE Mathematics (9 1) Higher tier Unit 6a check in test

6 Q9. A water company charges customers a fixed standing charge plus an additional cost for the amount of water, in cubic metres, used. The graph shows information about the total cost charged. Write down the fixed standing charge, and work out the additional cost for each cubic metre of water used. GCSE Mathematics (9 1) Higher tier Unit 6a check in test

7 Q10. Here is a speed-time graph for a car journey. The journey took 100 seconds. The car travelled 1.75km in the 100 seconds. Work out the value of V. GCSE Mathematics (9 1) Higher tier Unit 6a check in test

8 Topics listed in objectives Identify and plot points in all four quadrants; Draw and interpret straight-line graphs for real-life situations, including ready reckoner graphs, conversion graphs, fuel bills, fixed charge and cost per item; Draw distance time and velocity time graphs; Use graphs to calculate various measures (of individual sections), including: unit price (gradient), average speed, distance, time, acceleration; including using enclosed areas by counting squares or using areas of trapezia, rectangles and triangles; Find the coordinates of the midpoint of a line segment with a diagram given and coordinates; Find the coordinates of the midpoint of a line segment from coordinates; Calculate the length of a line segment given the coordinates of the end points; Find the coordinates of points identified by geometrical information. Find the equation of the line through two given points. Answers Q1. M (4, 5.5) Q2. q = 16 Q3. C (11, 21) Q (2 40) = 105 Q Q6. P empties first, Q contains 2 litres when P empties. Q7. Graph drawn from (9, 0) to (9.36, 9) and then to (10.45, 17) Q = 4.5 km/h Q9. 14 fixed charge, then 1.20 per metre of water used Q10. V = 25 m/s GCSE Mathematics (9 1) Higher tier Unit 6a check in test

9 Higher tier unit 6b check in test Non-calculator Q1. P is the point ( 4, 4) Q is the point (1, 5) Find the gradient of PQ. Q2. Which of these graphs shows direct proportion? GCSE Mathematics (9 1) Higher tier Unit 6b check in test

10 Q3. On the grid, draw the graph of y = 4x + 2 from x = 1 to x = 3 GCSE Mathematics (9 1) Higher tier Unit 6b check in test

11 Q4. Line L is drawn on the grid below. Find the equation for the straight line L. Give your answer in the form y = mx + c Q5. A line has gradient 2 and passes through the point (3, 4). Find the equation of the line. GCSE Mathematics (9 1) Higher tier Unit 6b check in test

12 Q6. The graph shows a straight line. Find the equation of the line in the form ax + by = c. Q7. Find the gradient of the line with equation 3y + 4x = 12 Q8. Here are the equations of five straight lines. Which of lines A D is parallel to line L? Line L y = 2x + 4 Line A 2y = 2x + 4 Line B 2y = x + 4 Line C 2x + 2y = 4 Line D 2x y = 4 GCSE Mathematics (9 1) Higher tier Unit 6b check in test

13 Q9. The diagram shows a straight line, L, drawn on a grid. Which of lines A D is perpendicular to line L? Line A y + 2x = 3 Line B y 2x = 3 Line C 2y = x + 3 Line D 2y + x = 3 GCSE Mathematics (9 1) Higher tier Unit 6b check in test

14 Q10. The graph shows the depth, d cm, of water in a tank after t seconds. Find the gradient of this graph. Choose the statement that best describes what this gradient represents. A The gradient is 2 3. Every 2 3 of a second, the depth of water decreases by 1 cm. B C D The gradient is 1.5. Every second, the depth of water decreases by 1.5 cm. The gradient is 1.5. Every second, the depth of water decreases by 1.5 cm. The gradient is 1.5. The depth of water decrease by 1 cm every 1.5 seconds. GCSE Mathematics (9 1) Higher tier Unit 6b check in test

15 Topics listed in objectives Plot and draw graphs of y = a, x = a, y = x and y = x, drawing and recognising lines parallel to axes, plus y = x and y = x; Identify and interpret the gradient of a line segment; Recognise that equations of the form y = mx + c correspond to straight-line graphs in the coordinate plane; Identify and interpret the gradient and y-intercept of a linear graph given by equations of the form y = mx + c; Find the equation of a straight line from a graph in the form y = mx + c; Plot and draw graphs of straight lines of the form y = mx + c with and without a table of values; Sketch a graph of a linear function, using the gradient and y-intercept (i.e. without a table of values); Find the equation of the line through one point with a given gradient; Identify and interpret gradient from an equation ax + by = c; Find the equation of a straight line from a graph in the form ax + by = c; Plot and draw graphs of straight lines in the form ax + by = c; Interpret and analyse information presented in a range of linear graphs: use gradients to interpret how one variable changes in relation to another; find approximate solutions to a linear equation from a graph; identify direct proportion from a graph; find the equation of a line of best fit (scatter graphs) to model the relationship between quantities; Explore the gradients of parallel lines and lines perpendicular to each other; Interpret and analyse a straight-line graph and generate equations of lines parallel and perpendicular to the given line; Select and use the fact that when y = mx + c is the equation of a straight line, then the gradient of a line parallel to it will have a gradient of m and a line perpendicular to this line will have a 1 gradient of m. Answers Q Q2. C Q3. line from ( 1, 2) to (3, 14) Q4. y= 2x +1 Q5. y = 2x 2 Q6. 7x + 9y = 63 Q7. Q8. D Q9. A Q10. B 4 3 GCSE Mathematics (9 1) Higher tier Unit 6b check in test

16 Higher tier unit 6c check in test Non-calculator Q1. Here are three graphs. Here are four equations of graphs. y = x 3 y = x y = y = 2 x x Match each graph to the correct equation. A and y = B and y = C and y = GCSE Mathematics (9 1) Higher tier Unit 6c check in test

17 [Q2 3 linked] Q2. Complete the table of values for y = 2x 2 1 Find the two missing values x y Q3. On the grid, draw the graph of y = 2x 2 1 for values of x from x = 2 to x = 2. Use your graph to write down estimates of the solutions of the equation 2x 2 1 = 0. GCSE Mathematics (9 1) Higher tier Unit 6c check in test

18 Q4. Frankie kicks a rugby ball for a conversion after a try. He kicks the ball from 6 m in front of the goal posts. The graph models the path followed by the rugby ball. Find the height of the ball as it goes past the posts. [Q5 6 linked] Q5. Complete the table of values for y = x 2 2x Q6. On the grid, draw the graph of y = x 2 2x for values of x from 2 to 4. Solve x 2 2x 2 = 1 GCSE Mathematics (9 1) Higher tier Unit 6c check in test

19 Q7. On the grid, draw the graph of x 2 + y 2 = 4 GCSE Mathematics (9 1) Higher tier Unit 6c check in test

20 Q8. Joy made a table of values for y = 4 x and drew the graph for 0.5 x 8. She made one mistake. What was her mistake? x y GCSE Mathematics (9 1) Higher tier Unit 6c check in test

21 [Q9 10 linked] Q9. Complete the table of values for y = x 3 4x Q10. On the grid, draw the graph of y = x 3 4x from x = 3 to x = 3 GCSE Mathematics (9 1) Higher tier Unit 6c check in test

22 Topics listed in objectives Recognise a linear, quadratic, cubic, reciprocal and circle graph from its shape; Generate points and plot graphs of simple quadratic functions, then more general quadratic functions; Find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function; Interpret graphs of quadratic functions from real-life problems; Draw graphs of simple cubic functions using tables of values; Interpret graphs of simple cubic functions, including finding solutions to cubic equations; 1 Draw graphs of the reciprocal function y = with x 0 using tables of values; x Draw circles, centre the origin, equation x 2 + y 2 = r 2. Answers Q1. A and y = x 2 + 4, B and y = x 3, C and y = 2 x Q2. ( 1, 1), (2, 7) Q3. x = 0.7, x = 0.7 Q4. 5 m Q5. ( 2, 8), (1, 1), (2, 0), (4, 8) Q6. x = 3, x = 1 Q7. circle, centre O, radius 2 Q8. x = 8, y = 0.5 not 2 Q9. ( 3, 15), ( 2, 0), (1, 3), (2, 0)] Q10. correctly drawn graph using table of values from Q9. GCSE Mathematics (9 1) Higher tier Unit 6c check in test