Name: Teacher: Form: LEARNER JOURNAL. Set: Mathematics. Module 7 END OF YEAR TARGET: GCSE TARGET:

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1 Name: Teacher: Form: Set: LEARNER JOURNAL Mathematics Module 7 END OF YEAR TARGET: GCSE TARGET:

2 MODULE 7 Unit 7A - Graphs Use areas of rectangles, triangles and trapeziums to estimate the area under a curve. Find the equation of a tangent to a circle. Interpret the meaning of the area under a curve. Draw a tangent at a point on a curve and use it to work out the gradient at a point on a curve Recognise and plot cubic, exponential and reciprocal graphs. Interpret the gradient at a point on a curve. Draw linear graphs parallel or perpendicular to other lines Transform a graph. and passing through a specific point. UNIT 7A TEST Unit 7B - Triangles Use trigonometric ratios and Pythagoras theorem to solve Find the sine, cosine and tangent of any angle from 0 to 360. more complex two-dimensional problems. Use the sine rule and the cosine rule to find sides and angles in Use trigonometric ratios and Pythagoras theorem to solve any triangle. more complex three-dimensional problems. Work out the area of a triangle if you know two sides and the included angle. UNIT 7B TEST Unit 7C Algebraic Fractions and Functions Simplify algebraic fractions Solve equations containing algebraic fractions. Generate the terms of a quadratic sequence from the nth term. Change the subject of a formula where the subject occurs more than once. Work out the nth term of a quadratic sequence. Find the output of a function. Find the composite of two functions. Find the inverse function. Find an approximate solution for an equation using the process of iteration. UNIT 7C TEST Add and subtract vectors. Unit 7D - Vectors Use vectors to solve geometric problems. UNIT 7D TEST

3 Module 7 Grid 1 - Area under curve (MW 216) The graph gives information about the velocity of a particle during the first 4 seconds of its motion. T2 Improve finding the area under a curve. Complete Perfect! Try solving more difficult questions involving curves. Complete Here is a sketch of the graph of y = x2 The graph is used to model the shape of a cross-section of a domed roof. The cross-section is shaded. Calculate an estimate of the area of the cross-section of the roof. Here is the speed time graph for a journey of a car travelling along a straight road between 2 sets of traffic lights. Find the total distance, in metres between the 2 sets of traffic lights.

4 Module 7 Grid 2 - Circle equations (MW 197) T2 Improve finding the equation of a tangent to a circle. Complete Perfect! Try solving more difficult involving circles and tangents. Complete Here is a circle, centre O, and the tangent to the circle at the point P(4, 3) on the circle. Find an equation of the tangent at the point P.

5 Module 7 Grid 3 - Perpendicular lines (MW 208) T2 Improve finding perpendicular and parallel lines. Complete Perfect! Try solving more difficult questions inv. perpendicular lines. Complete

6 Module 7 Homework 1 Reason for not submitting:

7 Module 7 Grid 4 - Graphs (MW 161, 196) The graph of y = f(x) is shown on the grid. (a) On this grid, sketch the graph of y = f(x 3) and label it G (b) On this grid, sketch the graph of y = 2f(x) and label it H T2 Improve on transforming graphs. Complete Perfect! Try solving more difficult questions inv. transforming graphs. Complete The graph of y = f(x) is shown on the grid with its translation graph G. Write down the equation of graph G. This is a sketch of the curve with the equation y = f(x). The only minimum point of the curve is at P(3, -4). Write down the coordinates of the minimum point of the curve with the equation y = f(x + 5) + 6

8 Name: Class: Score: Percentage: /38 Module 7 Units 7A Graphs Qu Marks T To improve your understanding of A MW 1 5 Gradient of lines Cubic Graphs Types of Graphs Reciprocal Graphs Perpendicular lines Equation of a Circle and Cosine Graph 197 / Equation of a Circle and Solving Equations Transformation of Trigonometry Graphs Transformation of Trigonometry Graphs TOTAL A Complete corrections in green pen.

9 Module 7 Grid 5 3D Pythagoras/ Trigonometry (MW 217, 218) A sign post is located at the vertex of a rectangular field. The farmer wants to span a washing line from the top of the sign post to the opposite vertex of the field. Find the angle α between the diagonal and the washing line. 2.5 m α 8 m 12 m T2 Improve solving 3D Pythagoras questions. Complete Perfect! Try solving more questions involving 3D Trigonometry. Complete A cuboid has length 3 cm, width 4 cm and height 12 cm. Work out the length of PQ. Below is a cuboid. Length AG = 16 cm, Angle CAG is 35. Work out the length of EG.

10 Module 7 Grid 6 Exact trig values (MW 173) T2 Learn the exact trigonometry values for 30, 45 and 60 degrees. Complete Perfect! Try solving more difficult questions involving exact trig values. Complete Shown on the right is a right angled triangle. Find the exact length of the side labelled y.

11 Module 7 Homework 2 Cubic/Reciprocal Graphs 3D Pythagoras/Trig Stratified Sampling Reason for not submitting:

12 Module 7 Grid 7 Sine/ Cosine rule (MW 201, 202) Improve solving sine/ cosine rule questions. Complete T2 Perfect! Try solving more difficult questions involving trig rules. Complete In the triangle, angle y is obtuse. Work out the size of angle y. Two triangular lawns are shown. Wire fencing is needed for all 5 sides. Wire fencing is sold in 50m rolls. Work out the number of rolls needed.

13 Module 7 Grid 8 Area of any triangle (MW 203) ABC is a triangle. D is a point on AB. Work out the area of triangle BCD. Give your answer correct to 3 s.f.. Improve finding the area of any triangle. Complete T2 Perfect! Try solving more difficult questions involving area. Complete Calculate the area of this triangle. Give your answer correct to 3 s.f. 8.7 cm 5.2 cm 32 Triangle ABC has area 40 cm 2. AB = 2BC Work out the length of BC. Give your answer as a surd in its simplest form.

14 Name: Class: Score: Percentage: /34 Module 7 Units 7B Triangles Qu Marks T To improve your understanding of A MW 1 2 Stratified Sampling The Sine Rule The Cosine Rule Area of a Triangle using Sine Rule Pythagoras and Circumference of a Circle 150 / Pythagoras and Trigonometry 150 / Volume of a Pyramid and 3D Trigonometry Area of a Triangle using Sine and Bounds 203 / TOTAL A Complete corrections in green pen.

15 Module 7 Grid 9 - Algebraic fractions (MW 210) T2 Improve working with algebraic fractions. Complete Perfect! Try solving more difficult questions inv. algebraic fractions. Complete

16 Module 7 Homework 3 Sine/Cos Rule Area of a Triangle Algebraic Fractions Reason for not submitting:

17 Module 7 Grid 10 - Rearranging (MW 190) T2 Improve on changing the subject of a formula. Complete Perfect! Try solving more difficult rearranging formula questions. Complete

18 Module 7 Grid 11 - Functions (MW 214) T2 Improve on inverse functions. Complete Perfect! Try solving more difficult inverse functions. Complete

19 Module 7 Grid 12 - Quadratic sequences (MW 213) T2 Improve finding the area and perimeter of sectors. Complete Perfect! Try solving more difficult questions involving sectors. Complete

20 Module 7 Homework 4 Rearranging Formula Inverse Functions Quadratic Sequences Reason for not submitting:

21 Module 7 Grid 13 - Composite functions (MW 215) T2 Improve on composite functions. Complete Perfect! Try solving more difficult composite functions. Complete

22 Module 7 Grid 14 - Iteration (MW 180) T2 Improve solving equations with iteration. Complete Perfect! Try solving more difficult questions involving iteration. Complete

23 Name: Class: Score: Percentage: /34 Module 7 Units 7C Algebraic Fractions and Functions Qu Marks T To improve your understanding of A MW 1 2 Rearranging Formulae Rearranging Formulae The n th Term of a Quadratic Sequence Algebraic Fractions Rearranging Difficult Formulae Inverse and Composite Functions 214 / Rearranging Formulae and Iterative Processes 190 / Algebraic Fractions Algebraic Fractions TOTAL A Complete corrections in green pen.

24 Module 7 Grid 15 - Vectors (MW 219) OAB is a triangle. P is the point on AB such that AP : PB = 5 : 3 OA = 2a OB = 2b OP = k(3a + 5b) where k is a scalar quantity. Find the value of k. T2 Improve solving problems using vectors. Complete Perfect! Try solving more complicated problems using vectors. Complete

25 Module 7 Homework 5 Composite Functions Iterative Process Vectors Reason for not submitting:

26 Name: Class: Score: Percentage: /21 Module 7 Units 7D Vectors Qu Marks T To improve your understanding of A MW 1 5 Vectors Vectors Vectors Vectors Compound Interest TOTAL A Complete corrections in green pen.

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28 Module 7 Revision List Topic MW Clip 7A Test 7B Test 7C Test 7D Te Unit 7A - Graphs Perpendicular Lines 208 Equation of a Circle 197 Cubic and Reciprocal Graphs 161 Transformation of Trig Functions 196 Unit 7B - Triangles Pythagoras in 3D 217 Trigonometry in 3D 218 Stratified Sampling 176 The Sine Rule 201 The Cosine Rule 202 Area of a Triangle Using Sine 203 Unit 7C Algebraic Fractions and Functions Algebraic Fractions 210 Rearranging Difficult Formulae 190 Inverse Functions 214 The Nth Term of a Quadratic 213 Composite Functions 215 Iterative Processes 180 Unit 7D Vectors Vectors 219