ASSIGNMENT FELLOWS

7.2 Factorising quadratic expressions ©Cambridge University Press and OCR 2021 1 7 Further algebraic expressions 7.2 Factorising quadratic expressions • factorising quadratic expressions of the form Reminder Two examples of quadratic expressions in the form are and . The highest power of x in these expressions is . Factorising an expression involves writing it as a product of its factors. You will need to recall how to factorise an expression by taking out the HCF (highest common...

8.1 LINEAR EQUATIONS ©Cambridge University Press and OCR 2021 1 8 Equations 8.1 Linear equations • A linear equation is an equation where the highest power of the variable is 1, e.g. x + 2 = 5. • Variable means a letter representing an unknown number. • Solve means to find the unknown number represented by the letter. Exercise 1 1 Solve these equations without using a calculator. Write your answer as ‘x = …’. a b c d −2x = 12 e f g h WORKED EXAMPLES a Solve the equa...

8.2 Quadratic equations ©Cambridge University Press and OCR 2021 1 8 Equations 8.2 Quadratic equations • Quadratic equations have at least one term with a variable that is squared, e.g. x2 . • Roots mean solutions. There can be zero, one or two solutions to any quadratic equation. TIP These two techniques may be useful when solving quadratic equations: • taking out a common factor, e.g. • applying the ‘difference of two squares’ identity, e.g. . Exercise 1 1 Solve to fi...

8.3 Simultaneous equations ©Cambridge University Press and OCR 2021 1 8 Equations 8.3 Simultaneous equations • forming two linear simultaneous equations • solving two linear simultaneous equations with two variables algebraically. WORKED EXAMPLE Two positive, whole numbers x and y have a sum of 8 and a difference of 6. If x is larger than y, find x and y. Solution Method 1 Solving this problem numerically If the numbers add up to 8, then the possibilities are shown in the table. ...

8.4 and 8.5 Graphs and their equations ©Cambridge University Press and OCR 2021 1 8 Equations 8.4 and 8.5 Graphs and their equations • linear equations • two linear simultaneous equations • quadratic equations • real life graphs. Linear equation graphs WORKED EXAMPLES This is the graph of y = 2 − 4x. a Use the graph to find the value of y when i x = 0 ii x = 1 iii x = 2 b What is the value of x when y = −4? Solution a Each point on the graph can be written as coor...

Exercise 1 1 Convert these areas. a 15m2 to cm2 b 8.8km2 to m2 c 3600mm2 to cm2 d cm2 to m2 2 Convert these volumes. a 6.2m3 to cm3 b cm3 to m3 c 750cm3 to mm3 d 0.6km3 to m3 12.2 Compound units of measurement ©Cambridge University Press and OCR 2020 2 3 Jack runs 42km in 3 hours and 15 minutes. What is his average speed in km/h? Speed = Common units are m/s, km/h or mph (miles per hour). Remember: m/s is read as metres per second, km/h as kilometres per h...

Exercise 1 1 The scale on a map is 1 : 400. What is the actual distance (in metres) between two points that are 15 cm apart on the map? 12.3 MAPS, SCALE DRAWINGS AND BEARINGS ©Cambridge University Press and OCR 2020 2 2 Work out the real distance in km that a map distance of 15mm would represent if the map scale was 1 : . WORKED EXAMPLE A map scale is given as 1cm : 20km. What is the actual distance on the ground that on the map measures 5cm? Solution 1cm : 20km Now multiply by 5. ...

6.3 AND 6.4 LOCI AND PROBLEMS ©Cambridge University Press and OCR 2021 2 2 The locus of all points that are equidistant from two lines will bisect the angle between the two lines. AB and BC represent the sides of a field. Jack is in the corner of the field at point B. He wants to walk into the field in a straight line, so that he is always equidistant from the sides AB and BC. Draw and describe the locus of the path he must take. • Draw the angle bisector of ∠ABC. For the metho...

4 Identify the shapes that are not polyhedra from this list. cylinder cube cone sphere cuboid 5 Make a copy of the table below and complete it for these four 3D shapes. a b c Solid Faces Edges Vertices a b c Reminder A pyramid is a polyhedron with a polygon base and triangular faces that meet at a vertex. 6 Make a copy of the table below and complete it for these four pyramids. Name Faces Edges Vertices triangular-based pyramid square-based pyramid pentagonal-based pyramid hexag...

1 Write down the mathematical name of the following triangles. Choose from the words in the box. isosceles equilateral right-angled scalene a b c d 2 What is the mathematical name given to a a regular triangle b a regular quadrilateral? 3 Fill in the missing words in each sentence. a A triangle that has 3 different side lengths is called …………. b A triangle that has no equal angles is called …………. c A triangle that has one 90º angle and two other non-equal angles is call...