![Algebra – what it means (2)
• Expand and simplify – multiply out the
brackets and then collect terms
– E.g. 2(p + 5q) + 7(p - 4q)
= 2p + 10q +7p – 28q
= 9p – 18q
• Solve – find the exact value of [x] that makes
the equation true.
– E.g. 4(2x – 3) = 20
8x – 12 = 20
8x = 32
x = 4](https://image.slidesharecdn.com/gcseaqamod5revision-101025102432-phpapp01/85/Gcseaqa-mod5revision-7-320.jpg)
Gcseaqa mod5revision
- 1. AQA Module 5 Revision Support Caroline Johnson Bristol LA Mathematics Consultant Based on an original by Steve Alexis (AST at Brislington Enterprise College)
- 2. Exam Questions – collecting marks It’s all about getting every possible mark Remember to: – record every step in your working – not cross anything out – check the sense of your answers – be aware of the number of marks available – use the correct terminology – take note of specific instructions – include units; give your answer to 2 dp
- 3. And so… The next few slides will re-visit some key points.
- 4. Rounding • When rounding to a given number of decimal places count each place after the decimal point • When rounding to a given number of significant figures, begin counting from the first non-zero digit. E.g. 27.35 Correct to 1 decimal place is 27.4 Correct to 1 significant figure is 30
- 5. Sensible answers If a question says.. ‘Give your answer to a sensible degree of accuracy’ you need to write the answer no more accurately than the values in the question. E.g. If a question has values to 2 s.f. then give the answer to 2 s.f. or 1.s.f
- 6. Algebra –what it means! • Simplify – collect terms together – E.g. 2a + 3b + 4a – 5b = 6a – 2b • Factorise – take out a common factor – E.g. factorise 4x2 + 6x = 2x(2x + 3) • Expand - multiply out the brackets – E.g. 7(p – 4q) = 7p – 28q
- 7. Algebra – what it means (2) • Expand and simplify – multiply out the brackets and then collect terms – E.g. 2(p + 5q) + 7(p - 4q) = 2p + 10q +7p – 28q = 9p – 18q • Solve – find the exact value of [x] that makes the equation true. – E.g. 4(2x – 3) = 20 8x – 12 = 20 8x = 32 x = 4
- 8. Algebra tips. If question says ‘do not use trial and improvement’, then an algebraic method is expected. Any sign of trial and improvement will be penalised. This is particularly true for solving simultaneous equations.
- 9. Drawing graphs • Draw all graphs in pencil. • Make sure you plot points neatly with a small cross. • If the graph has an equation with an x2 term in it then it will be ‘U’ shaped or ‘∩’ shaped. E.g. x2 – 3x – 5 If it is not a smooth curve check that you have worked out your values correctly and/or that they are plotted accurately.
- 10. Straight line graphs If asked to draw the graph of y = 2x+ 3 there are 2 methods you could use. (i) draw up a table of values to plot 3 points (why a minimum of 3?). You can choose the values of x, but keep them simple e.g. 0, 2 and 4 (ii) use the gradient and intercept method
- 11. Perimeter, Area and Volume • Perimeter measures length, so your answer should be in km, m, cm or mm • Area units are squared e.g. m2 • Volume is measured in cubic units e.g. cm3 • Remember that there are two formulae in the front of the paper. These help you to find the area of a trapezium and the volume of a prism. USE THEM IF YOU NEED THEM.
- 12. Some useful area formulae • Area of a rectangle = length x width • Area of a parallelogram = base x height • Area of a triangle = base x height • Area of a circle = πr2 Remember Circumference of a circle = πd or 2πr Use the π button on your calculator. 2 1
- 13. Don’t measure it! • If a diagram says : ‘Not to scale’ or ‘not drawn accurately’ to work out the answer you will need to do some calculation(s). You do not measure lengths
- 14. Angle properties Know your angle facts! • There are 360° in a full turn • The sum of the angles at a point on a straight line is 180 ° • The sum of the angles in a triangle is 180° • The sum of the angles in a quadrilateral is 360 °
- 15. Angles Between Parallel lines Parallel lines remain the same distance apart. Transversal Vertically opposite angles are equal. vert.opp. ∠s Corresponding angles are equal. corr. ∠s Alternate angles are equal. alt. ∠s Interior angles sum to 180o .(Supplementary) Int. ∠s
- 16. Bearings Remember that bearings are: 1. measured from the NORTH 2. in a clockwise direction 3. written with 3 figures e.g. 060°
- 17. Transformations Transformation Properties Reflection A line of reflection Rotation A centre, an angle (90°, 180°, 270°) and a direction Translation A vector e.g. Enlargement A centre and scale factor (which can be a fraction) − − 2 3
- 18. Pythagoras Is used for finding lengths in right-angled triangles b c a In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. Hypotenuse a2 = b2 +c2
- 19. The Trigonometric Ratios A BC hypotenuse opposite A B C hypotenuse opposite adjacent adjacent Opposite Sine A Hypotenuse = O SinA H = Adjacent Cosine A Hypotenuse = Cos A A H = Opposite Tangent A Adjacent = Tan O A A = S O CH A H T O A Remember
- 20. In the exam • Read the whole paper • Highlight important points (but don’t use a highlighter pen on your answers) • Do the questions that you find easy first • Be aware of the number of marks per question or part of a question • Remember units, rounding • Check your answers thoroughly at the end
- 21. ..and finally Good luck !