How can I prepare for the Mathematics entrance examination test?

Transcription

1 How can I prepare for the Mathematics entrance examination test? The mathematics entrance examination test is designed to help ou find out how suitable ou will be to stud A level mathematics. It uses algebra-based questions which are of a GCSE standard as it will be taken for granted that ou are able to use skills at A level. Over the next 6 pages ou will find man questions of the appropriate grade and which ou can use to judge how well ou could do. The answers ma be found in the document which accompanies this one. You can of course also use our revision guides and the appropriate lessons and questions of mangahigh and mmaths to supplement our preparations. What topics does the entrance examination test? All questions contained in the entrance exam are based on material in the algebra section of the GCSE sllabus. Specificall, candidates should know and understand: Topic Rules for working with negative numbers. 17 Questions. Expanding brackets in algebra and collecting like terms. 4, 5, 6, 14, 15 Forming and solving linear equations and inequalities. 5, 6 Rules of indices, including appling them to simplifing 1,, 4, 8 algebraic expressions. Changing the subject of a formula. 10, 11, 1, 1 Factorising b removing common factors of an expression. The equation of a straight line in the form = mx + c. 0,5 Solving linear simultaneous equations both algebraic and 0, 1 graphical methods. Factorising quadratics. 7, 8, 9, 14, 19 Solving quadratic equations. 14, 18, 19, 4 Algebraic Fractions. 4, 5, 6, 7, 8, Solving simultaneous equations where one is linear and the other quadratic. Constructing and using formulae and expressions. 16, 4 Fractions If ou have an concerns remember ou can see our teacher and that maths clinic runs on Monda and Thursda Lunchtimes.

2 15a b 1. Simplif a b 7 (). A rectangle is 4 9 m wide and 5 5 m high. Find the perimeter and area of the rectangle. Show our working. (5). (a) Simplif 8 p p (b) Simplif (w 4 ) (c) Simplif 5e f e f 4. Simplif full () (a) (x + 4) (4x 5) (b) (x ) 5 (c) n 1 n + 1 n 5. Solve 7(x + ) = 6. Solve x + 1 = 5x 5 x + 1 () () () 7. Simplif full (x + 1) 4x 1 () 8. Simplif full (a) (x ) 4 (b) x x x 8x + 15 ()

3 9. (a) (i) Expand and simplif (a b) (ii) Show that ( a + b) + ( a b) = a + b (iii) Hence, or otherwise, find the value of (5) 10. Make a the subject of the formula (a c) = 5c Make x the subject of 5(x ) = (4 x) 1. Make a the subject of the formula s = 4 a + 8u () 1. n + a P = n + a 14. (a) Solve 6x + = 4(x 7) 15 x (b) Solve = 4 Rearrange the formula to make a the subject. () (c) (i) Factorise x x + 4 (ii) Hence solve x x + 4 = (a) Expand and simplif (x 6)(x + 4) (b) Factorise completel 1x 18x () () 16. Eggs are sold in boxes. A small box holds 6 eggs. A large box holds 1 eggs. Hina bus x small boxes of eggs. Hina also bus 4 less of the large boxes of eggs than the small boxes. (a) (b) Find, in terms of x, the total number of eggs in the large boxes that Hina bus. Find, in terms of x, the total number of eggs that Hina bus. Give our answer in its simplest form. ()

4 17. D = ut + kt If u = 0, t = 1., k = 5 (a) Work out the value of D. If D = 50, t = 5, k = 5 (b) Work out the value of u. () () (c) Make u the subject of the formula D = ut + kt () 18. Solve x x 18 = (a) (ii) Factorise x 5x + 98 (ii) Solve the equation x 5x + 98 = 0 0. = 4 x 8 A = x + O x The diagram shows two straight lines intersecting at point A. The equations of the lines are = 4x 8 = x + Work out the coordinates of A. Diagram NOT accuratel drawn 1. Solve the simultaneous equations x + = 6 x =

5 . B eliminating, find the solutions to the simultaneous equations x = x + = 18 x =. =. or x =. =. (7). (a) Factorise completel (x 5) + (x 5) () (b) Simplif ( 4) ( 4) 4. Peter cuts a square out of a rectangular piece of metal. x + Diagram NOT accuratel drawn x + x + 4 x + The length of the rectangle is x +. The width of the rectangle is x + 4. The length of the side of the square is x +. All measurements are in centimetres. The shaded shape in the diagram shows the metal remaining. The area of the shaded shape is 0 cm. (a) Show that x + 7x 1 = 0 (b) (i) Solve the equation x + 7x 1 = 0 (Give our answers correct to 4 significant figures). (ii) Hence, find the perimeter of the square. (Give our answer correct to significant figures).

6 B C O x 1 A In the diagram A is the point (0, ), B is the point ( 4, ), C is the point (0, ). Find an equation of the line that passes through C and is parallel to AB.