MATHEMATICS National Qualifications - Intermediate 2 Maths Unit 3 + Units 1/2 Revision

Transcription

1 Mini-Prelim MATHEMATICS National Qualifications - Intermediate Maths Unit + Units / Revision Time allowed - minutes Read carefully. You may use a calculator.. Full credit will e given only where the solution contains appropriate working.. Square-ruled paper is provided.

2 FORMULAE LIST The roots of ax + x + c = 0 are x = ( a ac) Sine rule: a sin A sin B c sin C Cosine rule: a = + c c cos A or cos A = c c a Area of a triangle: Area = ½ a sin C Volume of a sphere: Volume = r Volume of a cone: Volume = r h Volume of a cylinder: Volume = r h Standard deviation: s = ( x n x) x n ( x) / n, where n is the sample size

3 All questions should e attempted. Find the equation of the line shown in the diagram elow. y x. Change the suject of the formula d = c to. A iscuit is in the shape of a sector of a circle with triangular part removed as shown in the diagram. R Q The radius of the circle, PQ, is 7 cm and PS = cm. Angle QPR = 80 o. S Calculate the area of the iscuit. P

4 . Simplify this fraction 0 x 7 x x 9. Express as a fraction in its simplest terms You must show ALL working. 6. The diagram show the graph of y x 7x y y = x + 7x x Find the x - coordinates of the points where the graph crosses the x - axis giving your answers correct to decimal place. 7. A company promised its employees a wage increase of 7% per annum for three years. Josephine s salary efore the increase was 00. Calculate how much her salary will e after the increases giving your answer correct to significant figures.

5 8. Show clearly that sin x tan x cos x cos x 9. A section of a roof eam is made up from a right-angled triangle and an otuse-angled scalene triangle with dimensions as shown in the diagram. The line AB is parallel to DC. A m B m m D 9m C (a) Calculate the size of angle ABD. () Hence calculate the total length of wood needed to construct the eam. ie the total length of all the lines in the diagram. 0. Solve the trig equation cos x for 0 x 60.. A paraola has equation y 9 ( x ) (a) What are the coordinates and nature of its turning point? () Write down the equation of the axis of symmetry of the paraola END OF QUESTION PAPER

6 Intermediate Unit Mini-Prelim Qu Give one mark for each Illustration for awarding mark ans : y = ⅔x + marks Marking Scheme finds gradient finds y intercept states equation of line ans : = [(c +d)/] marks adds d to oth sides divides oth sides y squares oth sides ans : cm marks knows how to find area of sector answer knows to find area of triangle answer sutracts to answer ans : (x )/(x + ) marks factorises numerator factorises denominator simplifies ans : ( )/ marks knows how to rationalize denominator simplifies 6 ans : 0 ; 9 marks equates equation to zero knows to use quadratic formula evaluates discriminant finds roots [no rounding] rounds correctly 7 ans : 00 marks correct multiplier finds amount rounds correctly 8 ans : proof marks m = ⅔ (0, ) y = ⅔x + = c + d = (c + d)/ = [(c +d)/] 80/60 π 7² = cm 0 sin80 o cm = cm (x )(x ) (x )(x + ) (x )/(x + ) x + 7x = 0 evidence of sustituting values 7 ( 7 + 7) ; ( 7 7) 0 ; replaces tan x o simplifies replaces sin x o sin x o sin x o / cos x o sin x o / cos x o cos x o / cos x o

7 Qu Give one mark for each Illustration for awarding mark 9a ans: ABD = 6 9 o marks uses SOH CAH TOA finds angle sin ABD = / [any ratio can e used] ABD = 6 9 o ans: 6 8 m marks realises alternate angles uses cosine rule finds missing side finds total 0 ans : 6 o ; 6 o marks BDC = 6 9 o BC = cos 6 9 o 8 m = 6 8 m a finds cos x o finds one solution finds second solution ans: (, 9); Maximum marks cos x o = / x = 6 o x = 6 o x - coordinate of T.P. y - coordinate of T.P. correct nature (,.) (., 9) Maximum ans: x = mark states axis of symmetry x = [must have x = ] Total 0 marks