Pegasys Publishing. Practice Paper F. MATHEMATICS National Qualifications - Intermediate 2 Maths 1, 2 & 3 Paper 1 (non-calculator)

Transcription

1 Pegasys Pulishing Practice Paper F MATHEMATICS National Qualifications - Intermediate Maths 1, & Paper 1 (non-calculator) Time allowed - 45 minutes Read carefully 1. You may NOT 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 ± ( 4ac) a Sine rule: a sin A sin B c sin C Cosine rule: a + c c cos A or cos A + c a c Area of a triangle: Area ½ a sin C Volume of a sphere: Volume 4 π r 1 Volume of a cone: Volume π r h Volume of a cylinder: Volume π r h Standard deviation: s ( x x) x ( x) n 1 n 1 / n, where n is the sample size.

3 All questions should e attempted Marks Q1. Solve algeraically the system of equations y x + x + y 50 Q. Find the equation of this straight line. y x Q. Charlene s house is valued at and is expected to appreciate at the rate of 10% per annum for the next three years. If this happens, what will the house e valued at in three years time? 4 Q4. Simplify expressing your answer as a surd in its simplest form. Q5. The diagram shows a cylinder with radius 10 centimetres and height 0 centimetres. 10 cm 0 cm Taking π 14, calculate the volume of the cylinder.

4 Q6. Part of the graph of y a cos x o is shown elow. y x o 6 Write down the values of a and. Q7. Sara kept a record of the numer of s she received over a 90-day period. numer of s Frequency (a) Make a cumulative frequency tale from the aove data. 1 () Find the median, lower quartile and upper quartile for this distriution. Q8. Simplify x ( x + ) x 8 Q9. A ag of wine gums has 5 lack, 6 red, 4 yellow, 5 orange and 4 green sweets. What is the proaility that one picked out at random is not yellow? y Q10. The equation of the paraola is of the form y (x + p) + q. (1, 6) Write down the equation of the paraola. 0 x End of question paper

5 Intermediate Paper 1 ~ Practice Paper F Marking Scheme Qu Answer and Marks Examples of Evidence 1 ans : x 4, y 14 marks sustitutes for y in second equation solves for x solves for y ans : y / x + marks calculates gradient identifies y - intercept writes equation ans : marks 4 ans : calculates percentage knows to add to total calculates percentages adds correctly / 4 marks simplifies surds simplifies fraction 5 ans : 680 cm marks knows how to calculate volume calculates volume 6 ans : a 6, marks x + (x + ) 50 11x 44 x 4 y ( 4) + 14 m / cuts y axis at (0, ) y / x + 10% of , , / 4 V πr h a identifies max/min identifies period ans :, 18, 7, 70, 8, 90 1 mark a 6 completes cumulative frequency, 18, 7, 70, 8, 90 ans :,, marks identifies median identifies lower quartile identifies upper quartile (x + 8 ans : ) / (x 4) marks factorises denominator simplifies fraction 9 ans : 5 / 6 marks evaluates proaility simplifies 10 ans : y (x - 1) + 6 marks identifies p and q writes equation (x 4)(x + ) (x + ) / (x 4) P(not yellow) 0 / 4 5 / 6 p -1, q 6 y (x -1) + 6 Total 6 marks

6 Pegasys Pulishing Practice Paper F MATHEMATICS National Qualifications - Intermediate Maths 1, & Paper Time allowed - 1 hour 0 minutes Read carefully 1. Calculators may e used in this paper.. Full credit will e given only where the solution contains appropriate working.. Square-ruled paper is provided.

7 FORMULAE LIST The roots of ax + x + c 0 are x ± ( 4ac) a Sine rule: a sin A sin B c sin C Cosine rule: a + c c cos A or cos A + c a c Area of a triangle: Area ½ a sin C Volume of a sphere: Volume 4 π r 1 Volume of a cone: Volume π r h Volume of a cylinder: Volume π r h Standard deviation: s ( x x) x ( x) n 1 n 1 / n, where n is the sample size.

8 All questions should e attempted Marks Q1. Shereen goes shopping in the summer sales. The store has an advert in the window. All tops one price! SALE All skirts one price! Shereen uys tops and skirts and pays 90. Her friend Nadia uys tops and 4 skirts and pays Another friend Kay uys tops and skirts. How much does she pay? 5 Q. Solve the equation x 8x 19 0 giving the roots correct to significant figures. 4 Q. A glass candle holder is in the shape of a cuoid with a cone removed. The cuoid measures 4 cm y 4 cm y 6 cm. The cone has a diameter of cm and a height of 5 cm. 6 cm Calculate the volume of glass in the candle holder. 4 4 cm 4 cm Q4. (a) In the Olympic Games competition from 1956 to 1976 the distances (to the nearest metre) in the discus event were Calculate the mean and standard deviation. 4 () In the six competitions etween 1980 and 000, the mean distance in the discus event was 67 and the standard deviation was Compare this to the previous six competitions.

9 Q5. A garden ench set has a tale in the centre with the seating area made from concentric circles of wood. In order to allow access to the seats, four sectors of 5 o each have een removed as shown elow. The radius of the tale is 45 cm and the radius of the outer circle for the ench seat is 90 cm. 5 o Calculate the area of wood used in the seating. 7 Q6. Solve the equation 8 tan x o + 5 0, 0 x < 60 Q7. Change the suject of the formula to a V a Q8. (a) Marcus ought his house in 001 for In the following years the value of his house increased y 0%, 0% and 15% respectively. How much is his house worth in 004? () If the value of Marcus s house is greater than 6 000, his dependants will have to pay inheritance tax at the rate of 40p for every pound aove this value. How much would have to e paid in inheritance tax?

10 Q9. Sketch the graph of y sin(x + 60) o 0 x < 60 Q Q10. Triangle PQR is otuse angled at Q. PR is 10cm, QR is 4 cm and Angle QPR is 15 o. Find the size of angle PQR. R 4 cm 10 cm 15 o P 5 1 Q11. Simplify x ( x x ) Q1. A par hole on a golf course is a distance of 10 metres from the tee to the pin. 100 m 5 m On his first shot, Bruce hits the all a 100 metres ut not at the correct angle. o On his second shot he hits the all 10 m 5 metres and gets it in the hole. What was the angle, a o, at which he hit his first stroke? 4 Q1. (a) Express as a single fraction in its simplest form a a () Express with a rational denominator 4 6 End of question paper

11 Intermediate Paper ~ Practice Paper F Marking Scheme Qu Answer and Marks Examples of Evidence 1 ans : marks 5 sets up equations strategy for solving equations solves for S finds T sustitutes values and calculates cost ans : x 1 67, marks chooses appropriate formula sustitutes correctly evaluates 4ac evaluates two values of x ans : 84 cm 4 marks T + S 90 and T + 4S T + 9S T + 8S 9 40 S 8 0 T Cost ( 4 50) + ( 8 0) 5 60 x x ± 8 ± 4ac a ( 8) 8 ± 16 x 4 x 1 67, 5 67 (4 ( 19)) 4a evaluates volume of cuoid knows to calculate volume of cone evaluates volume evaluates remaining volume ans : 6 17, marks calculates mean calculates and x /n sustitutes into formula calculates standard deviation x ( ) ans : appropriate statement marks makes comparison of mean makes comparison of sd V cuoid V 1 / π mean , s 5 s 4 5 e.g. second mean higher, greater distance e.g. second sd lower, more consistency 5 ans : cm 7 marks calculates angle at centre sets up ratio sustitutes large sector values evaluates area calculates area to e added ack in evaluates area of circle calculates required area (60 4 5) o 60 o angle at centre area of sector 60 area of circle area π π π If different method used attach marks as you see fit.

12 Qu Answer and Marks Examples of Evidence 6 ans : 148 o, 8 o marks simplifies equation evaluates tan 1 evaluates appropriate quadrants 7 ans : a (V/) marks tan x o 5/8 o 148 o, 8 o 8a isolates a isolates a ans : marks a V/ a (V/) evaluates first year value evaluates second year value evaluates third year value ans : 9616 marks calculates taxale amount knows how to calculate tax calculates tax 9 ans : graph marks correct sine shape correct phase shift ans : 19 7 o 5 marks 11 5 knows to use sine rule sustitutes correctly evaluates sin Q evaluates angle calculates required angle 5 ans : x x marks p/sin P q/sin Q 4/sin 15 o 10/sin Q o 10 sin 15 / Q 40 o multiplies first term correctly multiplies second term correctly 1 ans : 9 o 4 marks 5 x... x knows to use cosine rule sustitutes values evaluates formula evaluates expression cos A ( + c a )/c cos a o ( )/ cos a o a o 9

13 Qu Answer and Marks Examples of Evidence 1a a +15 ans : marks 6a evaluates denominator evaluates numerator 6a a + 15 ans : 6 multiplies y surd evaluates and simplifies marks Total 54 marks