Form 4 Mathematics
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Form 4 Mathematics
The marks scored by 40 students in a mathematics test were as shown in the table below.
a) Find the lower class boundary of the modal class
b) Using an assumed mean of 64, calculate the mean mark c i) On the grid provided, draw the cumulative frequency curve for the data ii)Use the graph to estimate the semi-interquartile range Form 4 Mathematics
A particle was moving along a straight line. The acceleration of the particle after t seconds was given by (9 -3t) ms^{-2}. The initial velocity of the particle was 7 ms^{-1}.
Find: a) the velocity (v) of the particle at any given time (t); b) The maximum velocity of the particle; c)the distance covered by the particle by the time it attained maximum velocity Form 3 Mathematics
A quantity P varies partly as the square of m and partly as n. When P = 3.8, m = 2 and n = When P = -0.2, m = 3 and n = 2.
(a) Find: (i) the equation that connects P, m and n; (ii) the value of P when m = 10 and n = 4. (b) Express m in terms of P and n. (c) If P and n are each increased by 10%, find the percentage increase in m correct to 2 decimal places. Form 4 Mathematics
The figure below represents a cuboid EFGHJKLM in which EF = 40cm, FG=9cm and GM=30 cm. N is the midpoint of LM.
Calculate correct to 4 significant figures
a)The length of GL: b)The length of FJ c)The angle between EM and the plane EFGH; d)The angle between eh planes EFGH and ENH; e)the angle between the lines EH and GL Form 4 Mathematics
The equation of a curve is given by y= 1 + 3sin x.
(a) Complete the table below for y = 1 + 3 sin x correct to 1 decimal place
(b) (i) On the grid provided, draw the graph of y - 1 + 3 sin x for 0° ≤ x ≤ 360°.
ii) State the amplitude of the curve y = 1 + 3 sin x. c) On the same grid draw the graph of y = tan x for 90° ≤ x ≤ 270°. d) Use the graphs to solve the equation ; 1+3 sin x = tan x for 90° ≤ x ≤ 270°. Form 3 Mathematics
Mute cycled to raise funds for a charitable organisation. On the first day, he cycled 40 km. For the first 10 days, he cycled 3 km less on each subsequent day.
Thereafter, he cycled 2km less on each subsequent day. a) Calculate i)the distance cycled on the 10th day ii)The distance cycled on the 16th day b) If Mute raised kshs 200 per km, calculate the amount of money collected Form 3 Mathematics
In a retail shop, the marked price of a cooker was Ksh 36 000. Wanandi bought the cooker on hire purchase terms. She paid Ksh 6400 as deposit followed by 20 equal monthly installments of Ksh 1750.
(a) Calculate: (i) The total amount of money she paid for the cooker. (ii) The extra amount of money she paid above the marked price. (b) The total amount of money paid on hire purchase terms was calculated at a Compound interest rate on the marked price for 20 months. Determine the rate, per annum, of the compound interest correct to 1 decimal place. c) Kaloki borrowed kshs 36000 form a financial institution to purchase a similar cooker. The financial institution charged a compound interest rate equal to the rate in (b) above for 24 months. Calculate the interest kaloki paid correct to the nearest shilling. Form 3 Mathematics
Solve the equation sin ( ½ x – 30^{0}) = cos x for 0^{0} < x < 90^{0}.
Form 4 Mathematics
The positions of two points P and Q, on the surface of the earth are P(45 °N, 36°E) and Q(45 °N, 71°E). Calculate the distance, in nautical miles, between P and Q, correct to 1 decimal place.
Form 4 Mathematics
In a nomination for a committee, two people were to be selected at random from a group of 3 men and 5 women. Find the probability that a man and a woman were selected
Form 4 MathematicsForm 3 Mathematics
The diameter of a circle, centre O has its end points at M(— 1, 6) and N(5, —2).
Find the, equation of the circle in the form x^{2}+y^{2} + ax + by = c where a, b and c are constants Form 3 Mathematics
Use the expansion of (x — y)^{5} to evaluate (9.8)^{5} correct to 4 decimal places.
Form 2 Mathematics
Find the value of x given that log (x - 1) + 2 = log (3x + 2) + log 25.
Form 1 Mathematics
The length and width of a rectangular signboard are (3x +12) cm and (x — 4) cm respectively.
If the diagonal of the signboard is 200cm, determine its area. Form 1 Mathematics
Eleven people can complete 3/5 of a certain job in 24 hours. Determine the time in hours, correct to 2 decimal places, that 7 people working at the same rate can
take to complete the remaining job. Form 3 MathematicsForm 3 Mathematics
An arc 11 cm long, subtends an angle of 70° at the centre of a circle. Calculate the length, correct to one decimal place, of a chord that subtends an angle of 90° at
the centre of the same circle. Form 3 Mathematics
The length and width of a rectangular piece of paper were measured as 60 cm and 12 cm respectively. Determine the relative error in the calculation of its area.
Form 4 Mathematics
The gradient of the curvey y = 2x^{3} – 9x^{2} + px – 1 at x = 4 is 36.
a)Find : i) the value of p; ii)The equation of the tangent to the curve at x = 0.5. b) Find the coordinates of the training points of the curve Form 2 Mathematics
The figure below represents a conical flask. The flask consists of a cylindrical part and a frustum of a cone. The diameter of the base is 10cm while that of the neck is 2 cm. the vertical height of the flask is 12cm.
Calculate, correct to 1 decimal place
a) The slant height of the frustum part b) The slant height of the smaller cone that was cut off to make the frustum part c) The external surface area of the flask. (Take π =3.142) |
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