Onlinetuition.com SPM Additional Mathematics
Question 15:(a) Diagram 12 shows a square and a rectangle.Given that the sum of the areas of the shapes is more than 8 m2.Using the table method, find the range of values of x.[2 marks](b) A quadratic equation is given by x2 + 3x = -4p, such that p is a constant.(i) Find the range … Read more
Question 14:Diagram 11.1 shows the relation of three sets.(a) State gf(x).[1 mark](b)(i) Determine f-1(x). Hence, find g(x).(ii) Diagram 11.2 shows part of the graph of y = g(x).Sketch the graph g-1(x) on Diagram 11.2.[4 marks](c) Find f2(x), f3(x) and f4(x). Hence, state f75(x).[3 marks] Answer:(a)$$ g f(x)=x^2+1 $$(b)(i)$$ \begin{aligned} & f^{-1}(x-2)=x \\ & \text { … Read more
Question 13:Diagram 10 shows points P, Q and R on a Cartesian plane.(a)(i)$$ \text { Find } \stackrel{\rightharpoonup}{P Q} \text { in terms of } h \text {. } $$(a)(ii)$$ \text { Given that } \stackrel{\rightharpoonup}{P Q} \text { is a unit vector, find the value of } h \text {. } $$[4 marks](b) Hence, by … Read more
Question 11:(a) There are (n + 1) points on the circumference of a circle. If each point is connected by a straight line to all of the other points, there are 4n straight lines formed.Polygons can be formed by connecting points on the circumference of the circle.Find the total number of polygons that are possible.[4 … Read more
Question 10: (a)$$ \text { Given that } \frac{\mathrm{d}}{\mathrm{~d} x}\left(\frac{1}{x^2+1}\right)=g(x), \text { find } \int[3 g(x)+1] \mathrm{d} x . $$[3 marks](b)$$ \text { Diagram } 8 \text { shows the graph } x=f(y) \text {. } $$$$ \text { It is given that area of the shaded region is } \frac{9}{2} \text { unit }^2 … Read more
Question 9:(a) Diagram 6 shows the rectangle ABCD.At an instant, the value of x changes from 3 cm to (3 + p) cm, such that p is a small value.Using differentiation, express in terms of p, the small change in the area of ABCD, in cm2, at that instant.[3 marks](b) Diagram 7 shows two lots … Read more
Question 7:(a) It is given that the first three terms of a sequence are 4, 8, 16.(i) State the type of sequence. Give a reason for your answer.(ii) Hence, find the n term of the sequence.[3 marks](b) In an arithmetic progression, the 2nd term is 5p – 10 and the 10th term is 7 times … Read more
Question 5:It is given that logmp = x and lognp = y.Using the laws of logarithms, express the following in terms of x and y.$$ \log _{\frac{m}{n}} p $$ Answer: $$ \begin{aligned} \log _{\frac{m}{n}} p & =\frac{1}{\log _p \frac{m}{n}} \\ & =\frac{1}{\log _p m-\log _p n} \\ & =\frac{1}{\frac{1}{\log _m p}-\frac{1}{\log _n p}} \\ & … Read more
Question 3:(a)$$ \text { Diagram } 3 \text { shows } \underline{a} \text { and } \stackrel{\rightharpoonup}{C D} \text { on a square grid. } $$(i)$$ \text { Express } \stackrel{\rightharpoonup}{C D} \text { in terms of } \underline{a} \text {. } $$(ii)$$ \text { Draw }-4 \underline{a} \text { on Diagram } 3 . … Read more
Question 1:Diagram 1 shows the straight line graph obtained when y = 4×2 – 5 is reduced to linear form.Express X and Y in terms of x and / or y. [2 marks] Answer: $$ \begin{aligned} & \left(y=4 x^2-5\right) \div x^2 \\ & \frac{y}{x^2}=4-\frac{5}{x^2} \\ & \frac{y}{x^2}=-5\left(\frac{1}{x^2}\right)+4 \\ & \boldsymbol{Y}=\boldsymbol{m} \quad \boldsymbol{X}+\boldsymbol{C} \\ & Y=\frac{y}{x^2} … Read more