# Cambridge International AS and A Level Mathematics Pure Mathematics 1

(Michael S) #1
``Exercise 1B``

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1

EXERCISE 1B 1 Solve the following equations.

``````(i) 5 a − 32 = 68
(ii) 4 b − 6 = 3 b + 2
(iii) 2 c + 12 = 5 c + 12
(iv) 5(2d + 8) = 2(3d + 24)
(v) 3(2e − 1) = 6(e + 2) + 3e
(vi) 7(2 − f) – 3(f − 4) = 10 f − 4
(vii) 5 g + 2(g − 9) = 3(2g − 5) + 11
(viii) 3(2h − 6) − 6(h + 5) = 2(4h − 4) − 10(h + 4)
(ix) 12 k + 14 k = 36
(x) 12 (l − 5) + l = 11``````

(xi) 12 (3m + 5) + 112 (2m − 1) = (^512)
(xii) n + 13 (n + 1) + 14 (n + 2) = (^56)
2 The largest angle of a triangle is six times as big as the smallest. The third angle
is 75°.
(i) Write this information in the form of an equation for a, the size in degrees
of the smallest angle.
(ii) Solve the equation and so find the sizes of the three angles.
3 Miriam and Saloma are twins and their sister Rohana is 2 years older
than them.
The total of their ages is 32 years.
(i) Write this information in the form of an equation for r, Rohana’s age
in years.
(ii) What are the ages of the three girls?
4 The length, d m, of a rectangular field is 40 m greater than the width.
The perimeter of the field is 400 m.
(i) Write this information in the form of an equation for d.
(ii) Solve the equation and so find the area of the field.
5 Yash can buy three pencils and have 49c change, or he can buy five pencils and
have 15c change.
(i) Write this information as an equation for x, the cost in cents of one pencil.