Question
(a) Write as a single fraction in its simplest form
\(\frac{x+3}{x-3}-\frac{x-2}{x+2}\)
(b)\(2^{12}\div 2^{\frac{k}{2}}=32\)
Find the value of k.
k = ………………………………………….
(c) Expand and simplify.
(y+3)(y-4)(2y-1)
………………………………………….
(d) Make x the subject of the formula.
\(x=\frac{3+x}{y}\)
x = ………………………………………….
Answer/Explanation
(a)\(\frac{10x}{(x-3)(x+2)}\) or\( \frac{10x}{x^{2}-x-6}\) final answer
(b) 14
(c) \(2y^{3}-3y^{2}-23y+12 \)final answer
(d)\(x=\frac{3}{y-1}\) final answer
Question
(a) Factorise.
(i) 5am+10ap-bm-2bp
………………………………………….
(ii)\(15(k+g)^{2}-20(k+g)\)
………………………………………….
(iii)\(4x^{2}-y^{4}\)
………………………………………
(b) Expand and simplify.
(x-3)(x+1)(3x-4)
………………………………………….
(c)\((x+a)^{2}=x^{2}+22x+b\)
Find the value of a and the value of b.
a = …………………………………………
b = …………………………………………
Answer/Explanation
(a)(i)(5a-b)(m+2p) final answer
(ii)5(k+g)(3k+3g-4) final answer
(iii)\((2x-y^{2})(2x+y^{2})\) final answer
(b)\(3x^{3}-10x^{2}-x+12\) final answer
(c) [a =] 11
[b =] 121
Question
(a)\(s=ut+\frac{1}{2}at^{2}\)
Find the value of s when u = 5.2 , t = 7 and a = 1.6
s = …………………………………………
(b) Simplify.
(i) 3a-5b-a+2b
………………………………………….
(ii)\(\frac{5}{3x}\times \frac{9x}{20}\)
………………………………………….
(c) Solve
(i)\( \frac{15}{x}=-3\)
x = …………………………………………
(ii) 4(5-3x)=23
x = …………………………………………
(d) Simplify.
\((27x^{9})^{\frac{2}{3}}\)
………………………………………….
(e) Expand and simplify.
(3x – 5y)(2x + y)
………………………………………….
Answer/Explanation
(a) The formula is:
\(s = ut + (\frac{1}{2})at^2\)
Substituting u = 5.2, t = 7, and a = 1.6, we get:
\(s = (5.2)(7) + (\frac{1}{2})(1.6)(7)^2\)
Simplifying this expression, we get:
s = 36.4 + 39.2
Therefore, the value of s is:
s = 75.6
(b)(i)3a-a- 5b+2b=(3a-a)+(-5b+2b)=2a-3b
Therefore, the simplified expression is:
3a-5b-a+2b=2a-3b
(b)(ii)\(\frac{5}{3x}\times \frac{9x}{20}=\frac{\left ( 5\times 9x \right )}{\left ( 3x\times 20 \right )}=\frac{45x}{60x}\)
Simplifying further by canceling out the common factor of x in the numerator and denominator,
\(\frac{45x}{60x}=\frac{3}{4}\)
(c)(i)\( \frac{15}{x}=-3\)
Multiplying both sides by x, we get
15 = -3x
Dividing both sides by -3, we get
x = -5
(ii) 4(5 – 3x) = 23
20 – 12x = 23
-12x=3
\(x=-\frac{1}{4} \)or -0.25
(d) To simplify the expression \(\left ( 27x^{9} \right )^{\frac{2}{3}}\),we can use the property of exponents that says \((a^b)^c = a^(b\times c)\), and simplify the base and exponent separately
\((27x^{9})^{\frac{2}{3}} = 27^{\frac{2}{3}}\times(x^{9})^{\frac{2}{3}}=(3^{3})^{\frac{2}{3}}\times x^{3\times 2}=9x^{6}\)
(e)To expand the given expression, we can use the distributive property of multiplication,
(3x – 5y)(2x + y) = 3x(2x + y) – 5y(2x + y)
Now, we can use the distributive property again to simplify each of these products,
=(3x.2x) + (3x.y)-(5y.2x)-(5y.y)
\(= 6x^2+3xy-10xy-5y^2\)
\(= 6x^2 -7xy-5y^2\)
Therefore, the expanded and simplified expression is \(6x^{2} – 7xy – 5y^{2}\)