IGCSE Additional Math 4.1.1—Solve modulus equations Topic Practice

• Solve equations of the type |ax + b| = c, |ax + b| = cx + d, |ax + b| = |cx + d| and |ax^2 + bx + c| = d using algebraic or graphical methods.

• For graphical solutions, draw an accurate graph.

• For algebraic methods, any valid method is acceptable.

[Maximum number: 3]

ALGEBRA

Quadratic Equation

For the equation $a x^{2}+b x+c=0$ ,

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

Binomial Theorem

(a+b)^{n}=a^{n}+\binom{n}{1} a^{n-1} b+\binom{n}{2} a^{n-2} b^{2}+\ldots+\binom{n}{r} a^{n-r} b^{r}+\ldots+b^{n}

where n is a positive integer and $\binom{n}{r}=\frac{n!}{(n-r)!r!}$

Arithmetic series

\begin{aligned} & u_{n}=a+(n-1) d \\ & S_{n}=\frac{1}{2} n(a+l)=\frac{1}{2} n\{2 a+(n-1) d\} \end{aligned}

Geometric series

\begin{aligned} & u_{n}=a r^{n-1} \\ & S_{n}=\frac{a\left(1-r^{n}\right)}{1-r} \quad(r \neq 1) \\ & S_{\infty}=\frac{a}{1-r} \quad(|r|<1) \end{aligned}

2. TRIGONOMETRY

Identities

\begin{gathered} \sin ^{2} A+\cos ^{2} A=1 \\ \sec ^{2} A=1+\tan ^{2} A \\ \operatorname{cosec}^{2} A=1+\cot ^{2} A \end{gathered}

Formulae for $\triangle A B C$

\begin{gathered} \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C} \\ a^{2}=b^{2}+c^{2}-2 b c \cos A \\ \Delta=\frac{1}{2} b c \sin A \end{gathered}

Solve the equation 2|8-4 x|+5=25.

[Maximum number: 3]

Solve the equation 5|5 x-7|-1=14.

[Maximum number: 1]

(a) Find the coordinates of the stationary point on the curve y=(x+3)(x-4).

Given that k>0, write down the values of k for which the equation |(x+3)(x-4)|=k has exactly 2 distinct real roots.

[Maximum number: 3]

Solve 5|5 x-7|-1=14.

[Maximum number: 1]

Find the value of k for which $\left|2 x^{2}+3 x-4\right|=k$ has exactly 3 values of x.

[Maximum number: 3]

Solve the equation 5|2 x-1|+8=23.

[Maximum number: 5]

Solve the equation $\left|2 x^{2}+x-10\right|=5$ .

0 selected

Question 1(a)