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IGCSE Additional Math4.1. Solve modulus equationsTopic Practice

4.1. Solve modulus equations

CAIE IGCSE Additional Math 4.1. Solve modulus equations question practice helps you revise this syllabus point with the course map in view. Use this page to focus on one topic, check the style of questions available, and connect each attempt back to the knowledge area it is testing.

EduNinja keeps Additional Math practice aligned to CAIE, so you can move from topic review into exam-style question bank work without losing the syllabus structure. Start with a small set, mark the weak steps, then return to nearby topic links when a definition, graph, calculation, or explanation needs repair.

Question 1(a)

[Maximum number: 3]

ALGEBRA

Quadratic Equation

For the equation ax2+bx+c=0a x^{2}+b x+c=0,

x=−b±b2−4ac2ax=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

Binomial Theorem

(a+b)n=an+(n1)an−1b+(n2)an−2b2+…+(nr)an−rbr+…+bn(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 (nr)=n!(n−r)!r!\binom{n}{r}=\frac{n!}{(n-r)!r!}

Arithmetic series

un=a+(n−1)dSn=12n(a+l)=12n{2a+(n−1)d}\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

un=arn−1Sn=a(1−rn)1−r(r≠1)S∞=a1−r(∣r∣<1)\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

sin⁡2A+cos⁡2A=1sec⁡2A=1+tan⁡2Acosec⁡2A=1+cot⁡2A\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 △ABC\triangle A B C

asin⁡A=bsin⁡B=csin⁡Ca2=b2+c2−2bccos⁡AΔ=12bcsin⁡A\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.

Question 1(a)

[Maximum number: 3]

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

Question 1(c)

[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.

Question 5(b)

[Maximum number: 3]

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

Question 4(d)

[Maximum number: 1]

Find the value of k for which ∣2x2+3x−4∣=k\left|2 x^{2}+3 x-4\right|=k has exactly 3 values of x.

Question 5(a)

[Maximum number: 3]

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

Question 6

[Maximum number: 5]

Solve the equation ∣2x2+x−10∣=5\left|2 x^{2}+x-10\right|=5.

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